What is the evidence that sound travels as a ha.,psj.x ree1 -6abvwave?

What is the evidence that sound isjldb e+ vs*b4u()cp;j a form of energy?

Children sometimes play with a homemade “telephone” vo:qnvzt;wg,r)+0si;) v rbg 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 t:+;iqgrv ;v,r0z))v gsn owb 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 i6s,wj.vj1 ii7s0 gn ornto water, do you expect the frequency or wavel s.n,vj6ori ig71 w0jsength to change?

What evidence can you give that the speed of sound- t0rt8;tof dkj36 knwo*z 1js in air does not depend significantly on frequenco6 -1w8sot;f30kz t jnk *tdrjy?

The voice of a person who haotp .otw,9 (hcs inhaled helium sounds very high-pitched. Why?

How will the air temperature in a roo gh c pp618zje(vxyu++m affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds 1jicb 3-pgt+ ay iau-/r2dx5 sin various frequen1s3a/rig py xc-ut2+bad 5i- jcy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced c( /ldlvq(2z2xg .me9nso 6s coloser together as you move up tqdcgs lnlmo.e69(x2zv(o/ s2 he fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hej 1q,q+m:z5pen -b0lph :*yylvyc/pi r o(py3ar it but cannot see it. When it emerges and you do see i3p(/cq hyq 1yy ib0r:jv:mpp z,+5 ll*po-ynet, 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 inrimfrk ;fi 2++zf j,7r space,” whereas beats ca fi,fizfm7j 2r;rr+k +n be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouldlw7 xz:k i6x5z*gh2s d the points D and C (where destructive and constructive interference occur) move farther apart or closer *xwk26liz s:z7d5hgx together?

Traditional methods of protecting the hearing of people who work in are0,x0;2 sn njcyt w0wpnas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, hj2;w s0 p0,0tnynxwn ceadphones 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 tw8nste 62ak:f hought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. 826a ft swn:keIn 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 inc l ;9lvunpm6d0- gk d).t:amh the same direction, with the same velocitpamvd 6kn g0lthm;c):l. u-9dy? Explain.

If a wind is blowing, will this alter the frequ1 wqc+e(uqhm ( wy3es/ency of the sound heard by a person at rest with respect to the source? Is the wavelength or vemqcy us3e h q+e(1w/w(locity changed?

Figure 12–32 shows various positions of a child in mt5un b 5w;fj6lkjw r77otion on a swing. A monitor is blowing a whistle rn5kj7 l wtfu b;5jw67in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of hev(m 3 5ps j)schfjt,a*:23vvuaxs ho 4r shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the la)m,ahs:js4(hx3vc3 2fs* v tvu5poaj ke. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below thuemy 0g7)f/j fe 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 po)j uf yemg07f/int? 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 dj0cbhf1 ,jc t9uxt1uz;yb:.lengths 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 just above 3m z8q:f fylwa6 i/ o,-nwv2zma school of tuna on a foggy day. Without warning, an 6,qm zl2 nafv w f-/8zio:wym3engine 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. The99; 6e1 ozjwhqsyze:h splash it makes when striking the water below is heard 3.5 s later. How high is 6eqz9j1w z;y oehh:9sthe cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the conc2+ n7xtqx*jga fox0 o7rete pavement. A moment later two sounds are heard from the impact: one travels in the air and theoaon*g7 x270fqxx +tj 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 o5tti hy89wu mcx4+ / +iw(by1ia 8pobuf distance by the “5-second rule” for estimating the diw 9t5ic/putboauw +mi (1y bh+x4iy88stance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at thg7 7ul-tqf85be5 y0ghq5 qg0mbt u ls0e 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 n)lt2ais e2fx) 9sie qy-4 gydbl59*f intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers dy9qqkv8hxgifr 0 . )oav0j5g0 *l.jeproduce a sound level of 95 dB when fired simultaneously at a certain place, what wiih50ylj 9)fq8.rx.og aq 00*v ejg kvdll be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four e0af( ;r2m9oz fhn ,2w(zmuiytqually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person 2 (mn u;0ho mrfawyf,(2zi t9zexperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-nois rs,0o3.b 9hbbitgw eh)3 yjm3e ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rati0t rboe3wb) h ymsi.b3gj, 9h3o 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 speaking in normal conv4i+ld.ewl cixsid (39 ersation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered (w dii3.4l +clsei9xd on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area is avu5/v hql330brw r32 1hnqmk $5 \times10^{ -5} m^2$ (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, z ;3xkx.jdob0pz.qj qp*.axl7 g4 59wk b4 tbdwhile 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 connected in turn to kzpa xq*;. j0 pow3t.d4b.95bxlgbzx kdjq47 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 2rm4u-6v h04ncqmcu+h.8 m in front of a loudspeaker on the stage. hqhu0c ncmv rmu 4+64-
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound lotcn0g5*g l 8eevel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levelsog8ltg*5e0n c differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wa8a bv, lf8ask-q-( mmm-3 2njrn +snjnve is tripled, (a) by what factor will the intensity increase? Increase by a factor ofmj3mna -8na q 8-2,vmn +l fksrs-bn(j    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement e8;8x7uxqpjiiq 6-p eamplitudes, but one has twice the frequency of the ot ejip 8;iqxu6p8 qex-7her. What is the ratio of their intensities?   

