What is the evidence that sound travels as a wd v: gsxd4ws58ave?

What is the evidence that sound is a form of enye1muat6nr. b9v 3p (8ag-df vergy?

Children sometimes play with a homemade “telephone”ca):wew8,5o.0qrbkczk1 pki by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Ex5oapk0ecc b8).:1r i, qwzkk wplain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air iy oi0j 2s,0ixqnto water, do you expect the frequency or wavelengt02y ji,s0xi oqh to change?

What evidence can you give that the speed of sound in air does not depend * o0 krab bzz*xwxj001significantly on fr0zw 0 x*bo0ja rzk1*bxequency?

The voice of a person who havdiy:we 4b t86s inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ piy5baah gtoh*27 ed:d u)sw b)7pes?

Explain how a tube might be used a1x1g fs qehh*p8ue b) ,6xzol+s a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a cago x q,f1+b z)pl*81h 6sxeuehr muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethe,t *wm g:wpaf9r as you move up the fingerboard t9t gw:w,mpa*f oward the bridge?

A noisy truck approaches you from behind a buil:tom v (lb0(59 vb*xe1yutje hding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sechtlvuvebjy b(t:15 e *x0(m o9tion 11–15 on diffraction.]

Standing waves can be said to be due to “inte7s3csc5tlh 2uf m3d 7-uzvu5frference in space,” whereas beats can be said to be due to “interference in time.” Es f2cts3l-d3uhv um5fuzc 775xplain.

In Fig. 12–16, if the fre9 w-3c;r.-eo z sgdzpdquency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart o cdge. -zswo9- zpd;r3r closer together?

Traditional methods of protecting the hearing of people who work in area g c 0 ;ad;:-5upei,ee8etxcqfs with very high noise levels have condxpta0c u:q-8 ,; 5;i egceefesisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each ew oybyjx vq+39e0)*q df2da4wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. Iqwevfx)e aj2y+y*b0 3doqd94 n which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direvh 5 w(bv5mj9o mdwq19ction, with5 m1vwjvo qhm5bd 9(w9 the same velocity? Explain.

If a wind is blowing, will this alter the frfxc0; 4qx9wb fequency of the sound heard by a person at rest with respect to the source? Is the wavelength 0x;c4xfb 9f qwor velocity changed?

Figure 12–32 shows various positions of a child in motion ona( i+ w ow+4w.loa+zqj a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of tolz.o++ a qi( wwa4w+jhe whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening fo qg3ght 1y: ui30hd2 kculz2r*7r2abir the echo of her shout refle27u2 r*i a1 qh2hg3yib3ltcz:0ug rkdcted by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the watevvr(s(+ ita/jyusa3.rline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.(a. a ji(/yv+tsu3srv    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in c of96 6wgenpl1/le+j air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above qt9t6 (jd62:q wx1h abpwklh 6a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses (216h6 :6qw lqxd jpwtha9bt kbefore the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikinn (sq hi+h1qon st-;;gg the water below is heard 3.5tsgq (+o-ns 1;;nihq h s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hr18fwe6w ioh9 uge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one6 o1iww8rhef 9 travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile( 2bjbbmo7 j-p of distance by the “5-second rule” for estimating the dist7ob2m p(bjj -bance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pained 8j+d),ttdqbijr61 level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level z igcw(d+d69y of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB id lzxf cbsde1r ():7/when fired simultaneously at a certain place, what will be the sound level if only one is explodeddse /)zi7f1 (bxcr l:d? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distagh) :z .jorv r*-n/ryknce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all burzh :v r-n.ygj )ro*/kt one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, wh7no0rn:q*x /ytm ps n2ereas for a CD player it is 95 dB. What is the ratio of intensities of the signa/*oq0xnt ynnsm 27r p:l and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in ark0rlmu5) w.wa htv7,uod90normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphem r9owrk t)ual 5 ahw,v.d700ure centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardru) y) ;hg t++m xyyzg*9;nvuoqcm whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 * 8(akuf ao lk*ev90hcW, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conne ckve( 0ka* hoa8*l9fucted in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when pla 7o;cn)uhg5/(yim ndlced 2.8 m in front of a loudspeaker on the sta7uinh om)y;5( dgcn /lge.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in jry 04y e tbp,r1d6tv0sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectionyrttv1 p 0red06j 4,yb 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wi)i hwyrbe--5hll the intensity increase? Increase by a- e i5h-w)rbhy factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have e+ryih u/t/6hu4df r. j7l4( y5waldqs qual displacement amplitudes, but one has twice the frequenyr/ a d u.q4f7hd (6wur+s5yhji/ll4 tcy of the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that correspoe5zx me ; /dpi5.tj)qonds to a displacement amplitude of vibrating air mole z /5toe)qp.5;e mjixdcules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sz0k)c 2fbg a+neem as loud as a 100-Hz tone that has a 50-dB sound level? (Senbafzc0k2+ g)e Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect w)g4:pr. rxuaxhen the sound level is 30 dB? (See Fig. 12r x.r:gua)p4x–6.)

