What is the evidence tp /vfjp7+oc* o*sv jr5hat sound travels as a wave?

What is the evidence that sound is a form of enerky3a0lo g.tk+s()vvj. is ,6 6b qzgspgy?

Children sometimes plprvy;,eh, 0(a2fetim ay with a homemade “telephone” 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. 1va(0tpeh r ;yeif2,m, 2–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do yomw;1 yc*d j knu5ym2,ju expect the frequency or wavelength to change2 ym ,15ncu;kd mjyj*w?

What evidence can you give that the speed of sound in air does not depen4 yvx 2:a+5q*o 7 m*cmtggcfpbd significantly on frequvxg*:2*m cmba4t y57qfo+g cpency?

The voice of a person who has inhaled helium sounds very high-pitched. xhht yfgp.6z d*k.g4 +Why?

How will the air temperature in +*l4fu8ycgp j1qmtrr;py m37ld(xb /x w7 .z ha room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduc(geiv4jo z4j,e the amplitude of sounds ie(zv oi44,jgj n various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as .yauc0pw;moqe fqn0 agdu7d/(d//;j you move up the fingerboard toward m; 0waj(;u.pa e0yg /c/ d o/quq7fnddthe bridge?

A noisy truck approaches you from behind a building. Initially you he cpmbpeu8 z8 ip.z, /eke7..wnar it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hearpk zpbwmc.p8eu.z/ .ene7 ,8 i more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interf3gur9w/ lbtiaf(bb .-+9wzn nerence in space,” whereas beats ci -trbwab 3n.z+f/bwu n( l9g9an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, jv1 gj:pemkk;xpy; ,8 would the points D and C (where destructivep8, pjkj 1vgky e;:x;m and constructive interference occur) move farther apart or closer together?

Traditional methods of protecr02tf7 q47 apzpgxy)wting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. fg4a7py02twqpx) z r7With 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. c/it xqh518drh6 dyp2 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) 2xcd/hpt158 6dqrihyor (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 theamhu6h/ qv2d4 same direction, with2am d4uv/h hq6 the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a,7)wr-zhb+b 2khd w jy person at rest with respect to the source? Is the wavelength2bb+ k-r, jy zwd)7whh or velocity changed?

Figure 12–32 shows various positd iz1*zuhadn+ od ctyd;+.02vions of a child in motion on a swing. A monitor is blowing a whistle in front of the z.+d2oduv dit; n1y0+h ca*zd 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 of her :f79 c,up7naqja t.y.u q1duishout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s yf 1,7 qp7uqtcu:.uad .aji9nafter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hisywk hf3smx0 a u 8zqszs19z*77 ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deeps zs*h0s 8 uy1xz7fk3mqawz 97 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.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air8+/vzoz+z cd l 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 ofc,,acx dm0vt xd:;td1 tuna on a foggy day. Without warning, an engine backfire ;,vtc1,c td0:ddmxx a 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. The splash it makesu xl y75t *q7th,cp 3ynap77uz when striking the water below is heard 3.5 s later. How high is tn 7p7 uly7*xcht5 zy7u3a,pq the cliff?    m

  A person, with his ear to the ground, si-77iq lolb o:ees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 7 lb-i:o q7oil1.1 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 of distance by the “5-secogr *07 rqf:iecnd rule” for estimating the distan:g qief7c0r *rce 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 pain liuj6;hz tn;6fevel 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 a sound whose intensityu* r cz3. l k)+yqua*z*crf77ald8k nj is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soa .tnedpne xwk21eq./;laei-ey 1s1jf 8j 4,qund level of 95 dB when fired simultaneously at a w;e14 q .qd.ej8lse,ykna/ naj-f1i2 te1 pexcertain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplacg8dm6lw v ))rne with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Whatc ) gw86rv)mld sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sign(5ghk5 +* mh bkae9mtnal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensitiam5e hg+b k9h( ntkm5*es of the signal 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()-jw xrt kzw1 normal conversation. Use Table 12–2. Assume the sound 1w(t -k )jrxwzspreads roughly uniformly over a sphere 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 eardrum whose aa, :,c a l+sa,kqjwx3area 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, while the m tap */ahsxghgb/o:2 5ore modest amplifier B is rated at 40 W. (a) Eh*sgtbaxa /:pog/ 5h2stimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected 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 pl agwuzka i,rf9)lh (:1aced 2.8 m in front of a loudspeaker on the sta9r u)1fg kzihala(,:wge.
(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 detecglb8:ccb:o6y +n+ w mnt a difference in sound level of 2.0 dB. What is the ratio of the ampligw:8lnobb+cy: 6 nmc+tudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor willcwn 1vh 7fq.ipvjtq /-.-0gwr the intensity increase? Increase by a factn/gv-wp wj vthrc.1q7-.0f iqor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves haveoqc;qd2iqdk6 1zuky)x- n.i2 j+m m r6 equal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their i2kyc uiixqo;k1nq zr-q. m+)d6 d6mj2ntensities?   