  What would be the sound level qm- tq6kwy6c-(in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molec t6mqq-c -y6kwules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loult 9zco(ccr.f)m; cq2d as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12z cfmrc92.)l;c(coqt –6.)    dB

What are the lowest and highest frequencies tha ujnl54 6l;a 7uxnfx/st an ear can detect when the sound level is 30 dB? (See Fig57lxxs6;/l ujf 4anun. 12–6.)

  Your auditory system can accommodate a hugg.w/irg) +mn njgaa35e range of sound levels. What is the ratio of highest to lowen+g 3g/ gwa.iajr)n5 mst 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 ofp4 0sc7jycpo g4ng ;-tp d/,mt the vibrating port,07t jcct/ppy- sg;44pmd ongion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and firstbbuv dw x 2oj/02x5)z6bq6scp three audible overtones iqxbu/6zd2ox052)wb p vbs 6cjf the 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 across thtqi /h;m8p9 nle top of an empty soda h l8mn/pq i9;tbottle 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 sah:rt2wp( -.9j 82n5g6 hmh2yj h)wfym vrw nnpanning the range of human hearing (20 Hz to 20 kHz), what 5 hnr6 ywmmn 2rw)tj : .f2aw2vyhh9png jh8(-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 third harmonic.;4zyw (6mshxd1 bo 7qh What will hdbo q( x76 z;m1hsy4wbe its fundamental 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 Ey/r7.j w gg(cy above middle C ygr/w7 .(cg jy(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 pdfmb+8k7r d vy;5n7p -qog7hu ipe that emits middle C (262 Hz) when the tempev5 hm8 ;udk+prygq7n od7-f7b 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 2kd5 5v82d4 t;s;yt8lvmafgjm - e( w3pvlemn60 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of thep, r h:xzwrs+0 flute in Example 12–10 should the hole be that must be0pwzrsh :x ,+r uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264cj.nu ladrl *m, 3o e-t-84tqi Hz, 440 Hz, and 616 Hz, but not at any jldi-.c,an3ml eo8* -rq utt4other frequencies 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 pj)xp8y mkf q:z;m-y2resonates at two successive harmonics of frequencies 275 Hz and 33 mj2q p)8km-fzx;yyp:0 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 do kq0 q;h-mn5$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orye4u 9.aso6fvxu j+;rgan pipe at 20+9oje vuy ;s4ufa r6.x $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is a.b uv h+*hvd+spproximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) *hvhvb+ sd.+u 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 ( y2 trs 2qulelic:/3-x7olsh2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in fxl-hiylou 2 l2c(: te3sq/7rsrequency is the other string? ±    Hz

