Give some examples of everyday vibratingo m y/n c: )/pk7tbvrv*z0aw-p objects. Which exhibit SHM, at least approxim/:n/* 0p z)7 topa r-wcvmkbvyately?

Is the acceleration of a simple harmonic oscillator ever zero? 8mfkaon+qz b;)k:vp / c85eqx If so, where?

Explain why the motion of a piston i uh+2bg bueg,8n an automobile engine is approximately simple ubb,8gu +ghe 2harmonic.

Real springs have mass. Will the true period and frequency be large)p w *rb1jns(er or smaller than given by the equations for a mass oscillating on the end of an idealized m (rn jpes*w1)bassless spring? Explain.

How could you double the maximum speed of a simple harmonic oscillator (SHO)(vyafugx3bwt4-u/3 z t(z*v y ?

A 5.0-kg trout is attached to the hook of a vertical spring scale, and themek)gck+p97jm7/.w iczoq .tn is rem)z/i w9kt o..qcm7+k7pgj c eleased. Describe the scale reading as a function of time.

If a pendulum clock is accurateqpl )dwecq1z(0 bcd 0+ r7tvl2 at sea level, will it gain or lose time when tak1 qdzv)(w dl 0rb+cpq7t c2l0een to high altitude? Why?

A tire swing hanging from a branch reaches nearly to the ground (Fig. 1a ,m7fc r6v:h0h hl hsc4v5k0x1–48). How could you estimate the height of the branch using only a stopwacc:hvl6a h0 r0f 457kxhm, hvstch?

Why can you make water slosh backiv (rm+ 3*gu mu 9juxt1xg.p+z and forth in a pan only if you shake the pan at a certain frj.(xp+r1i vx3m+ t uugz9u *gmequency?

Give several everyday examples nyv:hb d;1j 1glohw+(of resonance.

Is a rattle in a car ever a resonanc/lz)3) k, f bti td.sw3qn6vlre phenomenon? Explain.

Is the frequency of a simple periodic wave equal to t7x+deea j 2pa4 b-:bk.dfo h3ull j:;zhe frequency of its source? Why or waaeu34x - 7 kzjo.lj;fd+2l:bde:hpb hy not?

Explain the difference between the speed of a transverse wave traveling dowv0j m+ o1 l6w*btaj8k/ (qhomen a cord and the speed of a e1hj 8a+bml o(j 6/0*vwkt oqmtiny piece of the cord.

Why do the strings u +eg,zyg 4rdaor26f:xsed for the lowest-frequency notes on a piano normally have wire wrapped aroue:zyrd46x fg ,r+2ao gnd them?

What kind of waves do you think will travel; g- /tpcyf0jl down a horizontal metal rod if you strike its end (a) vertically from abov;/0-f tycglpje and (b) horizontally parallel to its length?

Since the density of air decreases fpw50z(zeb x 8s:0 czuwith an increase in temperature, but the bulk modulu:5ps0ew cbuf zzzx 8(0s B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperature?

Give two reasons why circular water waves decrease in amp*/dzn/*lpkkn .f0 9 +dbnzzx jlitude as they travel awn xbz*k/.*jpk0 ddf/ l+nnzz9ay from the source.

Two linear waves have the same amplitude and speed, and otherwise are identicrvl0 gd9sq /)ck:4evgal, except onrk) q/l:d c0 vg49vesge has half the wavelength of the other. Which transmits more energy? By what factor?

When a sinusoidal wave crb qa 6w3tsz/ (tabws:6osses the boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and velocity do change). Explain why.awbwa :q6zs tt3(6bs/

If a string is vibrating in three segmec (idnnnp;v;usse vj kg1))z2uv 1 /3ql0r4rents, are there any places you could touch it wit)ld;rivj s3/ zr ;n( e01ksvn4upcvq1ng 2 u)eh a knife blade without disturbing the motion?

When a standing wave exists on a string, the vibrations of ij1y)sa17iw vg ncident and reflected waves cancel at the nodes. Does thiyw7 vgsjia1)1s mean that energy was destroyed? Explain.

