What is the evidence that sound travels as0z u 2oj:ez6en a wave?

What is the evidence that sound is a fop dx77aluuj9rp nco20:a6: dl)3lhjj phi j/*rm of energy?

Children sometimes play with a homeh;os hj)d ng 70 16:+qg imghws9yl7wkmade “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. 12–29). Explain clearly how the sound wavs 90 wl gds1ijh7 q):hmyngwh6g7 k+;oe travels from one cup to the other.

When a sound wave passes from air into water, do you expect tf6cn ;bb/ skks 8)iji4he frequency or wavelength tok 6/k4bn)b8icisf;js change?

What evidence can you give that the speed of sound in air does notb7 j9 q4-l9sazakfkicq)mp +3 depend significantly on frequency?a 794 s+pbmkj)i3akqfl q c-9z

The voice of a person who has inhaled helium soundsvgl4.pc4yzv;3w+v m c ,q*mg b very high-pitched. Why?

How will the air temperature in a s;s*(o (0t0 abpy14dzm;l-dxmxai vnrbfh22 room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to redu7j q,a(tu a5xh4 (hzhjce the amplitude of sounds in various frequencht(auxhq5 4jaz 7hj, (y ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as 8ps g zyd8f3;boeh,(f you move up the fingerboard toward the bo( p d8ghbzf3s ;eyf,8ridge?

A noisy truck approaches8s 5smul5qiy6k7( hvf you from behind a building. Initially you hear it but cannot see it. When it emerges and yolsq mu 5hi58 v7sk(6yfu 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 said to be due to “interference in space,” whw) z 0 x;0dx9nkfik9ffereas beats can be said to be due to “interference in time.” Explainfdx9 ffz;iwk00 kx9 )n.

In Fig. 12–16, if the frequg5* ntrm;.dt3uhv 3*rw8 jfjkency of the speakers were lowered, would the points D and C (where desr jurv5* mt8hjf 3*tw k.g3;dntructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peop * m*lpanu dlz6hu8z7;cjq s9nz8k7-lle who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are wornndl*alhmz 7;lzs kq puj87cu6n-*98 z 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 -vam - g fvqvdo;yuacw47v7/+Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequenc;m4gf vd/v ov7-uca7wy -q+ avies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in bb-z /-e8is dythe same direction, with the same veloc-sz bed8iyb/- ity? Explain.

If a wind is blowing, will this alter the frequency of the soull;ti v5tsi, -iy*bd6 nc v1y(nd heard by a person at rest with respect to the source? Is the wavelength or vel15tiv-,vs6*i (dytlcn i ;blyocity changed?

Figure 12–32 shows var;z,trcc +y *u7e,jj1hqp m*xtious positions of a child in 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 hear the highest frequency for the sound of the whist ;t hzt*pjq*rm+,cc1 uejx, y7le? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of0hfd pro:)eoa3oaqc:/ k;r2 d her shout reflected by a cliff at the far end of the lake.d :k)r adqh fa3p/eo 2orc0;o: She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears thki.;f ifo qk,36zlki5e echo of the sound i. 3q,iz5 k lkffio6k;reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave mh-g37m7 hbg n8;abqflengths in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting-m hz7l )8ju1qfy;kdh just above a school of tuna on a foggy day. Without warning, an8 z7-yu1mlkhd)j;fq h engine 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 oflxb .6j7o1knualuatgz i(j1 ;9tt,7 x a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the ;jz9ib, 17t tt1xjk(lgu6 a nu.7aolx cliff?    m

