What is the evidence that sounrkpu+0 asxjc;q b. 3yh/(yi-ud travels as a wave?

What is the evidence that sound is a forc*j3qle3he7 g m of energy?

Children sometimes play ( jydijuhq;n1 1l (ar4with a homemade “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 dja; n(u4 iyh (l11jrqat 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 aiqrz :ny-c.9cur into water, do you expect the frequency or wavelec9 cq. :z-rnuyngth to change?

What evidence can you give that the qjmu*we;o.g ; speed of sound in air does not depend significantly on frequ;* moue. wjgq;ency?

The voice of a person who has inhaled helium sounds very hijds/if;m4w:8o*1 5zllrd t6bfz: xu jgh-pitched. Why?

How will the air temperature in a room affect thetfz*d1 lwiz i.u-fs81 pitch of organ pipes?

Explain how a tube mir57 d q;etas6i) ikl;dght be used as a filter to reduce the amplitude of sounds in various frequency ranges. dkat6di; se5i);rq7l(An example is a car muffler.)

Why are the frets on a guiuwgnd8byv *naff(z59b;7i lz0xpf1 8 0o(yk ttar (Fig. 12–30) spaced closer together as you move up the fingewnp(0 i0d5vx fu9b og(lf;bfzn* 8k1z87yyatrboard toward the bridge?

A noisy truck approaches you from behind a buij +014desix vclding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear mo0e1i4+ vdj xscre 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,” wh)i0o*t nprvz3i zj ;-/dr,qvxereas beats cnj)v *x zr3q;idro tz-p/ 0vi,an be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequewedh1*dfe*v6ebt5 l-m6i r5 z ;iz4pyncy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or 6 bze5e w*y1;zt d6d4p5f*ielimvr-h closer together?

Traditional methods of protecting the hearing of people who work in ap.*l0z*y b hmkreas with very high noise levels have consisted mainly of effp.zk*b lmy*h0orts 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 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. Eac2ts tro*g gw+1h wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whiw2r og1tg+ ts*ch 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 i+52*yw)yv zg2s 61hkxqycsmw n the same direction, with the samegys1*+5q2s x2hkv mw)6cyw zy velocity? Explain.

If a wind is blowing, will this alter the frequency of the soun :y,ps jb. bf7ik1n6v begi3,jd heard by a person at rest with respect to the sous n, 3 yfbb,gvj.ibj7e:1i6p krce? Is the wavelength or velocity changed?

Figure 12–32 shows various positionjhpob tk ,z;tm v1)+s+s 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 whistle? Explain your reason++stmh z;1bk ,vot)jping.

  A hiker determines the length of a lake by listening for the echo of her shoutv d1 /v iqn41 h+k( tjivtm(do;xwnj19 reflected by a cliff at the far end of thevt/ 4ok th1 ;n (x9jqjnd(v imv1w1+di lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the echop0m)rnmr bym z7 *0we8xd 1y9o of the sound ref or0b) yd m08*y9npmwe 1xzm7rlected 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 wavp 0yma4(ms2 c2o em/fuelengths 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 a school )4sw*gql8ju9tvj 1y0jg x tq-of tuna on a foggy day. Without warning, an engine backfire occurs on aq9 )ug t0v j*w tj-sxyl14jgq8nother 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. 9m+o.7j-h uhw nxmj fll+ *3xv(ehn(vThe splash it makes when striking the water below is heard 3.5 s lnj9+ x*h om e73xhv l((hmfn+juwlv.-ater. How high is the cliff?    m

  A person, with his ear to thwst;r+;d kp/r8 yye-6doky8 9wzb yk5e ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact zrdkykwe+dt8o/ r;5y68 s-yp y9;wkb occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over fjcoxxg +dx +n07/(zj one mile of distance by the “5-second rule” for estimating the distance fromzx+g (/+xjd xcnjo07f a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of 1pdk*bu. 4eevol hm zpxd/1834mfbr.a sound at 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 (68aeh*ng,t td(fghar98 jdz of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firevron5e0xs2p *u; 8rojxjk4 s4 d simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.] spxj4nk x0r4 jv5;*ou2r8se o    dB