  What would be the sound level (in dB) of a sound wave in air that coyr/)l7bn6 bbcrresponds to a displacement amplitude of vibrating air mole7c/ bbrlyn6) bcules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lo8pgtxssv n8 (1: eqp.vud as a 100-Hz tone that has a 50-dB.x1qgsvpp n(8t: es8v sound level? (See Fig. 12–6.)    dB

What are the lowest and dfo.3 ;;w ;bx k/plyighighest frequencies that an ear can detect when the sounkdgo;. y;wl ;p/3 fbxid level is 30 dB? (See Fig. 12–6.)

  Your auditory system can azc6zq 8c 6o*ccccommodate a huge range of sound levels. What is the ratio of highest to lowest intensity atz* 8qzcoc6cc 6
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a virgye1wy,c r)k c+6d( rolin has a fundamental frequency of 440 Hz. The length of the vibratgrr,+e( dcry16w kyc)ing portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are tt/avo8n 3f qnx.c1o2 qhe fundamental and first three audible overtones if the pipe isf8 3caonq.vo/2xtn q1
(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 frbxyv-r( u6i,m c)/fma om blowing across the top of an empty soda bottle that is 18 cm deep, if you assumedfummxyi )v6 -cab ,(r/ 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 s ,(lpl 2lo t-ft1pi;mkpanning the range of human hearing (20 Hz to 20 kHz), what would be thef l -mlk,p(2t t;iopl1 range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hasgm4l q/c7vv2 m a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a gmvm2l/ cqv7 4length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to peiao+-)vp9/4pso z l meu*)etlay E above middle C (33/+ee m9)pael u-)oovztsip 4 *0 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 a*o;pvmir,8nxfrp)x;; a/a m y n open organ pipe that emits middle C (262 Hz) when the temperature ;rvprxai y)p mn*m8;;af/,xo 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 lrgua h.i:6 v2p+dj9p20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shoulykzfu+an k: ;4d the hole be that must be uncoveredkk:a 4 ;yz+nfu 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 resonate at 264 n8e ut/ *ytq3kHz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this iseuk3t yq/n *8t 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 vna m fsshy:,y(+n7*hirh5s) long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is ,ymhs s5fn iahv()y:sr*nh 7+
(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 fr+ /ch)h 9hou$^{\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 th0r,z kfpiw/j, e audible range for a 2.14-m-long organ pipep,w0 , /rjkizf at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cmu /*e6u e1249dk *ajrluce;uh g:zyyd long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequendyk luz da9 *eu26*eu41yc:jgrh;/ue cies (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 s when trying to a h(lq;5 8vbxd+xis 8dndjust two strings, one of whlxd( dv;h sn88+bx5qiich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hvewtc. r/pe4)n2x3dld 1x 2ucz) 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/, h+vf/y tqtz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but/ +z/q,t yvtfh a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning xu7 1* v0*tupaz4ctlj fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? x* u j7pav1 *4uzlt0ctExplain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294c19lh2brt7 sx,vhq q2 Hz. The tension in one string is then decreased by 2.0%. W29q2 tsr1qlh cx vbh,7hat 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 flutes each (l-7 kdvzy+ m /r0ph:2pwkbqa try to play middle C (262 Hz), but one is at 5.0°C and the oq+h7:yl2kb/0z d vrwpa(pm- kther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 44147lmj1at7r3tm:n w xp 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 possible frex4j rl 7 m:1mtta37npwquencies 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 speake9e -yp4fystp93o*xahr and 3.4 9oa3* p- pyyxsteh9f50 m 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 5g su861g q5 mrfsql .*jsnh,p132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togethpm ,g u5s jlg1rs.sq f*q568nher. (a) If one is vibrating at 132 Hz, what must be the frequency 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 m and 2.76 m in air. How many ben3(f1o 42n sge+ oagmzats per second will be heard? (Assum(+og4 snm oea 12gn3fze T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1hg n)t /pkhp/lclk-1 ;550 Hz when at rest. What frequency do you detect if you move with a s1k; pc-)hp k/lg/ln htpeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequenhbf(9kji-93- e ,od.2klte joqbir; z kajx.3cy do you detect if a fire engine whose siren emits at 1550 Hz moves at ardt, zi2b .qe3a( kj;j 9okl3 heo9-jbfx-ik. speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source re*:v)abhl 8 svcl8:ois moving toward you at 15 m/s versus you moving toward iv lv8 re ob8:)*:sahlct 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 equipped with the same sinds.es c5i3 vodo 9v..ygle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frei.5evdcy.o. 3ss9 ovdquency 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 50.0 kHz and receives them up3kmu5h s:b. *fy- crreturned from an object moving directly away from it at 25 m/s What is the received sound frequencukh* -m 3y.fcpr: 5sbuy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall atgc;4 lffz6) xt a speed of 5 m/s As it flies, the bat emits an ultrasox)t cgfl z4f;6nic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a mor, q)4 ihw8wzo0udo-iving flat train car a-d8o4qwi zrh,ow ui0) t 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/s ?   Hz

