What is the evidence that soundep.q:+)+q+u uxkkfj1c ke d g: travels as a wave?

What is the evidence that sound i y/kgh8nu4/.d za76bf yxwry 0s a form of energy?

Children sometimes play with a homemade “telephone” f5,zup3e49:t0e-tyt3qu *crv69e el s ykk vwby attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Exp6 f, 35k3:c vyeke4* t-u9lvuyz trw9 et0sqpelain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency okub33;g cj;mqr wavelength bg;ckq3 m3j;uto change?

What evidence can you ve f(rn:*lnji(g+ a3i give that the speed of sound in air does not depend significantly on n ir (fjg: ilven+3*(afrequency?

The voice of a person who has j3;bgyh(,mes5cn paj.2 wq 2liyg:s : inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room af,vw23 m(*rpcd8g so btfect the pitch of organ pipes?

Explain how a tube might be used as a filter to r079k 9 hpuycfseduce the amplitude of sounds in various frequencf 979pyc k0shuy ranges. (An example is a car muffler.)

Why are the frets on a guh a3 /( pgi0dp-wbzbu(itar (Fig. 12–30) spaced closer together as you move up ha/ zw-b(3(d b0giu ppthe fingerboard toward the bridge?

A noisy truck approaches you from behind a buildwg2n9 hk u 6b*w5s-rnying. Initially 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-fs rw2*k 9bnhug5y6-wnrequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interferesd xf,2y( dv8snce in space,” whereas beats can be said to be due to “interference in time.” Explaind sx,28fy( dvs.

In Fig. 12–16, if th)x.xor h;kck6e frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther c koxx6.khr; )apart or closer together?

Traditional methods of prote(, wpp aqus4m1o;,ge+5mijp/ ,8n rc hkdc(tecting 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, headm5,ot php/p4,( s nw+8kui1;qc,e gm jad(c rephones 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–;6q8w43yrzlox g li yi92iso0onu :,2-gxzsv31. Each wave can be thought 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 frequencies farther apart? Explain.gw4yqi i og-zl23o9sy6v x n;ls82z0uxoir:,
(12-31)
(12-18)

Is there a Doppler shift if the source and obseyl+d 3te+vla mw9d +)zrver move in the same direction, with thw md)d ez3l9vy+t ++ale same velocity? Explain.

If a wind is blowing, will thfjq0 wi18 k/cyis alter the frequency of the sound heard by a person at resq j1/fi8cwy k0t with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing-ow0wc7mib(i0uxa6 y* *i yd1oom d c-. A monitor is blowing a whistle in fr-* m1uwodio- b xoia06 d70*wmycciy(ont of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for t8swrw/ep*ub+z(xm-1bg rt1m 2 m)g ethe echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after sho(e*r 2 8-) mb wmwuzp1ggr /sb1mxt+etuting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jus*l lf5qr q4gim 3/2tsst 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 sound in seawater is 1560 m/s (Table 12–1) and does not vary significal 2m gqq4ti l5ss3f/r*ntly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air an3ro,dv9so7a 9 w s2eesh58iqt 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 onkdp) 1k):bwe v a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33)k)w: 1bvpd) ke. 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 te(5o,ct olx(e b+oiz1 u;5 hbnop of a cliff. The splash it makes when striking the water below is heard 3.5 s later. Hoiuotzbo5b+x 5 co,h(een; l(1 w high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strik7 h/ e6hwzng7q4uy oz8e the concrete pavement. A moz8 eh67n7zwgqo yu /4hment 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 one mile of distance by the “5-secon:dgjlyxj70xldgus4et;v9 s,p e+9 . hd rule” f g0.9e,u: l4 7 dpeljs+;xgjyvth sdx9or estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of av mk0;aae1sk-i gz5bi*a *8ua 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 of a sound whose intensityhup* rx f4;g5v is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 950d2qob) gl i 4 zbi,e7du ,tkkpnie ou6nv+-/8 dB when fired simultaneously at a certain place, what will be the sound level if only one l o-/i8)+n0d n,,pq2be 7 gdokitz46bvuek uiis exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frowq,1sim 5 dtmb,vgj 55m an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: A5qgidb 5jmmt,vs1,5wdd intensities, not dB’s.]    dB