  A person standing a certain distance from an airplane with four equally noishfgg,*bg :utt w;g w+x7 (o e4ejhuhk 133av1ny jet engines is experiencing a sound level bordering on pa xghgt+,4:agtuh3 1ee b1(hjwv; g*wf 3 7onukin, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whe6 tr(w8csvv ldfi59k-reas for a CD player it is 95 dB. Wt -f65 vlv9ks(r8dciw hat 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 speaking b*qk d,uz4ul+in normal conversation. Us+*uu,q4 k bldze 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 strikes an eardrum whose area +e rm:xt4xrj 7uq9p1ais $5 \times10^{ -5} m^2$ (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 the more modest qg4w/;gg an v flwo4 il5y()-pamplifier B is rated at 40 W. (a) Estimate the (o4l4-gpan) w;gy fwq5vg/i l sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front of l 8yi3l1nz7v5vwjwa9wn 1w, sa loudspeaker on yn1w 9wiwn,l j 73z81s a5vlwvthe 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 det297; b 9w,pq1aztgwabmme 4gbect a difference in sound level of 2.0 dB. What is the ratio of thbab7gz ;qm,tb91wem g 4p9wa2e amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the3pk io e2 4,*cpn3td9kh8my do intensitp 43m i*oyeh92kod,c t8 3pdkny increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudesa6svxw0weimq, v9 f*., but one has twice the frequency of the other. What is the ratio of thefv0 9mwea ,s.iq*x w6vir intensities?   

  What would be the sound level64ps /p9vkj ;tvi)dp5hw v+ pf8t0 pac (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air mo0jt45ppp/tp)sk ;vpv +8fi9hacwv d 6lecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loup+ :c (* rcch6d/naipxd as a 100-Hz tone that has a 50-dB sound + *a:r(p/6cidchcxpnlevel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear ;:3xk /-pvx,scok-kgp s 7poncan detect when the sound level is 30 dB? (Se-s/gspkp:ox p-kk x;c v3 ,7noe Fig. 12–6.)

  Your auditory system can accommodate a hu i /l s,sdw *h7s3lhue,7wpzh;ge range of sound levels. What is the ratio of highest to lowest intens,hzw7ps *hs7sdl/ih3 ,u ew;lity 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 fund2k.l:jp4 ctpvamental frequency of 440 Hz. The length of the vpp4l2.:ctk jvibrating portion 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 fiqeof:u .d1ob 7rst three audible oveoqd: f.1u oe7brtones 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 expe*hax3ys*wkc v (6yak jt 0kh4*ct from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was av tkx *chsh*ay k4w3*a(j60yk 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 cgqd5jzqc 0rr/8sv;dc+ 9y(b-4 i jeaopen-tube pipes spanning the range of human hearing (20 dj v;8/ acc4 (isg5dqqrybjrez+c 09- 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 1 ly4q azo(rp/as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% o/ap1 ozry4( lqf its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middle m ydom):w)+ cfC (330 md)+o:)wfym c 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 ohu26 nli- li5emits middle C (262 Hz) when the teml lhiuin o-625perature 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 20 ugu+( /: ikhnl$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouth;g yw6j j:*setpiece of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at eyj;j:6ts* gw 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not ahgtekv/6) 9 w.7inw1mly 4z mlt any other frequencies in between.mw) l64ym 9/ghz.ie7v wtl k1n (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 two 73 ci;gzz8qwfl8kmb.-r w ;cqsuccessive harmonics of frequencies 275 qilz8bf- rw87mkwgc c;.q3z; Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 jt ip/e+ubznn *y +1w3$^{\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 p.m -ammg r6xime +mzua3c *(g;resent within the audible range for a 2.14-m-long organ pipe ar ig eu+m6(mmm.aaxc- mg;*z3t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approl*nav/3 nu7g(uay l2z ximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate thl ua 7uz(yla/ 3nnv*g2e 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 tryintqqfid.mq e 40fo+88uwa -2hkg to adjust two strings, one of which is sounding 440 Hz. How far off in frequetfof+q d42kh0 uqawe88qm.-incy is the other string? ±    Hz

