What is the evidence that sound . zyis8ed kbo84ckrcwa1*8g5travels as a wave?

What is the evidence thafpvvr 6+d h17y+q5v sat sound is a form of energy?

Children sometimes play with a homemadei8yiwct ) d5bjgd/u+/ “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 candti y/jib5/g8cud +)w 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 passes from air into water, do you expect thr 1.omnm5b 8tqe frequency or wavelengthq.m15o m8n rtb to change?

What evidence can you give that the speed of sound in air does not depend sign.r f79rk jn3-t nbnz9pificantly on fbnpkrfz t 79j9-rn3.n requency?

The voice of a person who has inhaled helium sounds vencz8f2 )se9 adry high-pitched. Why?

How will the air temperature in a room affectf aewa g jbxkl1,;:47l the pitch of organ pipes?

Explain how a tube migh7) r2d;pqrx tejqa hs6p1mb4z9(1tpc t be used as a filter to reduce the amplitude of sounds in various frequency rangeseq1 t)x ;j(hqr 97rtp1cpz map6bd 24s. (An example is a car muffler.)

Why are the frets on a guu;) xd9fgixe*6 bo p/xitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward x*i9gu6p)d;xob/e fx the bridge?

A noisy truck approaches you+oogsiq a6 * .g4zeww3 from behind a building. Initially you hear it but cannot see it. When i+6g eas34w.wz oqgio* t emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be saiklfy 9*r65 gi(fj+ww yd to be due to “interference in space,” whereas beats ckj+ ( 5wglir6ywff*9y an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of thd.hi.uas:4ycvl jd caq n6) 67e speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart ori6cd da7acvj)l : h.4 q6n.usy closer together?

Traditional methods of protecting the hearing of people who work iny9 o8k z bzjmn1an+3h9 areas with very high noise levels have consisted mainly of efforts to block or 1o nhk9 b938zya +mjznreduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a subz(ym ja5 dj5;perposition of two sound waves with slightly different frequencies, as dj5y ;j bam5(zin 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 the samaxkr1.f(0l w ,km54gys )breu e direction, y5.s )rr u(k fbea1x gw0k4l,mwith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the soundbppvy c2a3k48 heard by a person at rest with respect to the source? Is the wavelength or velocity chak8cp vb342ypanged?

Figure 12–32 shows various positions of a child i p;x.s(z jybd)uv+k(u n motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child svz jyuubkx(;d+(p). hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake -8mlh i5icdm+ i/qlq7 by listening for the echo of her shout reflected by a cli+ i -8liqhq mdci5/lm7ff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below t, 1:y-bynnzno /zm 9c8v:jwxihe 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 : wynv 9,x1oynm z-ni/jc8z:bpoint? 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 atmkv2fj:jt , 2i 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 foggy day.yii-jbox/ 87n Without warning, an engj7 -/8n iixbyoine 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. The(2 ;r7 q jzjbfoj h62zfxj6zp. splash it makes when striking the water below is hea xophz6f2jj6bz2; rz .f (jjq7rd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge s,2t foi *vzp hx(5cx9itone 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 1.1 s iitv ,ph2x(*ofc59zx 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-second ruc 4o fab8kmq q7 vp+,9ulf.1ysle” for estimating the distance from a lightningcfsq.vy o8kq4 1f 7b9la+u ,pm strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the e:jce5jh)b 6*gwlgy3u4 a9tppain 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 a sound whose intensi3vfqizr0mp1y ) l5 3mjty is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whzk.. n,boxp7 cen fired simultaneously at a certa b,z7npx .c.okin 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 fromxpaqx 7, )su1uab ;u0k an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one e;uu)a x1busk p0q,x7 angine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 .vjeh3o jvk/ f tte((pci-+fs7j7*d(3utij zdB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB zo37j-vcfjteej +7(.k( juptvti/h idsf * 3( =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person sp8/-ql4kmxm43 mhco,278 jc uxhjrslaeaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a s-uajx ls 48c 8h/3khlmm, c4ormjq72 xphere 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 awt/x bjdzg /bzu:y )+(pz), rtn 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 W6)viajn3hx s oms*z9gpb:5 l4, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connectedo4)v :gx sb9 563iasz*h pmlnj 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 regi)r6i- dn4g4,iv. qg9hvapouistered 130 dB when placed 2.8 m in front of a loudspeaker on the stagegpdi46gon ,q v- 4hiv9rai)u ..
(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 typicallm( y5 c dzc aoa,wlvw/jv155b1y detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes om5av 1oac1l v ydb/ 5j,z(ww5cf two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripleuttqs+gafy4 f y6qo8 0,.wo.nq c7fv8 d, (a) by what factor will the intensity increase? foqt7oy.f qf6,n +v.8 ugyasq4w0ct8 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 twi.)35 v0elnzpl;h edd * y-duotce the frequency of the otherd.ld03 -hvou; )znepd5t * ley. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air q -obj,7p-qidte36f xthat corresponds to a displqxeo, 7-p-t iq3d6jfbacement 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 t+x42rrus uhd 2one that has a 50-dB sound level? (See Fig. 12–6r rhx2du4s+u2.)    dB