  Your auditory system can accjdhmw : e3x59fxxe;)yommodate a huge range of sound levels. What is the ratwe) :5e9;hmydj3x x xfio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamentalcu4o4u,h e)xk frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensionohu 4,)4xekuc must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundameyo44n tfq ie t048ddebk(itwu03z 8v-ntal and first three audible overtoni -4fwdzutbd4ei (0v8q4ky0e t 38t ones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequqe f l7l;ap4g0ency would you expect from blowing across the top of an empty soda bottle that is laegl q4;7fp018 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipic8 0l,3qg oyzr+,pvpe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz)0cvgq 3 p opiy,lrz,+8, what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third su,(0xu6dkl /p ) lsiat u4go;harmonic. What will bela d xt /us6);opkg,lus40u (i its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string iasqa+t qtg. op :6hci8c5i/lc2n+fj( s 0.73 m long and is tuned to play E above middle C (330 Hz).ctc+5qa.h sl/na j+ qigp82:o ( tfi6c
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emi aj dzm(gy1p .f:(qk- a:xpj*ex2dh. wts middle C (262 Hz) when the temperatk*gdjh.x: x.ej(f a:mz(q p2dwa1-y pure is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2)nh.sit zy y d.dk;m+00 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thl0ok;t y 7js+ye flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz?jol y;+0yt ks7    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not atp 3tccw4p5 6sr any other frequencies in between. (a) Show why this iw rc5pt 4c6sp3s an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonate mk h,pjym8pdq7a*20 k p6dp,d6oofb-s at two successive harmo dmbp qdpfpa 6mdkhykjop* 80,2-, o67nics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 ;msg sn 3pq*.3d7 ye/)r 3ihdrx 5c+fwkzf8ek$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.lmitm(zk(:bjuw :/v- 14-m-long organ pip(-/ ::zui(btl jmk mvwe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is ojg i/g f-ue1e 5;fn3nxpen to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of 1gejf 3fu-nig5 ex;/nthe standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to 9i ox4e/e/(hw/ hk eovip 84mmadjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other i4o4eempih /m x /k(owhev/ 89string? ±    Hz

  What is the beat frequency if middle C (262 Hz) a - pj uu5.vs9;ba/ m4qm9fihgrnd $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) o81mm0bmg( gi r/ohmprj4 fc72perates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs rgpf j2mcrm bm4mo807h /g1 (iwhen they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 7zl:,uplgji,. ul9f q+cwu x; 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain,w;ulgzi9. c7fl j l qu+u:xp, your reasoning.    Hz

  Two violin strings are tuned to the same frequc44rehf 6g,ds ency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the b g fdhs46e,c4reat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if 5:+ud(ejb 1lkwxr /2e w nse6mtwo identical flutes each try to play middle C (262 j2 x6 en:5emwk1deub/r+ l(wsHz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has )w*j+sabk jk5a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. Whbk*k) aj j5+wsat are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker an-8axw oerz68r1jz+t l d 3.50 m from the o rwz86 jr81xleaz+-tother.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating axt xbt(u *+,gg0bfkc., z5 bymt 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency ofzft,0+xbc*u 5tbgbx k,y . (mg the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2. pal cnpn612w8h-k,(or0 o eoe76 m in air. How many beats per second will be heard? (Assume T 2o-(0wapp nc8le6 1eoh on,k r= 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren pka*wqqd:7 h.esn06o a: yq9vis 1550 Hz when at restq sve*:q0y7.d6npoka w aq:9h. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freqoa2 2j2 e8ewf bx2)dhxuency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 f hdb)222eeaow 2 jx8xm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz soob89,o() g,aa vwu c2c9r jypyurce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the twoc9yy vra ),,9jw28gbuc(o op a frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When ofc0qf16 y bd e-:tp4y73oixefne is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat freqp6 7 e1oetf3qy0f: -bx4yfc diuency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wkvz pvdj j:c +3j2.o/gaves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s23 o:jjg cv/. jkp+dvz What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emig yjv6y rloh: kbb)k9i(k (rb.+ 62ohjts an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in yhhj+:gby 2j9bkoor(i 6(. k) rvbl6kthe reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on n7fv/wn cvig, ;/(qtpa moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed ofqf7;ng ntvw i,//vp (c 10 m/s ?   Hz