  What is the beat frezjvui4qg- g1;* s ea8yquency 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, whilegft 18jd7 n3vb another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played se1 v nb7jgd83ftparately, but 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 350-Hw k3m ppbm)v-.z tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the)3-vb.mmpk p w vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sameq89e .zsg( fsew-rk 1f frequency, 294 Hz. The tension in one string is then decreased by 2.0%. qrf-e8e(zsk f 1s.9gw 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 heard se)zlva4pl0nb )x8)j if two identical flutes each try to play middle C (262 Hz), but o0l esj4x b8anv)pz))lne is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, a:)tr:eo(o4q l s mup8vnd C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is squpol) m ::t48rv (oeheard. 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 1.80l7tuj1q cc4;o m apart. A person stands 3.00 m from one speaker and 3.50 m from 7ujtq1l cc4 ;othe 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 are8 vfn(d 7 ox-y8effjslv.((k k supposed 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 132le .kxy((v -8 jf87fvkdfs(on 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. Howi0nh7( odcnn4 many beats per second 7( hdon0n cin4will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz /ijrptkt6) p7 when at rest. What frequency do you dep)k/ pt76jtri tect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stilxr-1r-wmzl/8a wmc gwe;ch,4sj , 6gel. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves a er14m/-mwcezlg ,;xcw86hgra sjw, -t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000- nu7jjkpw8 6*; be9sgfHz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Arjn7uk*f8;p ge9s6w jbe 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 frequencyb+a7 jec0 s*q )pi0rqn 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 theb jq0e7ic*anq s +)pr0 frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them mpy,; b/a 74ugep9 ogpreturned from /m94ugpbap,gep7 y;o an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat nrw.0a u;i5gzv 8niyr1 n+*jaemits an ultrasonic ra*iyui5vrgn0n1z; jn8 .a+w sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playepa48yxby yq+ ng449-a sy rfo8d 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 frequency was heard if the train car approached thy +na rqs-yy 4gaf4y8p x8o94be station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. p-jyii-z 0f o,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 ozi-fy,-ij 0pthe sound source?   Hz

  The Doppler effect u8l e kwr9f0 9u9mxny7 il30stpsing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequezzh7cs g /6xe)/* yyu9den2ho.cxu u*ncy 570 Hz. When the wind velocity is 12 m/syhu)scz6ez*n/*gu u.7d / 9 xoxy2ehc from the north, what frequency 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 moving p9hun q4:azjz ipn.bxg7 5z24on 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 soun/osd:m:thnmw s- /b9 id is 310 m/s (a) What is the angle the shock wave makes with the direc 9n:s/msw bh-om:d i/ttion 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 tit7z;8ri o-z sggek 1:he thin atmosphere of a planet where the speed of sound is only about 35 m/s -tr g7zkie ;g18so:zi
(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 oc)*nscd gnj1z /ean. Determine the shock wave angle it zdjn/1 *s nc)gproduces
(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 ;kq jno;r xkkq)p9;9 12j oxvn$/theta$ 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 j cx:ry5rl)r9 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 distancerxj:c5 l )y9rr 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 d)tg* +xqi7o snevice that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth fnosg )*q+i t7xor which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves ht363xw472gqq r yw- 0ya se;tnzh 1thare there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a disfo21i3-0wm a b,tybu cxnax-+ play called a sewer pipe symphony. It consists of many plastic pipes of various leiw -faom2a 1ybu,3xcb0x +-n tngths, 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 nz.*cj1u*tfs7o0 :o- *tqrsiaq n ) vsfrom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound lev*07so ar*z) oiut vf tqn:j.s-n*s1 cqel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and wnng:t : 1ek+fq)t-e p(lp1anan 87-dB sound are heard simultaneou t nn:t(knep1afw)+ qgp-e :1lsly?    dB