What are the lowest and highest frequencies thazx p6f-bg;/:yg,//oi r .wjp stujm.pt an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)tpg:pjxi .b /owj/ y f.-ug6,/pzrs;m

  Your auditory system ca-+k o9p odmqsa/t)i*ln accommodate a huge range of sound levels. What is the ratio of highest to low + a-piko)s/qlm*tod9est 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. The length f5kafe;4xl.21bzv v. +tx cji3ejso4of the vibrating portion is 32 cm, and it has a mass of 0.3ef;42x ejsavkft.j3.ovxb i+zl4 1c5 5 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What arxj9b o:x.un t ivg6(.pe the fundamental and first three audible overtones if b(..j9ng6oxp iu:x vtthe pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acroqr +mi xuvl 6*w.):apfss the top of an empt):flu *x6mwq aiv+r.p y soda 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 ge+*ngs9 y vfbc 1dep wc685f.spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the pc9vg58*6wce d1 +.bgfe y snflengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as bgcg 15 5glxzs z+iv87wwyj7: its third harmonic. What will be its fundamental frequency if it is fingered at a length oz5:+ vwlx7z s87 ij5 y1bgggwcf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above +nwk2qx02j1ag9fh y3:kmodr middle C r1o h09:aqgxf kmdw y3+22jkn (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 lengt5t*)g g7z e p0doq-xz,s aces*h of an open organ pipe that emits middle C (262 Hz) when the tempe*xaodg seq5e)s-p7 zgc ,*zt0 rature 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 20jnd) tm30h+ z1lo:lex $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiecawnw t)dj,(; ue of the flute in Example 12–10 should the hole be that must be uncovered to plw n ,)utdwj;a(ay 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 Hz, 440 Hz, and 616 Hz, but not at azr48jytj fi:pcw 3)j q+31chiny other frequencies in between. (a) Show why this is an3c8iy hp+:c f)3j4i1ztrjqjw open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at twogc+t,3 b7ua)lhu* ywj success)jtuhwyla,b 7cu g+3*ive 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 z bk0:2td)z e f7n,;6owlnwsm$^{\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 witv)t s(w, xkdl4r;9lz6 1jsvqohin the audible range for a 2.14-m-long organ pipe asv)kxd;zj6l ( ot,s vwr94l1q t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2ofpyk q22 qbggwk6+ mln+-;t*.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estl2y fktq2m++;gq wg6 kbno* -pimate 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 s when trying to u)jbyysq 8w - w--wgh.adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? --wsjhy) q-uw8y wbg .±    Hz

