What is the evidence that sound trgfs;9) uut s9i-(/ j7nuiw bnhavels as a wave?

What is the evidence that s )79uk/ify xtdound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a strib,sfwi/ k9b*y ng to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from b/bi*y9s ,fwkone cup to the other.

When a sound wave passes from avnpq1b8;m muqbfd9g aj6d .p,ij/r:q7 2x:yq ir into water, do you expect the frequency or wavelength to chanam8,bb72.9 g f:jmupqqdnj:r1 qypxiv dq ;/6ge?

What evidence can you give that the speed of sound in air does not depend iniprg/1z954h*i 4 r-hcyvr psignificantly on frequency/gc irrp19iv z*ihh45n r4 -py?

The voice of a person who has aajk :zw/yu- 0inhaled helium sounds very high-pitched. Why?

How will the air temperature: (im r2bdvao) in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reds 6ife7 /e+turqap cod2 do1(0uce the amplitude of sounds in various frequency ranges. (Asp+oe0 1e2 c/qdd6t a7 riufo(n example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) sgol )s a(ypkyh3.c uk4lx3*/t paced closer together as you move up th /xk (yk)lh3g3pycatu.slo4*e fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initix t7w 0(g: 1kj7kg804ah+lrwdiqvr dxally you hear it but cannot see 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 diff j xg84ddkaq+:0kvl1twgi (70hrx7w rraction.]

Standing waves can be said to be due to “interference in space,” whereas piedsuv5e) :cl;r-w; ci 3k7a beats can be said to be due to “interference in time.” Elw:k r-c;)ie3vcu a7sp5;de ixplain.

In Fig. 12–16, if thb5f.egjihw 6-)h5 fzpe frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer toge 5hg zbf5p).-f6jie hwther?

Traditional methods of protecting the hearing of people who work i/dauwr; 5-3gw7fu a dwnknl * ma83 m/xop1li;n 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 the noise, inverts it electronically, then feeds it to the heaanlam8mwfod;riwu; xpu* 17-a//gk w5d 3n l3dphones 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 thoug6s bxa+asm e mmf0;ep+nbo7(4fw1qg:ht of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component awogs m7eex f4qn1m;pf(ab6 : 0b+m+sfrequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direcef wawpf z .-is88f*l ub*l31dtion, wiz* f.8*weulpa-d ffw1bi8s3lth the same velocity? Explain.

If a wind is blowing, will this alter thz p2rs;70 xzt 3wok9dve frequency of the sound heard by a person at rest with respect to thdzs t 0pvxw 23z;ro97ke source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motv332c oev-x fakn-:n oion on a swing. A monitor is b2:3anv - xcokeo-3 fvnlowing 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 reasoning.

  A hiker determines the length of a lake by listening fcb)ec h.vxr5fs)+v gul.*d q0 or the echo of her shout reflected by a cliff at the far end of the lake. She hears thx0)hvsd vfclbrgu+ ). qe*5c.e echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of hisp m,zy y6t+nfk- 4/iqx,cij nd vh2t9* ship just below the 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 point? Assume the speed of sou +j chy 2 fixqztpn-49,v mi,k6y*td/nnd in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavcfr:w/4 hvfz7c r ny *mdrm(z 1vv6g):elengths 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 of tuna on a jbgm(s ju728kfoggy day. Without warning, an engine backfire occurs on another boat 1.0 ksu2jm7bj 8(gkm 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 it ma2hn4vp q;h/t s,g iqq0kes when striking the water below/nh40i2q;vtpqhgsq , is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr/dgxm3 k 7.*m5 wwk avk*k,qm x/2tqooete pavement. A moment later two sounds are heard from the impact: one trawt o 3mqk gmxwq/2x7ok*kk*m.5/v,davels 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 5jeln,y. mj)gzvk:sbm(q z,2 over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature ijvy2(b 5lke,) j:,z gzmq.ms ns (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levellr4 5 gyx6/dew 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 ofwe lwu;w2b*1 *(avtc *z qz+uj a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a 0gop4bwmpv6z2 +ifhl;fs;3i sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Addi0vzpg +3fbwm2os4p i;; f6hl intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally 3dt4+cr-nypae13bw1 zo g*ubnoisy jet engines is experiencing a sound level bordering on pain, 120 dB. What s 4c+1ue*owdb-p3ng13 tzyra bound 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, wherea8fgw/ q.kso 5(t),w i y gqnef/-uuge;s for a CD player it is 8qy,f5;gkq/eu(w/ge. - gounfw st ) i95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spejpuj.o* :,zda rxshlab i05s8 p.5 dd3aking in normal conversation. Upd ji3:z5jxp.os,u *5r .badd0al8shse 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 whosd5fbjh,7 quq86, nfdne 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 ra1cabl 72rm:fk9az8 ngted at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in8arm79:z cn12alkfg b 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 fl 4k z0b5n8 2usxxpbr6ho0tu,ront of a loudsp8kx0h6n0 2xlsut5b4ur pbo ,zeaker on the 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 typical;vd3 .1z on6nl5pvjhl ly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose 51l j.6nzvnp;d 3vhlo levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wilw)xwo e +ew,f:oa60v* t)azfj. zyb4gl the intensity increase? Increase by a facez a0w6x4bw f ota ,g foy.:z+*v)je)wtor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displaca rr;pnwiokis;7(4 2y h 7fhh, g,q,lqement amplitudes, but one has twice the frequency of the other.7 riy7okwhq 2; ,lh in4q gf,r,(phs;a What is the ratio of their intensities?   