  A cassette player is said//ydw1n qf3lq1 7qlw j ,broz7dy2h( y5; gyjl to have a signal-to-noise ratio 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 for each device? 5q7 n 251l qo(7jl;wddy,1l3qwyfhjrbzg /yy/8 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frudol*q fwk*ofn +26)jgw1y8xom a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly overu *x ywf2odjk1*q+)fgwo8 ln6 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 strikedqwl4: 1g/kpjd0dn.n*kd sn)s an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modes6ciw4*1 0zc)tikr: w 9enqqie exvshks68 3r9 t amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.56chiw*q6 3xeqe:v c ni0 skr 1z9et4wr98ki)s 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 u;/9kk6v78 az h mf okhs1yde4m in front of a louef897 /kok1 ku4 dahmzv6;y hsdspeaker 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 typically detect a difference in sound level of 2.0 dBb6n8+mj7p5 qh4yg aqv f8itw 9. What is the ratio of the amplitudes of two sounds whose levels differ by this amia9yq8 j6bh47m5gv fq 8w+ntpount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of 3qycdosmy9 .g*bwpg/ 9ju+;e a sound wave is tripled, (a) by what factor will the intensity increase? Increase by ed up3 bgj;+m./ysog*w9 y c9qa factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemerenua/53 7cnb nt amplitudes, but one has twice the frequency of the other. What is the rau/c nare7n35 btio of their intensities?   

  What would be the sos2w8so jy/m g3und level (in dB) of a sound wave in air that corresponds to a displacement amplitude ofy2 wmj8sgo3s/ 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-Hz tone thvme0pcn yl 0,3at has a 50-dB sound level? (See Fig3 ye,p lnm0vc0. 12–6.)    dB

What are the lowest g4;;nat w3g ozand highest frequencies that an ear can detect when the sound level is 30 dB? (Se4;oa3ntzgg ;w e Fig. 12–6.)

  Your auditory system can accommodate a huge raig4s.f,, -pna w0x)uzruzty+nge of sound levels. What is the ratio z4r. uga,0snzty) u, +piwfx-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 frequency of 440 l pci3 -wh3drq8rkno zi.a41 -Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under i1-rizh lw pa 43dcorn8k.-3qwhat tension must the string be placed?    N

  An organ pipe is 112 cm lon kg*6b( s ;d2(gwotm,n9tjahqg. What are the fundamental and first three audible overtones 6(wo9 2h j,tgs* bndam(qkgt;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 witg mmyz0is1t+ wfr l t(4;,l1ould you expect from blowing across the top of an empslm,gt t1wrt+ yl4( m0fz; 1iity soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a peciw: e1 p.rui,76i s wtzy30gipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kH3e izw6gw1t0c ,rse i.upi:7yz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its thhf 8 um0 .eau56jzh ;bcmd8h3gird harmonic. What will be its fundamental frequency if it is fingered at 8;azmmc6.fb d0ueh j8 h53hgua length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7313kfgpdu kg(y yj/o+, m long and is tuned to play E above middle C (33j dyof,y+ pukg(g1/k 30 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 jiw5f4us2ws lj 1,)a femits middle C (262 Hz) when the temper1a5ju ) 2fis4jws,flwature 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 39wcly4wjx.(k gp.+9zak lfa+ n 6 bup20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 s(0qyi*nc6 mrx hould the hole be that must be unyq6cxr m *n0(icovered 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 resonateux yafkaf/e 2; e6bxvy9v8x.; at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is anyu6b 98f;yaevakx. e;/2xxvf 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 succx4svhu ybgp 43is9q2i+h w 8p4essive harmonics of frequeyiuip9bx44 s h8423vpshwgq +ncies 275 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 -mpqcr* e46fry5 0no/(fzn fp6iwco4 $^{\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 aiu+ * 2.zxkxg b/wt+lrudible range for a 2.14-m-long organ pipe +w r+/ .xgizkul2b*txat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxim5xj afu(wl35o ately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audibxl5(jfa5o3 wu le 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 2z g9c5vhnq ot: fo,a:1.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the ot hnf:tv, :1og95zoaqc her string? ±    Hz