  The sound level 12.0 m from azz iodo8(o733z v8qx rqenck1.raj/ 0 loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiat/0ev o o. 1zdi8cjaqrz3orq7(3n k8zxes equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Thek a:1eit .guo*s4gp,0v xvpj, power output drops by 10 dB at 15 kHz. What is the power uj pt:e*ka4 svv,,gx0 p.og1 ioutput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over cs().5n2q1fpe;,: iku habxgyggh+ x their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140pnx c y5 ba2u hixk:q1 g.ghe,();f+sg 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, f)curj mc:q/,8gp;tm;)pih l $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned t:jwaif7mv8u +id+77zcny oqujsw) 5)o 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 fi54 :eos k/hh(scir2 ksp0uaq,xed points with a fundamental frequency of 440 Hz and a mass per unituri2 k phcssqae, /4o:0hks( 5 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-ulx eryz7j ,2p7glw2m xsv,* with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the airx* gs xpw ,vr2lljez 2,7uym7- 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 2.10d .51r hbh.f+wmi:5c y wgrjd3 g is near a tube that is open at one end and also 75 cm long. Hd m +h .:3fwhwrij55 .dgrycb1ow much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsp uvs+;en /my 9 beca*vzk;q)i*+1dwwerved to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming f phu*z vahx9a(v+:fl2 rom two sources. The sound is loudest at points equidistant from the two sources. +vzafa9lh2h: u(xvp* 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 stationary. The conduc6ui33bg-mprpgz4n8l:n f * m .qcak6otor on the stationary train hears a 3.0-Hz beat frequency when the other train approp qoka6.ug3b 48nnr f* c3:imzg6-lpm aches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle 9ht8 tn ang. y3+drn6ias it approaches you is 538 Hz. After it passes yoh nid8+6ynrant3 .g9tu, its frequency 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 tovl* sx(4f jm 6(ekm6dj,o zob5 the difference in pitch of the engine noise between approachin*zxl6k5,s 4fj (mbdj(me6o vog 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 be ),ov3kmjoomu8/h5 sc at frequency of 11 Hz. The shorter one is 2.40 m long. How long is the otherv u3m mo/c 5,hooj8ks)?    m

Two loudspeakers are at opposite ends of a ra(;ow/x+ : : f4 sy6drmutsqhtcilroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, atsw6t:hfrx4y s+/uo;dmc( :t q C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s wh.kv d9f dmg08rat beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected fromdrv9kfd 0mg.8 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 iozbpam zfbn-7br(s a: *c3*s;s flying toward the bat at speed 5 m/s The bat emi7: opzza*c*3( a bmrs fb-nbs;ts 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 higjw xd qy*2:jk:cg p ykjv-s0;m( obx5.h frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is wb :mojsvj:(;k0 cd.5ypj qy*kx2 g x-about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. ko.h/:jc hmzm( dg 26h12–38) was 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 rh2chhj/:om(d g6k.mzesonating. 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 compromised by thhky4-,x9bjhke z (n)we 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 wid e b(kx49h-whjy),n kze, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “szshc*n/jndxy5 naoz74;1( d kinging 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 ma (h754nnc*1dd ;xonaz z/yjks de 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 humai b6s s:p(ncclh ts5x.d7q f-+ce )1n zc/3kosn ear at a frequency of about 1000 Hz o:z3 ss .56xcth)cp nsdkf7/sncl(+q bc-i e1 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 2.0uxkv 1oj i(ei.m:l-*ikt)p u1 +vp vu*. An observer on the ground hears the sonic boom .pk pvvi-vu: xe l1i)+kj*uou1* t( mi1.5 min after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is /fraarp 3a-v*rz z 9lg1m3b 9o15 $^{\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