  A person, with his ear to the ground, sees a huge st )ziq(xqhki4+;wa s9c one strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in thex+k;z4 q hw)q a9i(ics 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 errh 1bwft9x+ oe-or made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature isw1xo th9-f+b e (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at o zu/jf8l)wbkaem*)7 the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity / 9hsxd6cw0uyis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneoz:4- htxvpbtr:6 w b5vusly at a certain place, what will w6v v4rh-txb z::5pb tbe the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain diss )efc z)ub6x4s /ms2stance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engiseb 6z4/) sf2)xsmsucne? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sdc+xoohd swc-1e5 /mh5 s33idignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dBd1d5o +hmhc3wx/si- s3c e5 od. What is the ratio of intensities 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 speakihils qax,17; -mcrty 7+-fv 4ateiyx 0ng in normal conversation. Usm c a+h14slia 70, xqy7-ti;-freyvt xe Table 12–2. Assume the sound spreads 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 strike4 o,4zist8rn*m 9mb o6lm*fyus an 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 W, while thec j6 op8c7ef/qmw 9j6f z olv3/*kpt;o 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 connectedkwcf*o8jeoj m3ot7 pp6z 6f9/v /ql;c 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 k ulv3zrz7(3q3jwc r0when placed 2.8 m in front of a loudspeaker on the stage. 7krl wcu(zrvzq303 j3
(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 typicalvtuflj7d 1a18ozz:;n ly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of t fjd1 u:8z1v;ozl7a ntwo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, .0k hcg ,p.vy7w t ,n0sibw-tf(a) by what factor will the intensity increase? tbt 7w.i0,yk,c-n fh pwg sv0.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 twicf 4ilkm//o1xwqq n* :te the frequency of the other. What is the ratio of their intensit*/qn4ql1/tfw :i oxk mies?   

  What would be the sound level (in dB) of a sound wave in aiflng9 ageuk0+t 8 m6/gr that corresponds to a displacement amplitude of vibrating air mole + 0met6a89u/gg glkfncules 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 z g:kv9dh z,3oo fjex:2y5/ 3vci moo+tone that has a 50-dB sogo vv/ 3oz9 xfc3+z,2hi yj:o:oemd 5kund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequen 970)j i ebob,luf0 se(rmkmj)cies that an ear can detect when the sound level is 30 dB? (See Fig. 12( 7bjm jo,frsb k0eel)9imu )0–6.)

  Your auditory system can accommodate a huge range of sound levels. Wsxpnt g- b 9;f;n9b dgybo46e+hat is the ratio of highest to lowest intt99ndsebgb-yxp+ nb 6 ;go4f; ensity 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 frequewh1 1gat zth07y/omh8ncy of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be plac1 tyat1z7hwgm oh/ 8h0ed?    N