  What is the beat frequg09 f i0wwz0znency 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 operats/qym wx- (6pbes 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 frequency of brand X.bq/wp( ys xm6-    kHz

  A guitar string produces 4 beats/s when sounded with a8 sz g+9-lqshm 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequencm-l s8z9s qh+gy of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenskk78:2or1 cmmiw m6s kion in one string is then decreased by 2.0%. What will be tis:mk2r8k1wo 6m k mc7he beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicay8 kf,g/r*q.u-rp gu i0)9oja 1n iauyl flutes each try to play middle C (262 Hz), butyiu*)yu a n1pgr-90.iuq , fgako/rj8 one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequenc-gf /mwnq1lohc4rm*k zo(-5q.wj0 j q y of 441 Hz; when A and B are sounded together, a beat frequency of-ojz5jl.-oqgr/f 1h(qq0c4 ww*mk nm 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker aj7mvm .r:+a(0bllpdb -9en s pnd 3.50 m pvld(b9 j0a mr7ls:b.+m-npe 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 supposed to be vibrating at 13 ;t 9v y)y2p.fhobd.ve2 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If bt)yvfo y2.h. pe9vd;one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wad e.e)fuu-f q,vj3xgm5yy: s 9velengths 2.64 m and 2.76 m in air. How many beats per second will be he. e3ffe:),-9ydm quvg xsu5yjard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencywhb6+en. akhfd j;:3i2zw+*abq d4 sr of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of jan whddhwabb3zr.: ei42q+6k sf*+ ; 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. Whtn1(ik;:eulc uw0qv /s h r*mg u3ez8)at frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a spechkgzr1q3 0 /t;mve)inluus:8( ew*u ed 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 youh+yfq3qswd 3e .u8 2x; fm9hbk at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they closef +.qfu3mw h9 bqeyh823xdsk ;? $f'_{source\,movine}$    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 frequenc1f pt 7datx)go5ed:ionk+fhkp9f85 /y horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at +)5ed9 it :7 dktganx 1pho8f/p kf5forest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receiveu2pf5t; 3b+ kv qpl(bhs them returned from an object movi q 5v(ppu2kf3+bh;bl tng 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 emits i glqb//wi;9man ultrasonic sound wave with frequency 30.0 kHz. Whatmbq/i9iw /l ;g frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tubax+5w/qmga;f x d61iu /k-bgpb was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached t/ib kd bf1gxu5m;qpgw6+x- /ahe station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blz;ff1t kg,dffc:6sz:c o2 8syood-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 k8g2,z: df1sf 6s focz:;c tfyaway from the sound source?   Hz

  The Doppler effect using ultrasonic waves of jxj;ug 0ga; xc83 x)asfrequency $2.25 \times10^{ 6}$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 is cdl 4c9dr8edx.i9 1cf12 m/s from the north, what frequency will 8cfdce.194c r9dxl i dobservers 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 speed4 j*js4 y *fesb;oibd; 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 axokw,r4 ti 9:zt Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock w:9xkoz,4r t iwave makes 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 + hkz57ld zhp4l9z.gh a planet where the speed of sound is only about 35 l.+9gk7hzh h4z dl5 zpm/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determinek05zmi+k*h4 0o)ck uafx,prj the shock wave angle it producesk+foija0 * , zp4c0mhkx5 )rku
(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 -aqkvq p+oz67 $/theta$ 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 ground *2tar)giy t;lflying faster than the speed of sound. r* t)2g;iatlyBy the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar devic ajm0ms ce*i1znnc274k s4q 8fe that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects ech2440q71zsnmaiscejm k 8fc* noes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many 8 g r cr2p.2st rww(ntea,yy+5;d /oxsoctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consisljwao qp37v5l a6/e f1ts of many plastic pipes of various lengths, whi5vj/la l6 aeowpf 7q13ch 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 /sg0cqmqxv9n9tn1.xu 7ii b 8the threshold of human hearing (0 dB). What will be the sound8 i9tuv7n i q9/qxs.c0bgx n1m level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound hv mw/lg pi,fj,t:0k pbjo801are heard simultaneousl:80l o h 0tvpwmf1pjijk, bg,/y?    dB

