What is the evidence that sound travel+hv7 s,u7 f wdsqs4p+gs as a wave?

What is the evidence thaka: aid8tt 83at sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to )k1 g; zgolqy6v +3gi0lkiz* ksoh4s4the bottoms of two paper cups. When the stri;k y01hk so*zk )o qi4v+3 ggls6i4lzgng 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 sound wave travels from one cup to the other.

When a sound wave passesmh3h fb6+syqikywo7 ,1de yv(7 ,v7p e from air into water, do you expect the frequency or waveleopysvm,ieqv (,7kb76 h1 +ye 37hfw dyngth to change?

What evidence can you give that the speed of sound in air does not depend sig8x -yh m;vl-ek p.rdx:;soxa, nificantly , xv.xd:e oyk8x ;sp;-mha-rlon frequency?

The voice of a person 5v 1oe;el6jh-hw,z hqwho has inhaled helium sounds very high-pitched. Why?

How will the air temperar4a4hrrwhq)) tq 9 a98s *lgknture in a room affect the pitch of organ pipes?

Explain how a tube might be used as0nmx f( lk;.;5u,isejoaz;n g a filter to reduce the amplitude of sounds in various frequency ranges. (An examplel oz(;,sgn.;;anmif0je 5 ukx is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer toget6ac1gd63r .qiwlvh- rher as you move up the fingerboard toward the bridge?wh1-. v ar6qgirc6ld3

A noisy truck approaches you from behind a building. Initially youqwq/:f -q+e6dnzyl w9lxfa 71 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 n 6qaf7wqlz:-wdxfy/ +q l19eSection 11–15 on diffraction.]

Standing waves can be said tqt0xm0 zt(ku 9o be due to “interference in space,” whereas beats can be said u0q0mkx9z( ttto be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the p 2 7t+j4+ff4kay v/*rjepvapkoints D and C (where destructive and constructive interference occur) move farther apart or closer toge* 4j/j 7kfvfa+apk4pt ve2y+rther?

Traditional methods of protecting the hearing of people who work if b5)um(v3+.p ygp d 68oaeqlun areas with very high noise levels have consisted mainly of efforts to block or reducf+beu5uo .qdyam) p3 g8v (6ple 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 wavp 1gts9;nn8r82ib a pa dn-tpr9up/7res shown in Fig. 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 wav9 ;pu t1aanp pn9-2s8r8 r7b pdgt/irnes, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source andjnq+ s fdyq-50 observer move in the same direction, with the same velocity? Expyq0jqn + s-f5dlain.

If a wind is blowing, will this alter the fr l0k6jnnyt5/j equency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocitjt n6/0ykn 5ljy changed?

Figure 12–32 shows various positions of a child in motion on a swing. A moymf p x-)ok5f2qw*t g 3x3+ujzkk:pn8nitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequ k8zx o-f5p):utqgp k+3wn *kjy3f2xmency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lisa( ouj:os,oyf( ,demhs m9op.80kq:j tening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the e j,muoae:sk(,.p:o dy0j9 (ohsmf oq8cho 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 waterlint0a n gkmmj+tl2 g;3egp0:hc 6e. He hears the echo of the sound reflected from the ocean flj06: mng+alpe3;h ct20 mggt koor 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.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air aty79d*qjdilzmv +r q/l jh ,z*/ 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 schooy :v60se uz 8eh)*zs 7c 2afqmef uw-se*fyi9;l of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much tim7fm)e zfs y i90hwsz*s:8*uce6uavqe2;f ey- e 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 m1v)p(y ed+of1i5h mfpzv 55e kakes when striking the watf15y dv+pok5eizp) v 51eh(m fer below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone str o(ztguui(0n*+;b2:4a yh kedpjtv i 6ike the concrete pavement. A moment later two sounds are heard from the impact: one travels in t t:zhni(aj0 ( vukyiegbp+ut6d; o*24he 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 of distance by theb;m1ja/ v) bq-9*ze1)po q.tsldulse “5-second rule” for estimating the distance from a lightning strik1um -;*p)q9.ltv de1l )bsosajq/beze if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB2at :4 md-(mk, evl-: 9etacv 6a x3bt)trmmrw?    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 sou , qacom1238xsjci7 )7wdl :zhgosahzmvz:1.nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB gu7zai:al( ir*itxy-0 xc; ( gwhen fired simultaneously at a certain place, what wilti lxi0(*g rza:x7iau-c(yg ; l be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an ai28bgqs c:d+-82nys-u qkb r vprplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 12s+dn v2rc b -:gbu2q-8psykq 80 dB. What 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 hy i, c-ejk5 rhm+3r8drave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of teyrc ,rdki-3j m+8 rh5he 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 normal cogr- kr1 p4fij3nversation. Use Table 12–2. Assume the sound spreads roughly unif rg1 4p3kf-jriormly 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 aq1 6c5+cxj ldnn eardrum 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 8qn2+m uc v2yfhfyxo+l7kzydg97-*k W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you l yfkv7 mz*+xfnk oygyu29-8h+d7cq2 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 placed)q nwt0+kbbiv3sa -1l 2.8 m in front of a loudavbns0k+3t)-w qb1i lspeaker on the 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 diffepg;txe9ohb+t)2,mm trence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]+ mtmeg)tbx,2h9;t po $\approx$   