  What would be the soun b 8wl( r1yi:6kfgzr8fd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating 8yf8l bgzr6 :i( fw1krair molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whi-:zsh7ivs b+toic (( at sound level to seem as loud as a 100-Hz tone that has a 50-dB souni:hs +czs(i(7-iov tb d level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detecbc htia25h5etm7hn . 1t when the sound level is 30 dB? (See Fig bt5t.e m1chihh2n57a. 12–6.)

  Your auditory system can accommodate a huge range of sound levels.ue26cxjuub9 xvsk ):3 What is the ratio ubjvuu29)kxxe3c6: s of highest to lowest 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 f 5aj3*a- oeuy*d5wrv*vlmi5z requency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pl5y53rm-av*w5doz*a uivje* laced?    N

  An organ pipe is 112 cm long. 6-b cm8l8 royxWhat are the fundamental and first three audible overtones ifb6 orl 8xycm8- 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 woub) 3xn*v48k q)kxqcwyb 5c gf(ld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubb 35nb )ycq kx*qf(gkv4c )xw8e?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ *p ;snex,nwv+ with open-tube pipes spanning the range of human hearing (20 Hz t, p;vesnn *xw+o 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 hasr 5b oywx( 9xf95sd4dg a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency iosrd4f(b599wy 5d xgxf it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m ej:z l,t**z1o6 qmu adlong and is tuned to play E above middle C (330 Hz61jqlz* um oz:t ade*,).
(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 yxkmf 4 ,5vuxsyu +,g.t*juhkl d+ s55that emits middle C (262 Hz) when the tempersmxk4kj55,5 + ytgu+uyx u d.vhlf s,*ature 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 2bbmlo rxu 9;uup1-v cio29j,k c/7+eq0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpie iye6, utji+f;ce of the flute in Example 12–10 should the hole be that must be unco6jift,ei +y;uvered 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+).a1d 4 q1z24zzxmwbdy tskqi-j lh- at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clkz qb12xm. -zh-la4w1zy4 )jisqdt+ dosed 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 95n rl bppy9+vn 4:b;r,sj bkdtwo successive harmonics of frequencies 27brjvy9n,;bb4 5kd:p+ 9s p rln5 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 c5 og0u6vw ux+$^{\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 op l9yff1b,p5vrgan pipe at 20 vfy,1pl5f 9pb$^{\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 t6 g3lv hg0uo6bhe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible gl6gh0vu 6bo3 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 whxfoti/lox0 - r)i2jc0 en trying to adjust two strings, one of which i0 / icj)txfo2 i0lo-rxs sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency fs- ((sd-/ +tt(jdr*hec-spjo0n ,egev 8r hnif middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) o1 y,3vnspd2g-( s onjnperates at an unknown frequency. If neither whistle can be heard by humans when played separatelynsvos,dngy2 (3 j1n -p, 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 souno9sj0 - u8runi4ubxxkrih35* ded with a 350-Hz tuning fork and 9 beats/s when sounded with a uxub834ijukihn sx- 5 r 9ro0*355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequenc7t/qcn d6q c9y7jm:tg y, 294 Hz. The tension in one string is then decrea ctm7n6djqt /:c9g qy7sed 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 heard if two identical flutes each try to placuyeu 8728mmzy middle C (262 Hz), but one is at 5.0°C and tmmcyez2 u 8u87he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequencys2q..f 9og/( qm zg eawjwu(pcm0)0rc of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded tg.c qrcaso eg2.pz( 0m)wjf (wmq/u90ogether, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker axigs4yucuz14i9-yj u o-*: uvnd 3.50 m frxc1 zvgi4*9j uus: i4-oy -uyuom 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 u,6 nr8,zclks 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 bsr8 k 6,lzu,cne 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 2jyrk( iis3)9ps, ,kyo.76 m in air. How many beats per second will be heard? (Assume T = 20yp o9) k,si,3(i kysjr $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at r24. a3wvqxb lyest. What frequency do youw3a.2lq bv 4xy 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 sti20hlmo0xc mc;ll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves a;lo 0xhm ccm20t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward ,y,s(yj z 4c,/3w0gjvq 1nenobkmr o,x ef 36myou at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Areo0y fgwo4,s3,,j jqmkm 3x /6en,nrzc1be( vy 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 frequenco lap 3zm7k*,tg;q n;ly 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 frequency the horns emot;,;lamz qp*gnlk 73it? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic s,5+q bqokdt+ yound waves at 50.0 kHz and receives them returned from an o5q qdkt y+,+bobject 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 ofclz98hw8kr8 awpvs*h4eh 2 g )8 teo3f 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave? zah frw4etp*8o)238s v h l8k8ec9wh g   $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubaf*j 28 (k+gzgw (cbcmv was played on a moving flat train car at a fc8j+c2 *fwmv( b(z ggkrequency 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 the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measj- ve6yp4 7x dbb8p4/ rbdj+pdure 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/pbp 4dejd +y xprbj/b-6v47d8s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frvu6g4-2u es5a 1um lqa+/ktnsequency $2.25 \times10^{ 6}$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 o9ys6 /kbg,d sla*vvv at 73td*f frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequen*kss6 d gy*vl3dtava/ v7 bt9,cy 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 on land if its/mnz( gax)e /z 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 if8 c j+xg)u,zm/s (a) What is the angle the shock wave makes fzcxgiu, ) 8+jwith 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 speed of soua3 46,b lv5/ffeicrnh nd is onv,5c6n4fhifb /a 3e rlly 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 t20l(f:rwuu r strikes the ocean. Determine the shock wave angleur r fu0:l(wt2 it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle :*d oobut3 lyh5 h t4m6ng-ju3$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the grtw)r ;l) ,1 cksn .*vhec2rksround flying faster than the speed of sound. By the time you hear the sonic boom, the plane ha*s, snkwkc;c1 ler)tv)h .r 2rs 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-H u99px b9cn6vxz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum xbcu9x 699nvp time between pulses (in fresh water)?    s