  The sound level 12.0 m from a )3ghny(s 8eigwmsx 0*loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates eqxnsym0)h 3isg*g8 (ewually in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output dr /jc n71vchw9j5nu x8iops by 10 dB at 15 7h15c8iu /c9nxjj wnv kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices ovej,5vt:t:1lywwxw- wuf p ty14r 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 wvjlt51tw1: tx fw4yy w p:-u,30 m from a jet airplane engine?    W

  In audio and communications systems,bxk1n a)4 a8dtvz ka6f dlsa7,+u(f e: 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 tunskppwu:8;;jqlomaa j;)be *t2yo0( g ed 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)bcrrd d+)k 2u 32 cm long between fixed points with a fundamental frequency of 440 Hz )r)rdcu2d+b kand 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 o/ x uzxz a j8*yh-(v(weom7vp4pen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tunihx jy/ezx7v* (u(- 8v o4pwzmang 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 gpv z+8b9myx/:,kwb j v is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamentalyz/mvwb vx8k:+p b j9, mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was o11s mqu*m,b. sojr5 lof)x-oiz:r)hjbserved 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 thtj4tf23dq3 lr jrryl gur3 zy15,pb3-e 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves abo,rtr33u4q3y1yjb rz3jlr g-f 25dltput 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 conductor on thf1ctkov0g4 q qb2 3+sqe stationary train hears a 3.0-Hz beat frequency when the other train approaches. Wha0 f+c2k 4s3tgvq1qobqt is the speed of the moving train?   m/s

  The frequency of a steam train whis) jq7vn1ty0ydt (* qfxtle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume ct ty7)1v( x ndqf*jq0yonstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening tl) ,2nth/1kapfz4) kr qr gbb.o 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 halved) as it goes by on tha14kpbrtr/q flk ). ,h 2nzb)ge straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The;k* 2nuh.hvthbf07k a*(afpb shorter one is 2.40 m long. How long is taub 7hb.h f ; k*vp0kt(afn*2hhe other?    m

Two loudspeakers are at opposite endsdrpjbd+m:kp58)-d r k, vrq:m of 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 (a) he listens fpb: )kvj,kmrddd-8q r:rp 5+mrom 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 yk ktm 8bj-zs t 88d-;kob7z2cis normally about 0.32 m/s what beat fr bk8 ksz jdkt 8czb82-oy7-mt;equency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward th)pm4sp 8 ny):+jwqhude bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is s+mpdj )pqh n):w8u4ythe 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 p fc8b:d4,7 fl lqtzls;ulses as it approaches 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 th78b,: lqc;lsl tzdf4 fat the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was;t.q+rvw)6fimgqste 39pes0 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 (or G flat) horn. What is the fundam +)s. gpv03 t;siq69eetf wrqmental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stery yrz3ri a;hfx3.0vds,cw3z / eo listening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the location;z x rz3wrdf3iy 3yhv,c/sa 0.s of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alyk rk /2:q k0vizm+r iow,*w/tuminum rod held in the hand near the rod’s midpoint. The rod is stroked with the otherm wk w,2ko:0zy/ ikivq*/rr+ t hand. 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 threshn s 2nnypa( ow-mo3f)fsbu8+,6v f)im old of hearing for the human ear at a frequency of about 10iooa,mnu(ms f3)-82yp w)sfb v6fn+n 00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears t;5rmdg/av.h x-7wmx3lx qw 3che sonic boom 1.5 min after the plane passes directly overhead. What is th3- chw5/l.r 7 vxa;wq3dxxmmg e plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isp7om *exxn6 )h .cv8se 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