  If the amplitude of a sound wave is tripled, (b5 l8p4onuo(ka) by what factor will the intensity i 5on bku(op48lncrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tw5jc0 i)d3xnnx*c 6yy dqg(u+h ice the frequency of the other. What is the rati cj+*c g 3(ixndyx0d )nu6h5yqo of their intensities?   

  What would be the sound level (in dB) of a sound wave in air tha owu1-x fo(j+ lq(v/dgt corresponds to a displacement amplitude of vibrating air molecules of 0.13fx+/u1d-o(v( l ojw gq mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem 0 ytdwiuc/ (s*as loud as a 100-Hz tone that hd*(is/ c0uwt yas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that a4 cjequ:h twj9cl;ry*q b8;b6n ear can detect when the sound level is 308:hbe6*j ;rjw49tlcqbuqc y; dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whamq,0+jo dx6a *kmf5gat is the ratio of highest to lowest intensi+ aqkjm6f* ,50mg aoxdty 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 Hzn 0cyugq)it4.zse;a8d9 z e j*. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensios*tqya0.zc) un 9d;e8iz4jg en must the string be placed?    N

  An organ pipe is 112 cm long. What jd9hu.lqna017 -0a )csdu uddare the fundamental and first three audible overtones if the pipuuda0hd1sq97jl d d-0n)c. aue 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 frequency would you expect from blowing across t ro7-+yj-fy )akl 6wluhe top of an empty soda bottle that is 1ykuy7a+) -f-l6lojrw 8 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 span tg:ia4tko r-rvt2 35z gz*j5qning the range of human hearing (jt-vtkrit *z5rq3ag g524z:o 20 Hz to 20 kHz), 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 tha ai em7dya2*uj w720zird harmonic. What will be its ydwi2*e7aaz u jma270fundamental frequency if it is fingered 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 middle Cv+-sm;bkj 5;1jzxdus -j;km+zbx5u d vsj;s1(330 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 open organ pipe that emits middle C (262 Hz) whem)n*fpkv *8*sql6 k v0i 2awupn the t l)qm*kv26waisf up8**0p nkvemperature 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 awzrho5u32:l 7p)awubp )o4zepxh+k 3t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece 9zkf mg93;gmt/7vgqv of the flute in Example 12–10 should the hole be that must be uncovered tofm79g;vgq/gzvm3 k9 t 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 uj v6 sy3zfil-gdh/2.Hz, 440 Hz, and 616 Hz, but not at any other frequencies3gy2id l zhfvj/.6-su in between. (a) Show why 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 open rm .9e7vtmh6f 9qd icw1sv.o2at both ends. It resonates at two successievrd2qmc9iv.owsh1t 9 m7 6.fve harmonics 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 rjhg/*)mm8+ 7oa ekkh+d g 1cw$^{\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 withim)n c* 1e x.gfge pmk4f(03zirn the audible range for a 2.14-m-long organ rk.f e 4cn3f1gi(*z)p ex0gmmpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 0qy1a f,/quvq 66uex ecm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible 16y/u,feqav qux 0qe 6range) 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 adjust two strings,uw )y;g is wa3:/ijz j5af(e2m one of which is sounding 440 Hz. How far off in yg 3mzaw) sf5 wa2iu ei;(jj:/frequency is the other string? ±    Hz