If we knew that energy was being transmitted from ones; ua3x n+1od(-lupqr place to another, how might we determine whether the energy was being carrio3d u xu (na;lq+-1psred by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.1pnu ;, f4qlfz9v-lgzxlh4za ;35 q 9jy-chn,p8 m, what is the total distance it t 5c l-hy ;lnjg3pq4zp9 ff9azz,xnql hu;,v-4ravels in one period?    m

  An elastic cord is 65 cm long when a3 c)ja30kxkn bo qh*5v weight of 75 N hangs from it but is 85 cm long when a weight of 180 N hangs from it. What nkjv 3ok3b 05*hca)qxis the “spring” constant k of this elastic cord?    N/m

  The springs of a 1500g.kykoy 3v.n:1wy 0qa-kg car compress 5.0 mm when its 68-kg driver gets into the driver’s seat. If the car goes over a bump, what will be the frequey1gq3 w.o:n0av.kyk y ncy of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kv o1b+ hw+br .k*xfm(bjg82 aig fish hangs from it. (a) What is the spring stiffness constvj+o(g8. wb*hb1rx2 +ka i fmbant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency -lvq )aoc fo5nyr0 d 6qm)nkqq.(6h/ zof 3.0 Hz when a mass of 0.60 kg is hung from it. What is its frequency if only 0.mlqfyq6 )aoq5(nq-o c ./vrh6zd k0n) 38 kg hangs from it?    Hz

Construct a Table indicating the 3 y hvo)aqhqj j7 3s7);oeq;raposition x of the mass in Fig. 11–2 at times t = )hjo)q; qa h;joq3vs 77 e3yra0,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught in a spioumvp9)ok: a; der’s web. The web vibrates predominately with a frequency okm:uo;oa 9p)vf 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibrates with a frequency of 0.88 5t ,pn*w vf6wzmdvt95 Hz. When an additional 680-g mass is added to m, the frequency is vm wdwptv6 zn5*,f5t9 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the ltg*xwodxg,l 5 wex3n.;-g ca9xcg)* end of a spring vibrates 3.0 times per second with an amplitude of lotw ,*g9cx5ac;.)*3xgednwg gl -xx 0.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium isqi9 f sui5,a3x the speed of a SHO half the maximum value?3iqx95au fi ,s$\approx$    A

A mass attached to the end of a spring is stretched a diwev ;5oc6ol) nc; zvlu9p+n5he (y e-vstance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0.315 m)d t.je ,kjsrxmh,u80. If the spring is stretched an additional 0.130 m and released, how long does it take to r, skjehr )8j,t mudx.0each the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stiffnhkgxwa;ld d69dz.k1 cgqet9ya- t(s/*nr/ t- ess constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m fr(- znh61dk*yql;.k//-xaetat9gd dwt g rs 9com its equilibrium position, it is moving with a speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to compress the spring of a3qo35vezsg s7 toy popgun 0.200 m to “load” a 0.153 oqs7s3ezgv 80-kg ball. With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionlecpnc4k y ; c-9:gmt2dbss surface is attached to one end of a spring; the other end is fixed to ;9cbygn-kcp4mt c2:d a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum acceleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45c0u-nzi4e;u7 .v3gg g cmxo j:slc//xq os6.4t where x is in meters and t is in secon -cx47ug g0snqe /3 omijluczg:v/x;.ds. Determine
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilib6cjpbjauuis.y- 9 6 /erium is the energy of a SHO half KE and half PE?pj uu9bj .yi66aecs-/ ±    A

  If one vibration hashem ;lwgq j60mpjsz r :s7qyf9k.9(0d 7.0 times the energy of a second, but their frequencies and masses are the same, what is the ratimhz s.d(mj9; :y pj09lk 7qq0r6 sgefwo of their amplitudes?   

  A 2.00-kg pumpkin oscillate1ntwm p 5h cgb5 ,mo:ovpq- uq9q;nsoqp1 927ws from a vertically hanging light spring once every 0.65 o 1ot9sbq2; n 9h5-g ,wq: ppnwmpqcuv71 mo5qs.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported bv( tmqr)mo n13i.c9 coy two identical parallel vertical springs, each with spring stifmm1) ciqtoov3.rc( n 9fness constant k (Fig. 11–49). What will be the frequency of vibration?