  What is the beat frequency if middle C (262 Hz) 5 -y8vjjl)ddlw on9( aand $C^＃$ (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) op2e(u) k6 qw;eptcn bq jzr5l;1erates 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, estimaejn52k r1uq cp;bwl;e6)z q t(te the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350u*d*ls 8 wl(brpdm.(-t p 9- wtjkc2y6zhk,lo -Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strj y(9tdpzu*,*82 htrlwlpldk -(.wm- kb s co6ing? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frthgc a1au-/.2t /rln mequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13m2clh1gau t-ra//. n t.]    Hz

  How many beats will be heard iz+pg 0x :wi*hnf two identical flutes each try to play middle C (262 Hzgw 0ip+hz:n x*), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C.jiknmpz c-n)6jf80p 4ca, /uf **taxi Fork B has a frequency of 441 Hz; when A and B are sounded togethera p, 0i zjc/paf)* x6utnfji8* -m4knc, 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 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 speakerv6+pqysb8f 0wj6/xzo and 3.50 m fq8spyx6 /ojv f06wz b+rom 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 t1 b )qc)u -4fjvqrw0rre on*bjqk9(2 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, qr*oecnwrub (0qf)b t1) r2jq-4v9jk 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 wavelengofr+/,1 coqmh ths 2.64 m and 2.76 m in air. How many beats per second will be heard? (A1c+ro,f / omhqssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequenc 77g p/j+2wzxfr bduf3y of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed f wbzr 7fgu d73xpj/+2of 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 engine whosg( +cgt.a 1evce siren emits at gvtc +ea1cg.( 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift i - 6;x ):vuikjj 9fbadb-do-h) srty9in frequency if a 2000-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? Are they close?s9- k;i 9hbj) xf 6bvyuj--td:r)o adi $f'_{source\,movine}$    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 wy7n;b tfhphnm 9 gu /y(p3va2;ith 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 g2y7an h ny; hb/vup;9 3mtp(fhears 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 u*nl9;rgw;p8yk eat )a;1fr w 50.0 kHz and receives them returned from an object moving directly away from it atkr w)lwgatfyp;; *9 a8ru1e n; 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 flgn nyi/f+mw/st be 52,ies, the bat emits an ultrasonic sound wav2/wsnngyiebf5 m /+,te with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplero:ao7c-qwdrq(nvd hr:36 e3h experiments, 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 a d6h-rq(v:q 3deowroh37nc :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 blood-flow speeds. S* s,6k3odi.wgcw)of fuppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/6o .cf fis)g3ww*,dkos directly away from the sound source?   Hz

  The Doppler effect us ,gg )hn/kxxc(ing 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 emits sound of frequency 570 Hz. Whett:c4bri1 a.qdv, a+qn the wind velocity is 12 m/s from the north, what frequency will observers h ,ab qa:41qitv.r +ctdear 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 67 ot4i crt:7ynu*ng )ultvb( moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the *t;kn us,kkex7;dw(m speed of sound is 310 m/s (a) What is the angle the shock wave makes with the directi(txs7k, n;d*ewkmuk ; on 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 b+sqkf9 cb,:qv( g kl9a planet where the speed of sound is only about 35q: ,b+kv sk bgl9f9q(c 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 strikek yn1vxl:q8+w)1ip r ks the ocean. Determine the shock wave angle +ixnk rk1 wq):p8y1vlit produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle 6m c+x 3x)snwa$/theta$ 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 qwx3 a8zo*5 zst/ 2xtnexactly 1.5 km above the ground flying faster than txqoa*z st2nz 835/t wxhe speed of sound. By the time you hear the sonic boom, the 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 thatjajhv:oj + + rm/zmx80 sends 20,000-Hz sound pulses downward from the bottom of the boat, h/z:roja0+jx 8 jmmv+ 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 there in the human audible ranget6a24 v;qaz*es vznw0ob0ct9 ? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display ca du,p1 bf .f)wlr nz9emphr+vr;q6c 97lled a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are operpf;r9hld6eb1fvnw qcu. rp7+zm,9 )n 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 makes a sound cljx +gzln(p*6xe ,.l;b/j-9z dlktmmyose to the threshold of human hearing (0 dBl yk*9t(6zmzjnj;lbgm xxd -+e l.p/,). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultantvmw fk*fz ;e1.gg6ixm3 -tf 3uoqk .-t sound level when an 82-dB sound and an 87-dB sound are heard simultan ;qzk-t.6g3m.ukige1fo vw-mtf* 3x feously?    dB