  An organ pipe is 112 cm long. What52* xrdm8 :) jbfapnin are the fundamental and first three audible overtones if the x*:dp r )a8f2n5 jnimbpipe 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 yow7gs vxv-) .r-ku bp.pu expect from blowing across the top of an empty soda bvpk-.wbgxsvur7.p -) ottle 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 o b-bqm2xnydgvc(v;+)rgan with open-tube pipes spanning the range of huma gn(mby+dvq-x;cb 2 )vn hearing (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 kqqi9wd /gsd0) nxv* 3third harmonic. What will be its fundamental frequency if it is fingered iw0 dng3d*v9 /kxqsq)at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to ps5v :gefkev;+i ena**z) i d22l /yynflay E above middle C (k*: 5 zf )iy/i2env;delyn*esafv2+ g330 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 pf2.3kh64 qv8ni1 vc paqf ,zlHz) when the temperakz2l vif4f3a cq. 1p ,n6q8phvture 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 ct:c1h)5r)c fpm pgkj qm,7p. at 20 $^{\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–ul9 lh0isu/vk-80j px10 should the hole be that must be uncovered to play D0 hi/pks 0lu9u8jvx- l 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 nagyxq(. rma y ;/c3d7616 Hz, but not at any other frequencies dc;g /xya7ym aq(nr 3.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 at both ends. It resonates at twro ffp 9dspsa0/ct, (1o successive harmonics of frequencies 275 Hz and 330 adr10o(p/9ps tcf ,sf 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 -86+ ywgf l xhmk3k.oy1zc- mp$^{\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 a+ qj +rc vg69r(cp:eture present within the audible range for a 2.14-m-long organ e tjqg69v c:+pc rr(u+pipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is a ku 97gq pc,+q3cu)ypk ai++oopproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Esti9++qco,q u7ko )y3pupagik + cmate 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 adjust two strings,jb77ch*ejd8zpij .61 3d qdstg f))gu one of jb z6*7j pu)tg8 df.c hs)j1idgqe 73dwhich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequeni afrtv2w9.7z cy if 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 X) operatei;ry ri7lk7cm 86m7g cs 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 simultane r6r87mglc 7mk7iciy;ously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork*tpt.cpcp( * 1xbceu, and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational freqxtp ub *(tcc., epp1*cuency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sameso2bwhqk/l/7 frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two 2bks/wlhoq/7 strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identi+ nlttw z )r q2jem5;:fgyqh;g.lwy. ,cal flutes each try to play middle C (262 Hz),ht2)fqe5g: ml.,lqy;wn y.+rjt z w g; but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork bq;1h4,3gn+2hsx;kpxg w g;6fjce hm B has a frequency of 441 Hz; when A and B are sounded together, a beat frhx 6j2q s 4bc3exgfp hw;1 gng;m,h+;kequency 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. qcoq 9ee,wp /dt 9pvvt-/v0/w A person stands 3.00 m from one speaker and 3.50 m from the oo/9qw-we vt9/qp0e pvt,dv /c ther.
(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 1p7) 1y bncpg;i32 Hz, but a piano tuner hears three beats every 2.0 s when they are played to)7b c1;ppygn igether. (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 beatb;2 5gze,ww m(furd(us per second will be heard? (Assume Tbud5zu,(w 2em(fg ; wr = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1l*u0dq 7gk gju)9 +aij cjm8,w550 Hz when at rest. What frequency do you detect if you movegj0u 8,7ld9kca+jg *m)wu qji 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 i6 giqf: jd8efva-(2m if a fire engine whose siren emits at vam2i:ei d(g8fj6- fq 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in ffq yhbejj2- 9 znf,o9 q5/qn:yrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward -jf,5j o byq29nqfhen9zyq /: it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Wh ii:)z xic+) ox9v cn9mhmn,e;en one is at rest and the other is moving toward the first at 15mv;mci, no +e)x:i c9h9)izx n m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultras,i ozet*c,kk 02c n/dconic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at , 0/ tk 2kccc*no,deiz25 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 flie)7iijt tdx v8ku h(dyi:6mo.0s, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in thei jttki y 8mx do:70i(duvh).6 reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plarv w 6r790ap /numr8t3gya+mxyed on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at p6 m9mvxrngtaur0y7a8 /r3w + 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 ulu-hx+ns6q dag-18gqi7exugz u 07w. rtrasound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beauq 17-7d-6u xeuggsxwq+ih an.z8 rg0t frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultra(sdi l wszdw;(d0srkfq(*9 o m6:.vk ksonic 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. When thx*f, t-)yqc :hp5fvsrykis78vg9e k +e wind velocity is 12 m/s from the north, what frequency will observers hear who are locat)r ,f+*ysqsve-ik7 5vp 9 tcx :kgh8yfed, 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 movi/ +jn 8ze6rrting 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 speed of souncskdvmq7f (cw*3 9d5(:yu - nin cnl3gd is 310 m/s (a) What is the angle the shock wave makecn y v:5cl*nd3-mf g3s (nk9uqcid7w (s with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where y ;+qof(mqvm9,0 qcqwthe speed of sound is only about 35 m/yqqf; qqmc9om (vw0+,s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes th+g - 4(0ca.vzuvvm ovde ocean. Determine the shock wave angle it produce uz0v-av+m4odv(g . vcs
(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 *xf ( o.ct4 tmdbmz21z$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above thb+3rn3 lqsee 4,)1lehrukjw. e ground flying faster than the speed of sound. By the time you hear the sonic boom,. ,3erw4eeq 3rs lbu n)klj1h+ 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 o4, w7r 2nrbcu. 1djnxsonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh.7 roxrcw2 n,1unjb4d water)?    s

