What is the evidence that sound travels as c7jl(vpki t84 a wave?

What is the evidence that sound is a form of en)l cuzl) 0d3ci/89e)s*0zr a mciztysergy?

Children sometimes p/ e)akcxy4j7 olay with a homemade “telephone” by attaching a string to the bot4e/y )jo7 caxktoms 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 wave travels from one cup to the other.

When a sound wave passes1soepvt 8v;/ f4u, ror from air into water, do you expect the frequency or wavelengthv4o8ep,1ur o rfts;/v to change?

What evidence can you give that the speed of sound in air does not depend signi*. 3ztf* 4c9dp7p owe 0ajuoinficantly on freq4fwn *o*uea pc90izj pt.3d o7uency?

The voice of a person who has inhaled helium sounds very high-pitchef6lwunrk l/hej 9re+ kq n0.(*d. Why?

How will the air temperature in a room affect the pitch of or1y )ri kayhewv-lxk17u 0k0j;gan pipes?

Explain how a tube might be used as a filter to reduce thvc kb:d3hc t2*n 8jfr9e amplitude of sounds in various fredhv:k98b2jrn 3c t *cfquency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced ipv lo16.nqim7 :) rftcloser together as you move up the fingerboard tow1i7 tnpi m6: )rfoq.vlard the bridge?

A noisy truck approaches you from behind a building. Initially you hmu) kpz(v2+gl ear it but cannot seep )u(kzvl2+g m it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said tk05 7lragczp d3 ,)nsco be due to “interference in space,” whereas beats can be said t0pz5klnr),d 3agc7 sco be due to “interference in time.” Explain.

In Fig. 12–16, if thbu*q3n;oa .ar5ciuv0nv1 t )ke frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur)a .13rvnqt)icu5un;vo0b*a k move farther apart or closer together?

Traditional methods of protectinwelq5/s- lyc.ggm24v g the hearing of people 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 worn that do not block the ambient noise. Instead, a device is used which detects / v4glls wqm5eyg.-2cthe 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.muo,c p ;r5h/,v+nzns Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in ;+ 5r,h vzc,nnosu /pmFig. 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 qys faa2:+8*jr1u7ze 6lmauy the same direction, with the same vefym azsq :6 ya2 er81u+7j*ulalocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heargs4wpud :8st;pjep (7d by a person at rest with respect to the source? Is the wavel t jd4s(7u:pgews;p 8pength or velocity changed?

Figure 12–32 shows various positions of a chgqgz tm(yo24ty 47t3rild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At234(mgzttyq g o 47yrt which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines th4nj a.o-by)nz/u/s v qe length of a lake by listening for the echo of her 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 laj4n o)ubz.s/-n/ vq yake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his shi2sqj-ee3m6i5 a:ho p/j vbq +fnz3ii0p just below the waterline. He hears the echo of the sound reflected from th/+ i jbqs-j on30p6:az3m5eihie2vfqe 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 wavelengths in air at 20 wmdkge.-g-ke-bp)ko-h3v j1*s abi4$^{\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. 3u g.h,l.g f j9kcfzy+Without warning, an engine backfire occurs on another boat 1.0 km3jg y+f 9zg. c,kh.ufl away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash itn qpu,i(;vvlp ;03;o.l ffyxqo mxg;7 makes when striking the water below is 3y; , q;.;fvgupxino;lv7xl po (qmf0heard 3.5 s later. How high is the cliff?    m

  A person, with his ear 5 ,jqcwrd ga..n )oyb0to the ground, sees a huge stone strike the concrete pavement. A mom ocq0)yaw,njb.5 r.gdent 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 apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over on..lmx x9yz aj;gg x3)je mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the tem xyg)9mxg.az3l.j xj;perature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain lef.3olw. vi-g ovel 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 intenp*y u7eco m3r.8r wb2ksity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9)t k/,lq vgud,5 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Au ktgl/, dq,v)dd intensities, not dB’s.]    dB

  A person standing a certain distance from an airplar4zw;uc rm wia;c2a+7c*)vklne 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 engine? [Hint: Add intens)7*v rruclw +4 az m;ikcw;c2aities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rauoo* sa2q 5n x/kb9ii5tio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise foiqxn2*i5b 9/koa uso 5r each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conve**j o csqqad5wckg81 7rsation. Use Table 12–2. Assume the sound sp q qo 1da8wccjg5s7**kreads 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 stri4iix( jep*kg 4mh0zf9 ub6w p(kes 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 Wks s-f/wo gjz 1km+s*:, 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 fro/sjom -fw*ksk+ s1 :gzm a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, avx5dl 6i6y-fidg+jtld33a )w dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on t tdy3)3-lvlxg6 dawif +ijd65he stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2qzdi2 bt4(ebj-r)p o ;.0 dB. What is the ratio of the amplitudes of two sounds whose l)jr i ob(2; bdzeq4-ptevels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factokyo(nl d 8cd k-*oa.m0d)2fhpsuey 6-r will the intensity increase? In*) nf -8y2osd 0ekpcl(.md6okad-yu h crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaceme 0sapy.c9c dp +dkg,a9f /a:vant amplitudes, but one has twice the frequency of the other. What is the ratio of their intendc sd.vy cp/p,9aa: 0ak9 f+gasities?   