  A Doppler flow meter uses ultrasona (kx4jfwf n n54.ifyxa1i6j 9s +3ygund waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly awn j64 ffwyf5s3(gjian ya n4i x+.xk91ay from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencyuaf8wz2yr6q 2 $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind ve7ea bxt j1yjbzj8*10wlocity is 12 m/s from the north, what frequenbxj8 tz j 71e0*by1jwacy will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its+1o8fu bx2tmb lv,xh 6 speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the spe47g xhwq )0cii2t3 ufxu-4tu ned of sound is 310 m/s (a) What is the anglequut43i4h 0f nig)ux7-2twxc the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speej7mc )a 1d,jo-l :r.;qa oildgd of sound is only abo m jqr jll:gaoc1d,) doi7a-.;ut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine th p,w7(j pq*mijg6eri qrat-4- e shock wave angle itr4q iim,6gr-pj*jpqe at -(7w produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 4x6 sg njmd68wklm.:1pmpj;q $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground fo-l4svo:;g stsw )g3t lying faster than the speed of sound. By the time you hear the sonic boom, the pg-s;oot 4vt 3ws :g)lslane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwardr6zx;wl*y-4 n s 1qm:gro;(hgi ljmg* from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum ilgm:l1(hzs*4m jwrg* y qrognx;;6 -time between pulses (in fresh water)?    s

  Approximately how many octaves wpkf..5qe re(+ zm7zqare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display caldj0-- sdvrou*nttw) 5/av 3rlled a sewer pipe symphony. It consists of many plastic pipes0at-l )owsjv5v / drd*3ntu-r of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a peqbrsx gupihqnex+f;ispw*72;ufw v67 /:9s: rson makes a sound close to the threshold of human hearing (0 dB). What will biu96:; 7:w ;uhfvseqr b + ngxqs7p2sw*xipf/e the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are himnn 0byx 6hrc1 sh-82eardc r8ixy2 h-6b hn0nms1 simultaneously?    dB

  The sound level 12.0 m frofbv,klmm.p 77o 7qjf ;m a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates.qf m;7o7 vmjpl7f,kb equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropse s(c:7fm,ft c by 10 dB at 15 kHz. What is the power output in w,fmetcf(7: c satts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their earsw3ku. ld1m.3 r( xvzee. Assume that the sound level of a jet airplane engine, at a distance of(d3 lwuxvrzee. 13.km 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the g2 -yd fb4vihtnk:p;(f2-cbar ain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned3av jb2ohqi,ko )q5 .p 5o0cpt to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betweenf hu.p3 c(v*av fixed points with a fundamental frequency of 440 Hz and*(u vph fa.c3v a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with watewhv-9b2x/mi 9y;l tfxr (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125xf2 9v ym-wl tib;x9/h m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 mdoew-u f0m j 01m9el(jlt9 2lg is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce09eolmufm w (t-j0elm9 1 djl2 resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as onu eeqma* gjzq,gf,c7ooq z2832* e*nre full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from t m )cbpj9m3-ynvl1wb:wo sources. The sound is loudest at points equidistant from the two sources. To determine exact-p3vm y1 9 :lm)bcnjwbly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationaryk( nbk5;bg1 ky. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other trkn ;kg5y 1kbb(ain approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you s( +x-+c pc4m n4fdmndis 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity nxcpf4-mdnm+4c+ ( sd)?    m/s

  At a race track, you can estimate the (/u 9h7cucut espeed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drou7cuu/ th ce9(ps by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, szfhq2in6l4 n*ce*bs( ounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long.*e 2zf*nb4hcq6(lsni How long is the other?    m

Two loudspeakers are at opposite en) yhd8e 6z).s)ysqft tds of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is th. fhdyt )yzs)es6t8) qe beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/ .hlzl*6;nvy ss what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves l*zlh;ns 6 y.vtravel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towardz-8jg,p 43-ryfv6 ndg xdbai, pk7/g a the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave d i 3d847ydzgfpp6n -k,a, jgg/-v xbraetected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. yo*3bocg*:upx p27sv h;,e swThe pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from onpg; :c3v*sbpw 2,ohxes*7o yue chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpr n). q:lg +hk ep:53al:vpghvine village to another. Since lower frequency sounds arp: .h+ 3a:relknv 5qh plg):vge less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromis2p(3rcu/xcxsr, nba ( ed by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing wavesu3,scnx2(/bpc rr( xa in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lony hn4 z5nz;(aig, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can(4ai n;h5z ynz be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the thres j0 iesc-aso 4:se;al;hold of hearing for the human ear at a frequency of about 1000 Hz ie -sao jse;i4l c:a;s0s $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at M3-w va2mhxh ,uach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is theu 3-w2hv,hxa m plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat 9 i7g) nd +lu)rjmw1geis 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h