  A 300-g mass vibrates according to the equatih4gwc+y f3iwsjx q9b*3z*6m+i z4uyjon x = 0.38sin6.5t where x is in me*36q+jmwwh*cz4 zi+i3sxjy f9bu4 y g ters and t is in seconds. Determine
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examples of SHM, 4;tor;u yrp2ezav5d 4labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at rest on y;vw0omto(ezk51, hdg 5 5vbrthe end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.96m/s Determwkemhdr z 1,5oov g;50 yb5vt(ine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/m vibrx7 xsn- 7p b;ha 5u/odyjmqv5u;kn 8m0ates with an amplitude of 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with pos;h0p msuqo7 ay -78 nk5dvx /5;unxmbjitive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected to two springs, with spring 9u pfc.g l* t1mz,k;destiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixed h rd)azvag0i3 1orizontal spring who giv3)aa r01dzse spring stiffness constant is $ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from ;esb -. yjdu(5pgsz3na high bridge. After reaching his lowest point, he oscillatenbpu;z-ysj5.g3e s d (s up and down, hitting a low point eight more times in 38.0 s. He finally comes to rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exactly u;(9bet7iunx uvd 3(t 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to make exactly one swing per seconb*hk9nr-1*e+vk g kcwd? (That is, one complete vibration takrkc* +k-kge nwv91*bhes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 s on Earth. What is its per,t e*cx q mz*4fei,tu1iod on Mars, where the accelerationx *,* efettu,1im4 qcz of gravity is about 0.37 that on Earth?    s

  What is the period of a simple pendulum 80 cm long * noifeo+ixrb0c w;;1xj4-cj
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendub9 rl4sk coa(+,qwi uzl/g1 (alum is 0.760 m, the pendulum bob has a mass of 365 grams, and it is released at 1 o glaikcab4rqs,9z ((l/wu+an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a q cgi(/j pyabc8mp- pimh(8;6 .5w xpjlength of 0.9930 m. If the clock loses half a minute per day, how should you adjust the length of the penc5hga(i8pxqjybpm (i/6;8jp-.c pmwdulum? shortened by    mm.

Derive a formula for the maximum jdht.+4hy.ik/ qm75 qad3dnqspeed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At t5vo,1 zbnh45l sgdr6it is released from rest starting at an angle6nv 5d,5 1b oshtzgr4l of 15 $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his an6-x bo)gd+)pht0*)wrfsmknp jx 5m;u chored boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast are the waves traveling?b0*xrt n-m)+x g;)pjpuws)f 6dmok5h    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a speed l/pi/n.lysk8d9pzs5u z 9n z3of 343 m/s How far apart are the wave cz /s. y/3 s995idplz8lnkpuznrests (compressions)?    m

  (a) AM radio signals have frequencies betweahat4 b fdwtjf /wb9ho03:x(/ en 550 kHz and 1600 kHz (kilohertz) and travelofjxf w(wa4h t/39:tbh a0b/d with a speed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of lo las*tacovnu k8++jz e rr,.)3ngitudinal waves in
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have theqj r(n7w5t*: aaaq0 pfw(cp/b same elastic modulus, but one is twice as dense as the other. In which rod will the speed of longit(a0 5(qtn*b7pwprfca qwja / :udinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched betwl3 y6kb*2cih:ral 7 mb 4fnt9heen two supports 28 m apart. If the tension in the cord is 150 N, how long wl* y lfcn6itbk7 h2:hr3ab49mill it take a pulse to travel from one support to the other?    s

  A ski gondola is connected to the top of a hill by a steel cable of leng mdfv ti1,kxjz i)+;9lth 620 m and diameter 1.5 cm. As the gondola comes to the end of its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed txz i ,1d f+kj)ilmv9t;hat it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the 5jel f.jzbo1-6 1d ehiside of his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep is the ocean at this6zo- j5j .lb1efhdi1e point?    m

  P and S waves from an earthquake travel at different speeds, andtw/5) ik7s61xapdm/r idmeqfx, + z w/ this difference helps in l5dsr xw+wfea 1dqp k6)/,/xtmm 7iz i/ocating the earthquake “epicenter” (where the disturbance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be approximated by a sinusoidal transv2ccde( /it;vryji*dur.i5)je/p b c+erse wave. Assuming a frejr /eu+/.;jv*e yid ic(c ibc)2tpd5rquency of 0.50 Hz (typical of earthquakes, which actually include a mixture of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensitiedk9d/o,y yq s+sesih -p 9t lv7mx(*m-s, and (b) the amplitudes, of an earthquake P wave passing through the Earth and detected at two points 10 km and 20 km from the source?(a)-vo m, i(d-hk+x *9yldtq7mss/es9p y    (b)   