  What would be the sounc22l m4kytlsebp3k p+:v h5j 8d level (in dB) of a sound wave in air that corresponds to at scpml423p lk hjkey5+8b:v2 displacement 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-Hle6: pg or7po/z tone that has a 50-dB souneg 7:lro6pop /d level? (See Fig. 12–6.)    dB

What are the lowest and highest fre xr./; avnq+h :pgf+jhquencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–nq+. ;hxv+hg:jpf a/r6.)

  Your auditory system can accommodatsw5ig3ke w, 2je a huge range of sound levels. What is the ratio of highest to lowest, 5w3ijweg2 ks 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. 9(2znirohd. d 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 pl(d2.hrzn9od i aced?    N

  An organ pipe is 112 cm - vvy3sq xatc8. gni*61w)zgylong. What are the fundamental and first three audible ovey83-cgvtg a. v*)qs6nwi1x yzrtones if 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 the tr+kjuif obk, (l 8::hxw nc;ma5+x7kuop of an empty soda bottle that is 18 cm deep, if you assummkux i;(lx:,r8+7 a5cb ofw j:k+nkh ued 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 openhhdde0:ll jwy7gi( 5.-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the diwj5 7g: ed. ylhhl0(lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz a) umcg 1i3xondv7c+. ss its third harmonic. What will be its fundamental frequencyog1i s7 d+mc v3cnx)u. if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar stm p:,p-z zfkr :h0fwa3sf5/4rfk e, kwedh++rring is 0.73 m long and is tuned to play E above middle C (330hk/ 3dewz, a+ f+psfwfk rk-z5::,rherm f40p 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 o( i 2k48abwblbrgan pipe that emits middle C (262 Hz) whenabbl ib8 (4k2w the temperature 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 2zprzd*:pb7o ges,4m 60 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the moubh)xiv3o4aeb ) 0(nsdr/c /wui x nq30thpiece of the flute in Example 12–10 should the hole be that must be uncovere(ensui xr qvw)4dbo/) 30/hbcxi a0 n3d 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 n q s.+mu6y v8x8dkrb bgl4d05at 264 Hz, 440 Hz, and 616 Hz, but not at any other fr bvqsnb8r ug0.kmx+8d5 yd6l4equencies 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 x-.:8;fqla: l /b bhkukzmr j3ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz../kja b::- fmzkb r;x 8h3ulql 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 zm4jbg2) q7g: fvcn 0t$^{\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 acua 8uxupru93 yij)p-v( :zs/ 2.14-m-long organ pipe at3 yuvp-8u)x i uc(9/zs upja:r 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsidec10 f tktgc)4ga48dhn and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of yh ct1804gngdf4tc)kaour 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 ads(kqu qs4z n2czd( 7c1just two strings, one of which is s2z s4cn qd1(u(7kq sczounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat fre 35)grcc),psthp jn 2gquency 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 whistlx-8emjik- ;*y 2n5xordoum9y :pk *agz0 vh6pe operates at 23.5 kHz, while another (brand X) operates 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, estimate the operating frequav *kpj:y0n g9 m uo6-z*d;xkoeym2p8-xh5riency of brand X.    kHz

  A guitar string producesev4n6ded)ws :u1p f 6o 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 361oe4pfn w)d6de :u vs55-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension 2 lbelic, -17n(ymnrd7 h0vrc in one string is then decreased by 2.0%. What will be the beat frequence1ndhib0 7rmcl(n lc, v2y7-ry heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pbdy8:+, h (dje3byp6b zg4lgjlay middle C (263bbj,z+ j:ly dbypd g6(84gh e2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, Bd,-h)a:skt-- nkp u 7jtnlbl0, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Whe-,jl ktdn: l)t0s bpa-n-uk 7hn 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 onulww.cpt9 8:kz (y4 ose speaker and 3.50 ls(cuk: z9.wwptoy4 8m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are sup-nv6b2clp3 ; rcyf-oq8;ute3 p pca(qtm7 w,kposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the othecu3ytr,6cqtwfppl 3c maeq(n; - v 72;o-b8kpr ?   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 waveleng483 p0k nvwayhwp4- lcths 2.64 m and 2.76 m in air. How many beats per second will be heardp4 pwh4w na3l08-ck vy? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cueq izv6d1;5u ertain fire engine’s siren is 1550 Hz when at restquu6e5 1vzd i;. What frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect ifl4 iwd).d4us xcus /l. a fire engine whose siren emits at 1550 Hz moves at a speed of 3 dll /wsd).cxiu.44 us2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz souwiomhob-* cuaj*) 9j3rce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Arei*h o mb *3o)jawujc9- 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 withgd,ehv4 u 29bdm5.bdl the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the freque 49 5egdu.b2,blvhddmncy the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoo-9zpv 6l5 f(e opue-v8awvjb +-;bn enic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it jne58o;+bzpw abe-9lvvp o-e f (-uv 6at 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 flies, the bat emits aslwzfn 8-n n/w5*osk;n ultrasonic sound wave with frequency 30.0 kHz. l5z;wn -ko sw8/*snfnWhat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was a op,,dfj2(kf 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 beat freqfj(fdk2 ao p,,uency 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 xbgy8;69jdg lc9xx 2v 9u /lfqb9 mdh8measure 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 beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?c 8q9x29b6 jdyf lgh; /xbm9gu89ldxv    Hz