  Approximately how many octaves are thea5 bn.g pz.vpb s65ru- r q fe:63;y.pn5wkebbre in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pun rv 04x mhpdt66m;+j(:k cwripe symphony. It consists of many plastic piper 6 kmch 4j+tm6nxpur;d(v :0ws of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold oldjdz jml0cs+v +80/vf human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?lmdzj0 /vc8v dslj+0 +    dB

  What is the resultant sm/pvu gc, quktg0zd me3 l3.;9ound level when an 82-dB sound and an 87-dB sound are heard simult ;u g.lm,me tud0/39vcg3kq zpaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.* c kdp *2a f1cnl:ag*hrxso e: ;x8gk2izf:g8 What is the acoustic power output (W) of the speaker, assuming it radiatgc p;k*gx*az:ifc :s2d2:k1ahlf*8rxe 8 og nes equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The powe2o:gjf 5)3t*z3b zrzjow 8 fjmr+ 1wunr output drops by 10:23zfoozjm )jt rzjuw*851 fbrwn+g3 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devirv/e jr,b18r sces 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 er/j,s re vrb18ffective 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 systewa(ybow:qr.4 :t *n+: kpuf okms, 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 t/x * i * brq8x1iyt4a5xnn:xwouned 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 fixed points with a fundamental fvz)b .9w0zsx 7 ehh0g.y/t,xk l qhim,rh e/hsz 0ih)mg .vlyx bw7, t,.qx9zk0equency of 440 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 6mod 0sj jbahqy t:d2g x2s933water (Fig. 12–35). The water level yo b2:d0at2633 dghx jss9m qjis allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 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 tubestq+ zztrn6;8(jv2 od that is open at one end and also 75 cm long. How much tension should be in the string if it isq;tjz8zn(2 ovr+st 6d to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full 3 mj+ 9l 0sao1s1bl jpzyjli6/d.2nz dloop ($\frac{1}{2}\lambda$) 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 c0pue (t85lpu soming 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 from one source than the other. What is the frequency of lpe t805 us(upthe sound?   Hz

  Two trains emit 424-Hz whistles. One trt 4kb02fo7 bflain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed 0k lo 2t47bfbfof the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 5sal; h:85mwri,dzb1t 38 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train,tisl8haw5;: 1mb rz d moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just b32naa ad) ya9; )xe);dccanfcy listening to the difference in pitch oaa y)axn;c aec9 dcd2))a3f; nf the engine noise between approaching and receding cars. 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 together, produce a beat frequency of 11 Hz. Tiorkbc r +w/ym o4) +* xc7)al-vz-cdbhe shorter one is 2.40 m lonkd y+o-r4cmbz bwa/vc+-lro))i*c 7xg. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it movec; y:2rff5cpzs past a stationarycc ;5fpfyz:2r 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 they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beasvdf*x9 knnao,/ vya( ;1kt) ft frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red bln fd,tav fan/1x;)v9(okk*y sood 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 toward tod+xb7vtkiv3 g 5+tyw0 0niv 5he ban+wgv5iov0di5 bxv t3 +yk07t t 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 moth?    kHz

  A bat emits a series of high frequency sound pulses as it approachewh,c:0kwd g zxg3 z,p)n10jkbs a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth bn0dk wgw3c0, bpkg z1:)h, jzxe 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 qk5tv (ztq.,bwa3t w1rt4 g ;uyr vu46signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtonb q4u 1 trgktu5t,r3;.zww 4tv(6yqa ves 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 compromised5r-h50akw con by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves io5hnk0cwra 5-n this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singit6p3fk/ pf 9prng 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 practice, the rod can be made to “sing,” or emit a clear, loud, ringing sout/f3krp69p f pnd. 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 ear dxare+74 zn5e4r *wvr*k.jxdat a frequency of about dvkw*e+.r*er 4xx7z5dr 4nj a1000 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 observeo7zujxi2(,n4s: l;tnci6c c why6ru,r on the ground hears the sonic boom 1.54,ojhtzinyw cnl 2u6;rc6,7u(x s :c i min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatcdm sroci 1yd7 )2f,y4 .b)tnh 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