  The intensity of an earthquake wave passing through the Earth is meas :q,,qdfxx+ zknc a*2vured to be f*+,q n x:z,vdcqkxa 2$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion9g x+ re bhurdn+e(1:n of the Earth, but onn1 9he+b:(n g+rexdu re is carrying twice the energy. What is the ratio of the amplitudes of the two waves?   

  Two waves traveling along a stretched string have the same frequency, but one trhbe.uj. /hop4fq egty /3 k s,0i-wf2lansports three times the power of the other. What is the ra.sip2wkj h egt b-0/y u4hq3 f,.l/eoftio of the amplitudes of the two waves?   

  A bug on the surface of a pond 6w,kp1zixpl -90plu: em2mqeis observed to move up and down a total vertical distance of 6.0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE cmmk9e,l ppx0eq:z 1 iw-u2pl6hange?   

The two pulses shown in Fig. 11–52 are moqv) hbv 0rclh+wh8l0./i k1opving toward each other. (a) Sketch the shape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments . +/c8wk)lvbh1oi0 hrhq0pvl later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates lq2p( 1fx,up/x iae g6at 440 Hz as its fundamental frequency, what are the frequencies of theag2 pl/,e x (q6f1puxi first four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294 Hz when unfingered. At what frequen0ke70daw o o*fcy will it vibrate if it is fingered one-third of the way down from the end? (That is, onwe7*0a of0od kly two-thirds of the string vibrates as a standing wave.)    Hz

  A particular string resonates in four loops at a frequency of 280qkcw k9jr ;fre0r(c5 9 Hz. Name at least three other frequencies at which i rkj c(fr9k;crq59e0 wt will resonate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s If the frequency of standing;jatbcsapt5jy 0;m 9m0 d au8, waves is 475 Hz,5typ ; cu8aad;0 b,at 0ms9jmj how far apart are two adjacent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz an,wup/xq 9e mr9vi8:(ac8xso od 350 Hz, what is the frequen8 qaix/(cs:99,p woeom8 v uxrcy of the fundamental?    Hz

  A guitar string is 90 cm long and has a mah85 q kvlu +2t+fpxnf,;azy6pss of 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension of 520 N. Wh6fpz u lfthka+q v+n 5x2;yp8,at are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is supposed to vibrate at 200 Hz, but it is measuredi/bnhar c:2n f ve9y.( to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequei9:/rc hn.2y( vfe banncies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is j ua1 snn*r*i3vvq 7m-supposed to vibrate at 200 Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in thjiuq*r1 sa*7v3mn n v-e string be changed to correct the frequency? decreased by    %

  One end of a horizontal string isn ,v:fs9l /tfm attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit leng9tf vsm/:n,lf th is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string may be adjusted by moving the pulleh*c3xkbp8*a:i q8hs-to a kk)y. If the hanging mass m is fixed at 0.080 kg, hoa kkqcxktbh*)p s8o8 h-3a :i*w many different standing wave patterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the watey)4 *; 5ptxaezyw)hlkr back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0.85 Hzl)*5hzx e pa4 )kwyyt;. What is the speed of the water wave?    m/s