  Approximately how many oceef0 3(5zlj6-9l p g sj3kkfuctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display c)u8 p ;.:tlhx /hikzsmalled a sewer pipe symphony. It consists of many pl shukm.pt) ix;/:8 hlzastic 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 of h3q x bs/q3.4ihq)3y zx.u,ptv rgod2yuman hearing (0 dB). What will be the sound level of 1000 s g x)hqq,.oys34u3qx vyz2b .p/dt3riuch mosquitoes?    dB

  What is the resultant sound level when an uyzr :i gpax/l cn*/+*82-dB sound and an 87-dB sound are heard simultanex+/alp /u inczrg*y: *ously?    dB

  The sound level 12.0 m from a loudspeaker, placed in thes+uzr 9xh c+),r)k*vz*llf ke open, is 105 dB. What is the acczr , se9+krz)+l*u xk)fl h*voustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po 4vh,i624puo2p xeodqwer output drops by 10 dB at 15 kHz. What is the power output in watts at 15 42 q4vixd uph6po,e o2kHz?    dB

  Workers around jet aircraft typically wear protective devic*3k6gs bx- g dhk+ktxj+1b;xyes over their ears. Assume that the sound level of a jet airplane engine, at a di++6*bdxkg b sxyhj;-kt3g 1xkstance 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 airplane engine?    W

  In audio and communications sy6j2l.1 ta3khy l1cq wostems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to k yqdw44v7b/ va 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 32j1g1ai 7c j:zg cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit c:ggjz 17 iaj1length 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 fi mr/ykhigyi1x60 1 x+m7;u ixxlled with water (Fig. 12/hkr+1i7;xyg0m 1mxu xxyii 6 –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 opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is openf *yt oi12a:vk at one end and also 75 cm liak: yo* fvt12ong. How 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 w)htld bd4g. k5as observed 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 from two sourc)lisu,xb k/t ) ga/ak6es. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequel)b/uaaiks)6 x/g k,tncy of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. Thyf22n,lxv bfz* / 2d3dozj6r*bojyd*e conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is z*b3o2j, j nob/lx**z6 rdv2dfydfy2 the speed of the moving train?   m/s

  The frequency of a steam trrspo5 m3 juuyk h3-o86ain whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movir3pm6u8s5 3okyo-uhj ng (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jusvd k3j-cu78 clt by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halv 8d 3uckvlj-7ced) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes,d;1hn/ 1.m c2p ohryka sounding together, produce a beat frequency of 11 Hz. The shorter one is h nmk;2/y 1hadp1or. c2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroads1v ojq)j9xub/7 ux noc;l,c, 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, atxlq b uccj 1ov n;x,o7u,j9s/) B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 mh 4gi.*.jirfc /s what beat frequency would c. ifjhi 4g.r*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 l802v0 ja ksv i/meo5cmoth is flying toward the bat at speed 5 m/s The bat emits a sound vjs v8iecamkl 00/o 25wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mpra p ,,64qd jbnx*n fb.,rup,oth. 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 returns be b,faj * .pb,rpuqdr6n4n,,x pfore the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sendr8g)gx41v,wbf6p/q fig q o1c signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to crea iq gg)/w6x 1,4cff8qr vbo1gpte 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 (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 cod* nqknc-0c*k mpromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes.0*kck c nd*-nq Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singikz;f bf7rbo,, 9 nli9*i d0uakng 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 bkidfz;ni 9lf9uo,rba *7kb0, e 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 human ear at a frequency i90.p sgx lh/7tbtf.48*rlyvv gwfh 2of about 10hw7 r 8xb/ 4ggpts9 2vyf0*f.illht. v00 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. beq.-vv6pj 8b An observer on the ground hears the sonic boom 1.5 min after the plane pasepb8q- bj6 .vvses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb 7/)r8u da6 qksap4glmoat is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h