  A Doppler flow meter uses ultrasound waves ta y ulmdu1i62(o 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 th16dm ai ul(2uye 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 waves of fjz*19yxwospq x. b fs .h5m,5orequency $2.25 \times10^{ 6}$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 wdb 2 gm1)v1*x pbnqb,ww9qqc 1ind velocity is 12 m/s from the north2nw91*c1gb )bbqwm1x,dv pqq , 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 5r;86ruqr;ohqd t9e4c d7o3 y4j kj ng1 l0rfiits 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 2v53ud n6 fiwj0.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of tjifdn 0v uw563he 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)jj7 ;xf qh sa:1gs((c4pnbfw a planet where the speed of sound is only a7j(s jc:xqhwbspn(fgf 41 a;)bout 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 travelin a) iasd)f e5tixd+iw w.6hpi;/dt),x-epc/pg 8500 m/s strikes the ocean. Determine the shock wave angle it produces x65/iied+ );d pdxpfh iw)pwta e-s)/,.ic ta
(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 jv /+q-6sdnoi$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead siv+q.to36 wd e;4rhsand 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, the plane has traveled a sr.+d hso4v6ew 3tiq;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-Hzi /u,kqv-;9dtlgisl/ 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 frl/ ,uglsidk- viq 9;t/esh water)?    s

  Approximately how many octaves are therey*vtw dh(k4mniem 2 .1 in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphonyyaa .pikkvf xud6 ez /e0p88lj8-r+ t2. It consists of many pyx8lr.0k6a epd2vt8 ifaupke- /8jz+lastic pipes 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 fro w*i.l ,e05pzfhg cer7m a person makes a sound close to the threshold of human hearing (l.zh w,g7ipc 05*erfe 0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sox bu6-g9pf js4 m)h /uwvt)g/hund are hearv/ g9f-)m6bg) htju4/ swxhp ud simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the+smc(-m5 e 18idpzpu,ikxc c- open, is 105 dB. What is the ace -pxm ,c + pizc1ksm8-(uic5doustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at sv19c 8x(vd:cld t) c)iwo+h e150 W output at 1000 Hz. The power output drops by 10 dB at el s )cc)v(owd9xi18:+thcdv 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet airca00el 6a8i gx tv)p9;uhtu1nhraft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, anx1ihpu0 08l e )g;a96natht vud 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 syst0d sit gzopw;niu0xo(p3t)xl;. x 44gems, 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 tune3.v7u35rtc *9q feaakz e8f vvd 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 betweeb/,.plvz bp3en fixed points with a fundamental frequency of 440 Hz anzbebp,3p/ .vld 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 0hrq8,bmd;3nus mq4fa vertical open tube filled with 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 to resonate with the tuning fork when tm qu,fb0 n 4;mhq8sr3dhe 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 that is opyp2hbwf vs/ ya9+kf ;u9l,py. en at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third har2yu bpfha99y ,flv .yw+ ;sk/pmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to3s9cu fi j6u300ya j zu*a7--oif irop resonate as one 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 tonk(jgqb,c c-tw ) :o8j 7;i:nw(rephbze in the 500–1000-Hz range 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 level is minimal at a point 0.34 m farther j w-;bgbi)ck:oew (z,n:h8jpct(7qr from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is mtd uq8fv-ejr48flu 6*d rz(,stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What8elujd-r, rm(fftduzvq6* 48 is the speed of the moving train?   m/s

  The frequency of a steam train wde67nl7yqyj(z s5mw 0histle as it approaches you is 538 Hz. After it passes you, its freqmse 50 z dly76nyqjw(7uency 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 cars ju) rxjtgk4 w3qtk: z*k:st by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency hatgt4:*kkjqxr:wk z )3 lved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequeqda0 ,uja6b q;ncy of 11 Hz. The shorter one is 2.40 m long. How j0udaq,a ;q6blong is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a yf/er)sl0qrx-zh9z 4 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 frequex)yer0z4rq9lz/- hs fncy 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/s what +8 wa3ugx8ano cp r):l,hjg)(sqlq u: beat frequency would :qsh agn8wlu c,+ ) guopa)r3x:(jlq 8you expect 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 while the moth is flying,a9147ls;mtm w/akot/ t1nscd dq rc ; 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 by the bat after that wave reflects off the 4a, mm7dt1;; dwcnt tck1r/os s9qal/moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mog/w1)qt uc lo6kxie:( th. The 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 echok : goce i6xt/q(1wul) from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals b n4:rk s 5uk -ref69j9za:6b5soeusifrom one Alpine village to another. Si9 oe6ufssa5:rz 96kbs -bnej 4u:rk5i nce 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 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 compromised by the presence f,bk+ 0rj:xvnof 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 mjk bn0fv :,x+r wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender w4 t/pfjk78a(wckt+ daluminum 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 be made to “sing,” or emit a clear, loud, ringing s/ k 4p a+dfttj78wkc(wound. 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 threshold of w03 5;w36 90 osubvzl0 t.zrbtdfvd d/-cqz kjhearing for the human ear at a frequency of about 0/0-z3fq960cv;bbsdt.k jzdtoz w53l ur wv d 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 +rmom8tj0bi, at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly ovb+ jmo8itr m0,erhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15m.dv, n+bs i8i $^{\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