  An earthquake P wave traveling at k.0 km/s strn 8bffkr(k9o7mb3dw; ikes a boundary within the Earth between two kinds of mate 7bfknmodk3;9(f w8 brrial. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwate0/h+(ev kyvkv r “shelf” where the velocity changes from 2.8 m/s to 2.1 m/s If the incident +k/ khvvyve0( wave crests make a 34$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm airml4:e sw6ti0 s when it hits a layer of cold, dense air. If the sound wave hits the cold air interfac0: 4 iletms6wse at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave stxb45r8cs;co s rikes a boundary between two types of rock at a 3sc r;4b oc8sx58 $^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diam).dw 5gxb; pkyviz7k7eter. According to the user’s manual, the dish has to be pointed in the direction of the.igkpy7k57w)xb;vd z satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and 6) aek:rvtm2;eu e(zm prl/7ivelocity 750 km/h travels across the Pacific Ocean. A()/7rv; 6r upe ltm:ki 2maeezs it approaches Hawaii, people observe an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car b2w ak (cjlgs;tjz4t+9umper has a spring stiffness constant of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (appro ;zt(wj sc+942 tjlagkximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 /jc) oooeh ;-uf)dc*r m below, which stretches the net 1.1 m. Assume that the net b hde) j/-oof) roc;u*cehaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freensc,viahk 4k *fg(k89 e 7ycduf(0-q u dzj.9ely hanging spring. The mass then falls 33 cm before it stops and begins kgua s7u 8q9idk*e0d.y h vcnkzfcf4-((9,ejto rise. What is the frequency of the oscillation?    Hz

  A 950-kg car strikes a hustw*v. +to 7mage spring at a speed of 22 m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What m vtts*ao.7 w+is the spring stiffness constant of the spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (di8/qrs-yih 6al* j ,qshameter 8 cm) at just the right pace of about 1 step per sechrq i aqjyls 8*sh/6-,ond, the coffee sloshes more and more until eventually it starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain grooveq-792t+dxglki yh+m a 10.8 cm from the center of a 33-rpm phonograph record have a wavelength of 1.70 mm. What will be the frequency of the sound emitted? tah2-lmxd79q+ g ki+ y   Hz

  A 2.00-kg mass vibrates according to the equation x=0.650c -qszw*+. ahktjwd+az(,hj8 tos7.40t where x is in meter.jt+kas*wj(w8az t, -h z +qhds and t in seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates with frequency f. What; mc.qil m+ rp5p95hhx is its frequency if it accelecm9mqrp h;5i.h+l5xprates at 0.50g (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a 75-kg man s)svs6a ) 1zb5wud irb2tands on the raft, it sinks 4.0 cm deeper into s5rbd 6 uvwisaz2)b)1the water. When he steps off, the raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical instrumenri-n g3 m8ul)vb-ts:ht are tuned to play at 392 Hz (G) and 440 Hz (A: 8 )msut3gl-ihbvr- n).
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling down the stretched two-part cord of Fig. 11–n l2p xupgbzc)8.ot469r* oma 5 tja(w33. Determine a formula (a) for the ratio of the spepoalc8put5n t(4m j6b xzao*g.)r9 2w eds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sections. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency of 264 Hz, and the tip of each prong 0py0- 3bgf .ng6ahxsi8 pqvu8 moves 1.8 mm to eith 6 g-v0a ghsfu08pyb3.xniq 8per side of center. Calculate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with simple harmonic mot/ ocijey6y1r5ion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lose contact with the board during th /y5eiy6r1jco e oscillation?

A string can have a “free” end if that end is attac,y jn*fdgdk8 7*u( 2yvoazat +hed to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wa ant*7u2 +yz 8vdakgy(, jof*dvelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a pe 20f 9ca;yg h0we;.wcditz,wv riod of exactly 2.000 s — each one-way swing takes 00cacy.v ,iw;ewz;2wgdtf 9 h 1.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscillate in the vertical direction vnr j:ihk /33-otrsjvj,3tx , or can swing as a pendulum of small amplitude, but not both at the same/ ,thij,xv r3 jnv: rjko3s3t- time. Which one is longer, the period of the vertical oscillations or the period of the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g is stretchix ,16sxxpu-ac 5m) yued under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second 5xci)1us-x6p, u amx ypulse is generated at the opposite end. Where will the two pulses first meet?    m

A block of mass M is suspended from a ceiling by a spra)us5el7q; 6 za(cmj 4h0ecuf ing with spring stiffness constant k. A penny of mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the pennyc(lh7zu 0a)fs6m;ue5ea4j c q to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-kg car at the junkyard. The stee g6xlr:x.30n:q ,uvi1kt gwndl crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period of the bouncing? [Hint: rvt,qn.ni 3kw 1dl:0g u :xxg6Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11exfkk7g3h . b/–58 (which also gives the dimensions of the block). You push it sideways as shown, and then you let go. The jello springs back and begins to vibrate. In analogy to akh g7/3x.bf ek mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz