What is the evidence that sound travels as a c/aiav60qk( t; ou3rbu4a q1)9revrb wave?

What is the evidence that sound is 3/,proi7.thzq lxgv +b0 l/jxa form of energy?

Children sometimes play with a homemade “telephone” by attacvsv7lq.-sz ctvyh sdn *+p-+1hing 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). Explain clearly how the*npsdsly t1+ v-vq7s- zc+h. v sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the fr9gg+) l9uxr boequency or wavelength to ch+urgx9b)9 lg oange?

What evidence can you give that the speed of sound in air does not depenw55kjrm289w fgmn) ,zae 9pus d significantly on fnmae gwz m8,w9u52k) frspj9 5requency?

The voice of a person who has in;y0ar+hdjvrp: nwo): xmi1 t1haled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orgur2q7nm9eeiha:i3kg5 k*jl w 6n*db 0an pipes?

Explain how a tube might+ 6rtt9tqs*r/ rftszc7(: v4 vah3bau be used as a filter to reduce the amplitude of sounds inzsrcs(rha tvr:b7*43uq ttavt69/f + various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer tog k25v93d bjca-3 ycdyoether as you move up the fingerboard tojb3 odkc2d vc-y359ya ward the bridge?

A noisy truck approaches you from nu9g+u d *vr/yd6) a9jok:acbbehind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound: kcu /ju+d *a99bg a6dnvy)ro is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due topv .nnkntk1)nf(/(24 tes sj o “interference in space,” whereas beats can be said to be due to “interference in time.” Exsn(ktsjf( ne)on pv/k1.t2n4plain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poin1pt 0)-9vvmevxawbwc,.l e0 vts D and C (where destructive and constructive interference occur) move farther apart -mal.0ew 0bv9 )wxpv1ce,tvvor closer together?

Traditional methods of protecting the hearing of people who work in areask3luk17wy:z e with very high noise levels have consisted 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 electronically1:y zu3k kwle7, 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. nqtkz 2. v+zz,p5 id(j12–31. Each wave can be thought of as a superposition of two sound waves with slightlyij+v,nz(zkqd 5z2tp . different frequencies, as in Fig. 12–18. In 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 t /-zk 0hhro5r;radt:q )o0ylghe same direction, with the sar0h d5h-;:t )zq/rogr0a loy kme velocity? Explain.

If a wind is blowing, will ths4qfbuw2)cb6 is alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelengc)s2uwbfbq64 th or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing 0mgxoyzm4-czg0x .h 9. A monitor is blowing .zg4z09 ymc gox-x0m ha 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 the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo ofgw mg+v.*is.ncc* z4h her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Es w.sc*. z4im*vn+gchg timate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side i 5-5,uulfye9rw bol8of his ship just below the waterline. 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 5bi l w8rlf5u-oyu9,evary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in 5i m-1tg5 hkgrair 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 a school of tuna on a f ; pnvx3z5c+ zw7/lldzoggy day. Without warning, an engicn7/+ d3 l5vw ;lzpxzzne backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. Thv8diynm4t k-5cn n1q 9gy9a.me splash it makes when striking the water below is heard 3.5 s aiyq 9 1nkn8- 49 t5yd.mgcnmvlater. How high is the cliff?    m

  A person, with his ear to the ground, sn0o+ u(,if :9ppwhcsn : ktc6cees a huge stone strike the concrete pavement. A moment later two sounds are heard from the imhio :0nu pc,c9nptw sc(k6:f +pact: one 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 errohb y7rkn6,e; s4: bvdujy z*g*r made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike i7g sdke,* hzry6;yn :*bb4uj vf the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound a;t+qll5omu sqa ,/mv9t the pain 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 of 8qf4*rk hgxwaxj o6 *)a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB 4dyo/j-v0, epn 7 8jgdj gn)trwhen fired simultaneously at a certain place, what will be the sound level if only one is exploded?dn8n v j40-e,r)/ ojpgt gyjd7 [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisyo (hqoh 7.vc8b jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captaiovhco .qhb8( 7n shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nonev0/tvs-p l6ise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgroun etv0v nsl-/p6d noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in nni8bym q 6n51gormal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere qnn6g b1iy 85mcentered 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 eardrn84 /ef9qt mwss+.b heum 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 W, whilris0y*g+ d 9mbibu,wd(9;icz e 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 connectedy9;9rsbdi wzb+u , cgimd0 *(i 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 met mw5zd 3a1j1vqer registered 130 dB when placed 2.8 m in front of a loudspeaker on th1qm z3jva5w1 de stage.
(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 sound level of 2.0 dB. Wha2hcp v1pndd3epve 87 5t is the ratio of the amplitudes of two sounds whose levels differ by thiec3v2dpv8hp5 71 ednps amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will th(d +d64aqfwem g i+oi(e intensity increase? Incddg +fo6ii aq(4(m+ewrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hasrg uuponql +.p,o2q8 *.9rhq 6tdhp /c twice the frequency of the other. What is the ran9ul+oh.* 6 ogp8/qchq 2.rqpd t ,purtio of their intensities?   

  What would be the sound level (in ds7 nlrw:rt 3r8B) of a sound wave in air that corresponds to a displlr:s7nrr 3t 8wacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz f3fh;bx0k b7 vtone that has a 50-dB sound level? (Sfb7 kfv; h30bxee Fig. 12–6.)    dB

What are the lowest and highest frenr 1)xxysb4up5 nn( x2quencies that an ear can detect when the sound level is 30 dB? (See Fixrn5 xxbn1)u(s ynp24g. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is thes34fxohtyi1d w* r2.kr/ vr)6rk3a dz ratio of highest 1 si r/) *dkxt2akhv3.ozr3 dywf6r4rto 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 fundamental frequency of 440 Hz.kd(i* gvp z(7-aifwak:xd h :- The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension mustkhi:k( va-( gxfd:w-pid7*a z the string be placed?    N

  An organ pipe is 112 cm long. What are the fundaqv5(qo( sx4 qr4kmc a4mrw(1ymental and first three audible overtones if the pipe is v 4sq5yo k(( 4wm4cm q1(qarrx
(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 frequency would you expect from blowing across the top of yce0 m4a i t -fllw817fs intb3qj/v.l6qf7h;an empty soafehf7v w7tj; 0n 3yic l8qmq.6l fslt14/-b ida bottle that is 18 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 pipe organ with open-tube pipes spanning the rhyw h* 0m mw.fak(v05/ tsxj.uange of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pip 0muh5ts(. w/.m*kf 0xhyavw jes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as 83 q5mq5hw0kudz*nx dits third harmonic. What will be its fundamental frequency if it is wdx5z03du*mh n8qk q 5fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middz 0edswax2/*n u6;j cble C (33dz;je nusw0/c *62bax0 Hz).
(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 ov ag5zk9y7 ;7t 3o4ti(ihlkj ipen organ pipe that emits middle C (262 Hz) when the tempal h;k (4z3jk9 viotiy77i g5terature 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 59:dnnf 2xrdg 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutlv: sbp;cn yi6fhhs/ y;4jse:9nm7 ;ie in Example 12–10 should the hole be that must by9:f : p;s lemhn6 4 yvcbs;;/isnjh7ie uncovered to play D above middle C at 294 Hz?    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 mb u1ryb9eo/p0j )a/pana 4g2resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whnmpaaa ug4)1 po/j b/er9y20by this is 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 opendmzh2*m-jof *f7 rdlaj.j:(u at both ends. It resonates at two successive harmonics of frequencies7*mzjj afm do .(l-h *2djru:f 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 b3yca 9: 75)gpclqm+ isg xb,o$^{\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 pr*; cd bbrcvh;j(* y*kaesent within the audible range for a 2.14-m-long organ pipe a ;*jyhkccdr*(vb;b*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 open to the ryg99p ph .2 r7yapur(outside and is closed at the ot(h7gyr y pr92uaprp 9.her end by the eardrum. Estimate the frequencies (in the audible range) of the 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 g y2n icy8n;*fs when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequenc*;ycig2nfyn8 y is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz)q-y-mhtca 0xw;,mr: j and $C^＃$ (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) operatm 8i; s92kpohu2fkv /ees at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequehe 89ki2;o2k /fsvmup ncy of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork anh .ku0t y:5rcfd 9 beats/s when sounded with a 355-Hz tuning forkyh.fr5cuk 0t:. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequb /uribt 6i8cpn,l: 2apy1 (l9ouarry7rt*4 q ency, 294 Hz. The tension in one string is then rcb ,ipl/tbruy8 *a71ql4(u9 aynr2:ot6p i r decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flup-i2go/md l; gtes each try to play middle C (262 Hz), but o-/m2iggl;d op ne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fod-n/ -2 r1sa3ecued zbrk B has a 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. What are the possineb eus2a/dzc3 d1- -rble 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 frxiqgej /x f:9hku- h69om one speaker and 3.50 m :hh/xx-ju9fgkqi 9e6 from the other.
(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 at 132 Hz, but a piano jk:u;vqtkn muj(+d )t,qw2i dq6l4+n v*.ahntuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequejqun wt iqa.2nq*ul)d:t vh+; , dkkjnm6v+4(ncy of 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 i,o)vkc4y 2woc 0yp,:) hm2jiops ,pfm and 2.76 m in air. How many beats per second will be hea),,s:k mvioi2o),4j0ofwcyppcy2 hprd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren cyu:qb82xk+ ois 1550 Hz when at rest. What frequency do you : +kycx2bu8 oqdetect 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. 5cer5d 382+;p dw qb*wmey5ev) vtyj qWhat frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s dwc2p53y8w)tqjr5mqb* e vd;+v e ye5
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in /ur (gjv6f.,d35fey*p6 bdgp)q ul-t ozis1r frequency if a 2000-Hz source is moving toward you at 15 m/s versus youqido3 6zjr p5lbtvg)s(ury6/p*f-f,. gud1 e moving toward it at 15 m/s Are the two 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 equippedm-,; oi)xkgj uhc(t-l with the same single frequency horn. When one is at rest and the other is moving to -gl tm;c -(iuhk),xjoward the first at 15 m/s the driver at rest hears a beat frequency 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 waves at 50.df vw(m, iew0+hr 6+eh0 kHz and receives them returned fro fd m,0++vwherw6(eih m an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it u2m ;uw(-5jr vypcaj, flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflec5 pvm2rju,w uayj -;c(ted wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimen gjtal6+2sjk 0w*xel+huxk* (u;9 dsf ts, a tuba was played on a 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 of 10 m/swsdh6felj +*j gk( *+xultxk2s 9u0a; ?   Hz

  A Doppler flow meter uses ultrasound waves to measu4kgmt3d 0 *1 lvapptw v)u4ncvmn; +l0re blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken tomu40v)+t*3n4lt v 1 n w;c0dglvapkm p be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic 4relzt vy- 1/kq te9)zwaves of frequency $2.25 \times10^{ 6}$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 velocity slg0yu*(zhzz uh3,w( is 12 m/ss ,z(0 ul*uh( wzghz3y from the north, what frequency 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 speed c u8oigs407n+mg .dmk 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 speed of vlxg j.tlh+t1.d0o-j qjn5jmd5 (*f fsound is 310 m/s (a) What is the angle d*5olt.gjdq.h-5 lff nx+t01 (m jjvjthe 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 ,q1/)ip.h;kzaoby epng.c;d planet where the speed of sound is only abou1kn ,)hdpi;/ .ae.pc goyqz;b t 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 theof)m 0rbm5qs jy8z xbca1k30. shock wave angle it producocb z)rfm30 5kjq. 0 ayxb8m1ses
(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 pczd i:3nb:6k$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overh-;vmmhd3 ik; t;vh.y zead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, t3 h- iz;ytvh;;mmk .vdhe plane 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 serh ;,aazb 99s i6)srggnds 20,000-Hz sound pulses downward 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 time between pulses (in fresh water)?h9bsar9g6g s, zai;) r    s