  What is the beat frequency ifmxbi 34au k d 5nomcz.g1p: ngkq. /m:a3mhi;; middle C (262 Hz) 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 o*l /k)8 gbs*8dbp zxyX) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shb)gszbdxol/8 p**ky8rill 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 tuniia9 fv: bqaz7l;i+jd1 qm *nxlhr5n;,ng fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational fr dq fq: n51+ahjr;7b;za,i9lln *xvi mequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same / g67rtrmcbn.frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when tcbt7g.6 rm/nrhe two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes e6- mgj./x cv(va8 ehniach try to play middle C (262 Hz), but one is at 5.0°C and the other v-a c8vjxi/ .nm(h g6eat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,2r,/ucp4hskycwe fc w :68m7n A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of cehfm,86p rnycu2:/4 wsw c7 k3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What 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 spel a.fjj2 jtks. 1v/w/7 huocj;aker and 3.50 m from the otheruk/jth/j; lof27va .1jcjs w. .
(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 supnc vq+91bhyxq m-m/w5posed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 1/v cn-m qmb5yqx9w+ h132 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 manyl xv+9nqo9jd+ih *d jgnsd0 *1 beats per second w*dl9qj g1 jnd iv9 +0xhsd+*onill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when eaas1r; zw2i5 at rest. What frequency do you;iwz5ae1r a2s 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 frequency do you detect if a fire enginezkf25 ult:2rd whose siren emits at 1550 Hz moves at a speed of 32 m/s 5l2t u2z:drkf
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20y/n /e)c/vqk a00-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Ae/kyv //q can)re 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 equifir3* 8jxv654nq m 8t5of qjmipped with the same single 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 frequency of 5.5 Hz. What is the frequency the horns emit? As3 8rmfx4f5 toq*8 i6v mnjq5ijsume T = 20 $^{\circ} $C    Hz

  A bat at rest sends m1tixh0 lm+2d out ultrasonic sound waves at 50.0 kHz and receives them returned from i1hxm dl0 +mt2an 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 cnhu6 j.o twyhd9,vj9l- 2z.rat a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat h9jt.zh9oy-njrl ,c.hd2v6 w uear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the originaltmllfc4lo.3 1;hai 4pdc a*0z Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identicalzf3a0l 4td1mca.i *clphl4 o; 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 to measure ll:w0i2i +: :u98nz uho jbrvjn)u6vvblood-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 blvuzl n +w:i0v 928)uo::unb6lirvhjjood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usinq( bz7e9gu5o dg ultrasonic waves 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 emib, 76g+s5iop c-gl+ rpucjbzynw8u71 ts sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear o8iz, 5-17y+ sul67gugbcrwj pc+ bpn 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 at 20 s1()xldb9ej- j8yw o+ qcc2kf$^{\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.rj09na 6lb9xk3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motion6bk alx09j n9r?    $^{\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 atmosphe 5.iat+cfsz4 bre of a planet where the speed of sound is only about 35 m/s +.a 54cstfbiz
(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 the shock waveuvl 5-+h i /i72maxygl angle it pgx/ hu2ili m yv-a75+lroduces
(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 (im9bv4c3:y-cb rm9 dx4 zsn l$/theta$ 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 ,z8imti)0*lq/l,vwwq7z i kb1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horwb7l qizzimk 8,)q vwtl,i0*/izontal 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 downward fro dgy mb1ml1a;6 e-7gigm the bottomdy1gi ;-7 1laggmbem6 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)?    s