  The Doppler effect using ultrasonic waves of frequel8k:5aj md 1dih-/2:uuer nvcncy $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity m tcs posd3+j1o o1:u)n v/qa0is 12 m/s from the north, what frequeoj1p / 31v tdsun:as0o+)cmoqncy will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object movinn,ip ;qy:svuz tb99 9y :1rw(zt s9oawg 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 sound is 310 m/s (a) )srs:rr . -iwcWhat is the angle the shock wave ms: r.rc)-srwi akes 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 the sp6cen.7 1fbv sabcfb -2eed of sound is only about 35 m/nbec72 a6c.bbs-vf1 fs
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine( /-ieaq7 1nwnn::.y egmg tzq the shock wave angle it produces1 qt/ ggqni7w. anz :y(een:-m
(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 g 4jr p/w5b f*xbc2-wz$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead ans w60hii/43/zv ilv3ju m)ecdd see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine h3s/ei 34viu/ m vcd0j6wlz )i
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downw)5gzhz/ +yme aard 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 m 5+hz)ae y/zgis the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rangenopi/:*ge ykkmt 5, l*? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displax26 .lexb ra2hy called a sewer pipe symphony. It consists of many plastic pipes of various lengthea2rxh bxl .62s, 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 perso+v-h ;dhesum. gmp )+an makes a sound close to the threshold of human hearing (0 d;h a+vm+e.- mhs) gpduB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are 0vt4i abr z6c9uo0p,eheard simultan iez 6a 9bc04,r0ovutpeously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dds7tx:r zel 2ynn bu(ox0r e j*/er;-6B. What is the acoustic power output (W) of7(r lnj0terbz xo;rsd/e* -u ny2e 6x: the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dr35qpmx g km z80bw+im+ops by 10 dB at 15 kHz. What is the power output in iq0mx83 p+k z mmwg5b+watts at 15 kHz?    dB

  Workers around jet aircraft typically/ppjee3fko):wso+ ;l 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 power intercepted by an unprotected ear at a distance of 30 m from a jet lo/+we kfe:s3) o jpp;airplane engine?    W

  In audio and communic w5bu ( ):elvbkln:u/7d mjce9ations 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 viol l prvu+ yn5ap9bmu4))in 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 fixed points with a fun:qe kp9 j7w,q0vku4*angzj m)damental frequency of 440 Hz and9k*7qg,ka pj:e)vqwzj40mnu 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 wateibf+ukp 8a5g. roz 30or (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube op +3 5i.p0guofbkroza 8ening 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 opm-q e9 v;-0u (3ov ldlxewp6mcen at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamentalxc -d6lm;wmovpul( -3e0 qe9v mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fd )y5p. d+bvhyull 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– nvl0.d -pbz0b1000-Hz range coming from two sources. The sound is loudest at points ebdnzb0 v. -lp0quidistant 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 whistlesm gttrq 7d ;7tseb1(7j. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approgsr7met;7q7t bjdt1(aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. A krgp*(k3 gj do8,vs:pfter it passes you, its frequ d ggpork* :jkp,vs38(ency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to th (t5.8sm naudme difference in pitch of the engine noise between approaching and rmtnma5ud( 8.s eceding 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, soundi e7rjdw2 6mz g,gc)cotp/ z-7t1 hhs+lng together, produce a beat frequency of 11 Hz. The shorter onrotsc6cl)+j7hp7 d-wzh1 gz,t /e2mge is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of (zpm 5zk2b2+. mjoqvu a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when .52 2zj+ b(zv okqmupm(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 normallf; lht s34- (o)p ia/xmffcc/iy about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasoumf;-f ci/ lp(ihotf/xa 34)cs nd waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towarenf* iwsj. fxro*x *)rn.d h)0d the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. Wha0jrrn)**s owe)xxh..f id n*ft 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 appro(1 9 5d,fnbesfr:gw.osdk8dl aches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp retf95w, d:bogld(nss.kf8 re1d urns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was :gqk(h17wyal ,xj4qm once used to send 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 is called the F sharp hgxj7kl,q (q y41m w:a(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 stereoj eaau2z:y3g0/jz4yvlh; . p a3qrim 0)cl8b l listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes2l4avu3mqj;j.0l:izprebyh)gya0 l /3cz8 a. 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 demonstrat:/z bww ovn0t)ion, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hb vn/w)0 towz:and. 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 threshold of hearing for the s//wmk.isi 4 z c7mlg:human ear at a frequency of about 1000 Hz lw c/m:/4zi7imks. gs 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 Machsd8-1xd+u8v, a5lquj bvmb f1 gc8n6u 2.0. An observer on the ground hears the sonic boom 1.5 min afjv81g, s+vbcal x-b8u6n dm5f1 udqu8ter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i0e7cdzdzp (d 8s 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