  Approximately how maniaid5x x)7)yuy octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewris902 ab lj7(:snk3 k0pcgswer pipe symphony. It consists of many plastic pipjc0 ssg2p0w br:ns (i9kak 37les 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 person makxcug dw-5k6j .es a sound close to the threshold of human hearing (0 dBk-cwd. 5xug6j ). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB s ipdvb);e)y r)ound and an 87-dB sound are heard simultaneously))br)idy;v ep ?    dB

  The sound level 12.0 m from a loudspeaker, placed in the o+d9i* f 2in7txpo 6d ,zz5 igr6x1oqvspen, is 105 dB. What is the acoustic power op61s* ,d 5zr +oq dfgz9i7ovxxntii62utput (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dropstq2ekwd0; js q+d:8e5 lnf m7p by 10 dB at 15 kHz. What dsd kt 8q2e:0mn 5;w+j fqpl7eis the power output in watts at 15 kHz?    dB

  Workers around jet aircramvehf/s f:, wk5n7sx )ft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30hf ms)xn:f/ w7,k sve5 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 system*gr 0ho +xmxv5s, the gain, $\beta$ 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 tunedzw nl/9 mrig/*zfhv/ / 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 bety+1:x )wvob mh jpvltm.:m+f9 ween fixed points with a fundamental frequency of 440 Hz and a mass per unit length of +wmp1 )lymxtob:9. vh:jmf+v$6.1 \times10^{-4 }$ 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 w3zzm- lwx4, 6 wqkrxe28unp u)ith water (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 uwxe34-npzuk )2 wql6 8m zxr,to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 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 g is near a tube thnqyep,ilw;- 2 2 uab)a t-c7vvat is open at one end and also 75 cm long. How much tension should be in the 7aawt le ip2vyc;n2qvb,- u)- string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as on*v- *dx 6 x-rgxtks+ht/i rj7he 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 rango+g (-edr. q3,ujx:fqhhdz,r u ,mtx4 e coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound levro r,(e43t:gx + q- uufjmhqdz hd,x,.el 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-Hzr1) (*etgasmiy,tsczrr. 17m/h 3inq whistles. One train is stationary. The conductor on the stationary 1.qr s mnhc mrg e/szti)1*7(3ryat,itrain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Ad,uw) nf byey1l)h+ zh:e/hyn/s 9rc2fter it ph 2cs/re9wf)ly:),/hn+eb dz y hyn1uasses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of carsfs dd*;: )9mvvo /6:re foyahc just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops :om96f /) d:f cv vdsy*roah;eby a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding to 1jgfe;3) fyd lz;u7vigether, produce a beat frequency of 11 Hz. The shorter one is 2. ely 3fdz)f1;j7vug; i40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a ip 0ir1s8kt )xrailroad 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 the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the spea1k8 p)xri t0sikers, 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 abog47( qp y2e 9 boamty+fh1cs,cut 0.32 m/s what beat frequency would you y1(bf c2tq y49ecgm, hpoa+s7expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel 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 whiler p6s28d2b/ fbba1 oe2y egu02e ean5x the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected 2gs rxbe2a2e 82 n5ub e6/a0byfode p1by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high f;t*viaulyjv0 d,r+,l requency sound pulses as it approaches a moth. The pulses are ap a*dvt,; lv0 ,yuj+ilrproximately 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 one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once use ad7n)*eb it*5p pq-nyd to send signals from one Alpine village to another. Since lower frequency sounds are 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 c)ib5q **ey 7n- nadptpalled 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 compromi; 2s7k0 t3tyw9n dcm9mh7kckp4jm sg4sed 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 waves in this roohpmgct 7s7j9 wc9 3m 4n0 ;ky2k4sdkmtm.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratiyl7 bsv)v g2(oon, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod ()o vvs gylb27is stroked with the other hand. With a little practice, the rod can 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 threwvo 2all76tw*ng 58 eyshold of hearing for the human ear at a frequency of abou l2lt8y5a wve6nw*7got 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ 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 Mach 2.0d:5rx9pi/vw8/vbuc6 t j8wkp . An observer on the ground hears the sonic boom 1.5 min after the plane passeb:vidcu j//ppx5688w 9rvk wts directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboaai mksrs4flx2v;y *.8t is 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