  Approximately how many octaves are th j 0ppaa27 t0f1,ulvywere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists op k+tjqq gtoqb ,m4h-79ds( i)f many plastic pipes of various lengths, which are open on botdk4 ,jb+(o)i- 97thgsmqt pqqh 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 makes a sound close to the threshold of;h(;x me)rc yfksr 4t) human hearing (0 dB). What will be the sound level of x(kr se 4c;ht m);y)fr1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB zzkgjv:e dsjj* ;0orti0.5p; sound are heard simulttiz r*0j;.0e5j spvjkz: ;ogdaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed i uo 9 ormfh(,d,+cbz,ln the open, is 105 dB. What is thd fz9,u +l borc(mo,,he acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz3fy- 3pl. 24d1xxrisxk81 k0 anoaw pb. The power output drops by 10 dB at 15 kHz. What is the poip2brd.x1pn38- a ykf1 0slxowx k34awer output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective - h;kejut4( u/s6beyh devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 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 mh bstyu ;4(6-/kuhe je from a jet airplane engine?    W

  In audio and communicationsilkvkn5k9ywu:eoww2- 29 : j5-nm bgp systems, 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 tuneh)ow8ijmt e// d 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 between fixeg:zbv)8hj.ho7 xs2,/yjxs s3g cd gl +d points with a fundamental frequency of 4l zjsc73j gso:dgv+2g,y)8sh/hb.xx 40 Hz and 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 ;wcp ,ya iz9z6water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air ip6,z yw9 ciza;n 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 0.125 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 opiq k.a51 nwd,wen at one end and also 75 cm long. How much tension should be in the string if it is to produce resonancdnw.wi 1, a5qke (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed na-nkk4l0,.6w nx gd0 8wrxh2aoi fs,to 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 tone in the 500–1000-Hz range coming from two s9wu6u aa:gqm: tu-*cqe;rh-gources. 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 from one source than the other. What is the frequency of the- ga uarg9:-uwc;*qt6me:qu h sound?   Hz

  Two trains emit 424-Hz whistles. One traik ii.vmsv+j 1ozh7i* bn851zy;nc v; fn is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed offzvi5nj.;7n ;m8io1 kyc z b* i+1svhv the moving train?   m/s

  The frequency of a steam trainf 1tqgaxgmy- -rs v)6* whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assu- m6*qf-1 tyvgsxrag) me constant velocity)?    m/s

  At a race track, you can estimdl5 fz91n;kje ate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding caldk5 en;1zj 9frs. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetherb4, hr njos)zq0s u5r8, produce a beat frequency of 11 Hz. The shorterrhqu 48ojns0bs)5z,r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite enb12a.4 vm9ny bfr 6yxids 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 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 speakers, at B, and (c) he hears the speakers after theynifr1bm ayb2x9 4yv. 6 have passed him, at C?

  If the velocity of blood flow in the aorta is normr2pl 4vis ) am.g8h ffi7i;o,oally about 0.32 m/s 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 travel with a speed ofapio2, ofr4i;hf)i glvm s.87 $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speedk7qs3:e s3zn-szo ss9kb4wy , 6.5 m/s while 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 by the bat after that wave reflece3q4n3 9w, :kb kz7yszsso s-sts off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth u (jxj-,9j 1(ocyuvwp :a+sfh. The pulses are approximately 70.0 ms apart, and,v (pj+s u9(f-xwc1 o hj:uayj 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 used to send signals from oeeq1 v k78 unuo4q6yn0ne 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 blow8 6nn4y1ke vqo 7q0euun 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 listeninyc 6 ftnax50,mq7:z vfg can be compromised by the presence of standing waves, whic6 axm cy7f tnv5q0,f:zh 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called pc bkakc spz0*2.bmc:78gef uzl*.u7 “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little prg a*uksl7 2k:*.b.8 0zcup pec mcb7zfactice, 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 threshold of hearing for the human gr7r.vwashx) *v :.dqear at a frequency of about 10*: wr. 7h r.asxgdvq)v00 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 2.0. An observer on the ground hears the sonic bo8sr 8/hlauduh 0z2 b,bom 1.5 min after the plane passes directly overhead. What is the plane’s altib2 hsd8ra0ul,/ uh8bztude?    $ \times10^{4 }$ m

  The wake of a speedboat.pt+lnkl,jlr: kn i- 60jw -uv7wa, ;gtkg /ug 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