  The sound level 12.0 m from a loudspeaker, pldy6+ylfx v;r- p xy:y-6zxle( aced in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direct (v6f6ey+px-y;x-l xzryl dy:ions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outputs)a iu y(/l0yl3c:dn:jefd eq ,ec52 d drops by 10 dB at 15 kd q2if3 ayul(ed5 d,ec seycn:/l:0)jHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicall6v;j p;ugg s-x/el*x ny 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, and that the average human ear has an effective radius of 2.0 cm. What would be the xgu;lse/ gx*vp6-nj ; power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications os v wo jh.+6x2upfi5,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 tuned to a frequency 1rm (;1 qiwrvv7.a fwz1*4u umc$\frac{1}{2}$ 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 fixed poin mkn/uk 7,t5m++s b2p-jttoxqts with a fundamental frequency of 440 Hz and a mass per unit lesmot-2pm7b+,xn t5k j +tkqu/ ngth 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 abov)qu o)c6o)jpgttq 7x x9aig:4e a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it doe: j9tg)47pqco xtugaqx)oi6) s so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 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 ope gd4,i*w. evf,,4xzedtlv x1pn 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 *vdtgiz4 1ed fxwve,p l 4x.,,harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonnt hgeqtx.: ,2ate 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 btl* r9v;iw+uc 2tk0 efrom 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 from one source than the othe0k ut r2+b9c telw;iv*r. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. Oncyai yaf+d(y8 o4egdkd9o1 r9qw+09ke train is stationary. The conductor on the stationary train head wqo9 eyd(+9g a409oc+8krkfai1y ydrs 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 youqa,++a gpkfehmc+y l0z3b /:n is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train mov+ hk 0 +3lb: acfaq+mez,py/nging (assume constant velocity)?    m/s

  At a race track, you can estimate tynfh5bs *u45ta7kwd /he speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a cerwu 4y*db fk7ha t5s/n5tain 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 together, produce a beat frequency of 11 Hz. T7wu0 og.* pgq1 c1ikithe shorter oigp1ut q0ig*o. k1 wc7ne is 2.40 m long. How long is the other?    m

Two loudspeakers are kk0kpp oj0.j-z6p0 cm at opposite ends 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 ojk0 jmppzck0p -6 ok.0bserver 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 c3qzlc8 (o4a/g e;e m):72ec l cqnzkrabout 0.32 m/s what beat frequency would you expect ifq:zee 2zl aeqc c4 3/kn(;gr 7)mo8clc 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-r4z 8df5cdjx -2gv ug moth is flying toward the bat at speed 5 m/s The bat emits a soundv x g42ufgcdr8jd --z5 wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a q4l-tt56 wtf-k crp)xrg 5 ;dumoth. The pulses are approximately 75ukp6 gdrtxtc5f )rl;-wt q4 -0.0 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 used to smr)2qim; 11dvukpdo 5 end 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 musiuq5 1ro)dim2 p;1mdvkcal 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,dpu /ecyzb1c- f;fm/ can be compromised by the presence of standing waves, which can cause acoustic “dezy f-;c1bc/pfde/mu , ad 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 “singing rods,” wk(cen. c ;y8ucoj0-2dvo0ti involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is .o;tde8juowi c0cn 0(k-y 2vc 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 thr ;1cvw fxj4(xoqcup,)v.t 1 tweshold of hearing for the human ear at a frequency of abt ju 1cp ww)v.x;,1vo(qcx f4tout 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 2.0. An observer on the ground h5watcd- g-or3 ears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitu acw d3-r-o5gtde?    $ \times10^{4 }$ m

  The wake of a speedboat is yz+z4u6mp- ,0p6of dz 7vlrlz15 $^{\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