  What is the beat frequency itpu723qxwpf8em xd c ;( h4f4i-pk8oef 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 ;eq9s 20vpueeX) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, butu9qvepe0;e2s a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3 n5* f0+v+bhtfnsntk 450-Hz tuning fork and 9 beat+f +5nsk4 th0* fbvtnns/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tu iqxa06ee84g;e1 : 2gdhxl yrjned to the same frequency, 294 Hz. The tension in one string is then decreased ygl 46eq :g0e1 2ijx8xe dhra;by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be h04(y 9t3f w0yv .2nxws urskeex5mjm6 eard if two identical flutes each try to play middle C (262 Hz), but one is ats 935m2wkxe vj t fym.se4xwu (0ry06n 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fr; 47jrk+t ;6 llf8v2f8dmxa v; jobcepequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the posvapx8 f6dmvb 2 rl74ctfj+;;ko;l8ej sible 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 l 3r r2y e9uuwr 0u tfob44.5+sdu+cxcm apart. A person stands 3.00 m from one speaker and 3.50 m frb4uwe o f4cltrd+.+2u09x yu cr3 5ursom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tu-b+mpu(e5u (. *tn0v zlf ( qkqedx0jsner hears three beats every 2.0 s when they are played togebm pq(t* d5+ef0ujuv.lqe (xn kzs -0(ther. (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 beset ak0f7l bbac *tmr5- 5fj* r-4s(vgats per second will be heard? (Assume T = g(b rtrsc* ft fasa-kj4*5v el- b05m720 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wh3nyi81 im /pl iuahs2:en at rest. What frequency do you detect if you move with a speed of 30auy2 np3ihl/8i:sim1 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if ab9 )t2wbycg)j fire engine whose sirenty gb)w9cb 2j) emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fr3n )z :te4+u 1nhgd1fbyv8 bwmequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving3 1)4 wumnv:zyebb thf8 1d+ng toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equomff4jji6w7gvf . s-kh 9x67mth +mw,ipped 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 9mkgwh6+os4.h,7wi jv-mff 7m6jx t fof 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wa:jb5 r+anbh e3)xltqg92 )tnwves at 50.0 kHz and receives them returned from an object mjb:n3rhn)2wt e59bx+ ) ltgqa oving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a qr3v xz*pb8v h*, x:pjspeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave wit vb,x*prz qv3h:pj8x*h frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experzo1uq:j8e0)iq fgxb .iments, 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 raig xz0ojufi.8qebq:) 1lway 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 5k1 )*fdp vkprblood-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 bedpfprv51kk) *at frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasm 9npi gq+*:,m0:jii fhred d+onic 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 hx,mhblv0pi b 17pd3;Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at re 7;h d mpl,03xihbv1bpst,
(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 n0sb8tj4uol ;k l:deh3,d g5j20 $^{\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 sound is 310 m/s (a)/lcz- ccg*a6o09vy tk What is the angle the shock wave makes with the direction of the a /yc l0k*9 -ocgcvatz6irplane’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 the speed of sound ijq 5y i/f5cn-isqi-fjny/i 55c only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. De ( +wtwahx3 89udcbg.ptermine the shock wave angle it pc.t( 93dax+wbhgpu8 w roduces
(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 cf+at8f7qf 6f $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly ov.yzo8j4zn k 3oerhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane hk .nz o8yo34zjas traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz soun,kq97 aem3 avw hpm6opa 7kl):r oh/*cd pulses downward from the bottom of the boat, and pqm3e6w9 vk*m7,ahop/h ar co: k)l 7athen 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 hum:c o5e mujaj,;an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mak s/:(d3a;2lmxntnjy ny plasti;:/nkj2 stdal (3xnymc pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold z.epns0b *56 jqcc 1al k;ic+aof human hearing (0 dB). What will be the sound level of 1000 such mosquitb+z. n1eic j*6;k0alsc5pa qcoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB souzc- +eoc 2w6i/ + 6fjwa0fau)ctub5q;n 8mqjtnd are heard simu/ aqt5a c fm6 zubw28juj 0to6ec)+fw;n+i-cqltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB.h: q*c7 mh- uqb3olzn7 What is tqqc*n ou 7lhh:7m- zb3he acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output8/gic:d-jp0g m ttt -h at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wh /d0-:-tjpghc gtt8miat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft tug 2lee(jqio 9c:s/5w ypically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 35usjlw:/2ic qge (o9e0 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain,y .a a)u2abmxa,hd;ela,2 dx9 $\beta$ 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 +9-ulxg,ybb9tc t 0+ zx55towc.cxmx is tuned 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 fixep s0 7twf+-wvhd points with a fundamental frequency ofs+0 pwv7-wht f 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 op+ysw-k2 j8anma x)p 4nen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard pnyks-8 a+a j4mnx)w2to 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 thatp9yd ct,o ri;45 xui0j is open at one end and also 75 cm long. How much tension should be in the string if it is tjriixy5c4t p ou ,;0d9o produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed trzg /z-zv7bd mcms)7ta2m -m 36 vkr*fo 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 nv ys flm,d:6mp:yd,7from two sources. The ss pdm7yd,, ymv ::6fnlound 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 sound?   Hz

  Two trains emit 424-Hz whistles. One train is statib;h;e); k udg; h9mmnxonary. The conductor on the stationary train hears a 3.0-Hz beat frequency when ;h k ; nhuxm;g9;dem)bthe other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whoq+ uq-ap2-3ij feh*2g5 xu wuistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How foh2*w+uu -qg-a3qxj 2i feu5past was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars ( :8wc(vvkd8y(w g lmn(, ztgkjust by listening to the difference in pitc( c8wt zldwvkm8n,g((v y(k:g h of 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 t3 :re3 d2zc qji9peij4ogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 4 de: pqc33eijirz2j 9m long. How long is the other?    m

Two loudspeakers are ffv-, i x/p.c;kk .ecbat 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 spea.p.fck/e-f ;ib x, vkckers 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 y fqbx6e+p8qahd-c t5bpf2 870.32 m/s what beat frequep +baxpy7bc2d -h8fq e8tf 65qncy 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 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 flypar6x kr05x g5 u)habeb); 4 ee0qxr )i4ipfa(ing toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of t5e4efxa0 4br06arqap)huxg) x5r)i b p;(eik he wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency soundamvl7 r b22gm; pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far awavglammb 2; 72ry 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 s3qhc2v h-)xvg smg9n *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 musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it i2n)- x *h vv9gsqmch3gs called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by h/,0)t*m:oqh d 2xulmmygb ;vthe 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 fundamentalm xl* b0)v ,htq2om/hyg;d :mu frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singin;k snt5nvbe 0l.d9 4jv avjl.g 8jm/y8g 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 clvvjj.ye l 8. 4a;v8ng bdtn0s/9m klj5ear, 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 t5l ,wd(kq.yb)p f rv,she human ear at a frequency of aboudw v. 5,fp (),bklsryqt 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 hears k*nnnga7zfbb)- y 2p9.f + cqhw,tge7the sonic boom 1.5 min after the plane passes directly ov fz-gf+e.q9 wkh7t 2*,pnna)ybc7nb gerhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is eh 6 1ou047j;mvxcd xm15 $^{\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