What is the evidence thq ly(/u lh;r)rmz:n,oat sound travels as a wave?

What is the evidence that sound g7v+v)+fl xob is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thk1)k b(w 1x1ksi f zbpp9wuiq98;w8h7s zbc,we 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). Explaiswi(zu 1pk kbq8;9,ik91 71 sbcb8hx)pwzfwwn 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 freqi5 r)i:cc 5 bk6sat)pwcyu3d,uency or wavelengthri yc ) d6i:pcwka)5s,u5b3tc to change?

What evidence can you give that the speed of sound 8 k38jtbbdp kt,ctjryf5*5 xs7 +8kduin air does not depend significadp*t5,kr8c7+stbj8j5udbk y f8xt k 3ntly on frequency?

The voice of a person who has inhaled helium sounds very high-pitchc 2ihxhe4xf. y(5j5vaed. Why?

How will the air temperature in a room affect the pix4 h1(wc0c t osvs4tsee(ubv 4c(9v 2htch of organ pipes?

Explain how a tube might be used as a filter to y-lwfegl673q reduce the amplitude of sounds in varie-ly3 g7l6 fqwous frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig ur.vdg i8w0 b)x .6.e,ro.gv,nuwykg. 12–30) spaced closer together as you move up tv.y gd0r6 ur w)iw8g e..xg,b ,kn.ovuhe fingerboard toward the bridge?

A noisy truck approaches you from beh7oioxk)+ese/7u* (k / ehm oyvind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenle ku7vo+7e/h)y * o mkose/ix(y “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be s q3wuk,w();0xperpz7jc,r i taid to be due to “interference in space,” whereas beats can br ),cewpk7(pj ;,wu z3qri x0te said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency2qyu-q 7 h*7c g4y 73et5o)znhhu cwwv of the speakers were lowered, would the points D an7 2twyu c53h7o*ceu7nzhhv ) wqqyg4-d C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting th s0sr*s q9 tf4lb,cx+we 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,q*9cs4+fw0rl,bt s xs 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 xx e q:get,n9d2ge3 *qin Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different tgqdex*2 n e:gqx9,3e frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift i*u* jy5d.ohib f the source and observer move in the same direction, with thijby d5u.h* *oe same velocity? Explain.

If a wind is blowing, will this alter thejj 0i0j50nsmc frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changed?j0 c5 jim0js0n

Figure 12–32 shows various positions of a child kr4b.9h ou fo9x q)ed+wdp6 (fin motion on a swing. A monitor is blowing a whistle in front of the child on t4od) + ( d9rbf h9o.pf6kewxquhe 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 avd-a e.(amg s6mw )wd2 lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s aft a-.egwvm(dma 2s)w6der 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 ec -s(dolzu ogv)8 xbl.+ho of the sound reflected from the ocean floor directly below 2.5 s later. How d()+g z- b vlsx.oldu8oeep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air axyws3g iq 19vg6w06n gt 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:d 8qa/v lamhqzgsf/(n: z(1k ts -jq; a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) bslf ak z- sm/1vq:j(( d:a 8hq/q;gtzny the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clif(hqxr ,5f7;po uazo a3rh0/)8nnxsw rf. The splash it makes when striking the water below is heard 3.5 s later. q)80;n5oafrr /p(n,hahuxwx 3r7zso How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concs11xcc9)fhxo1mqwd:0 k cw-xrete pavement. A moment later two sounds are heard from the impac xx-)0xswm1cqof1:9w dhk1cc t: 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-secov//jf kuaovwge.f*40h l9p4lnd rule” for eph4l e ul.9wv4va/f/ 0g*kj fostimating 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 a sound at the pain level of 120 dB?g-71x-k ro6w xk/2zjgxa vl5q    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 w;6i*peekin,g(4 j 8kagwz m 4sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produceiomd 0:lb 65n3pk 3dn zh:o4ev a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add int lo:nmv3z: 3 0ndhi65bpek4doensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with oxt:e 265 yqew+.al edfour 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 engqeda6.2+:x le w oy5teine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signamp3+ t+j k,cn s+fe1sjl-to-noise ratio of 58 dB, whereas for a CDnm++ kstpj+1s 3ejfc, player it is 95 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 speaking in normal conomv/b 86d kd2wversation. Use Table 12–2. Assume the sound spreads roughly uniform8k6m/bv do2dw ly 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 eardrld+r0trk 7c;u um 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 motf8pxx 4v* 3mure modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expx4v8pm*uf tx3 ect 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 xrbjaxt swt/ud) r)804/w/x f m in front of a loudspeaker /j b)xuxr w4dtxtrfw0 a//s8)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 typicallywicq37 l5 bamdx3f76 u detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amountfdu i c 6w7m3aq5l3bx7? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triz3 1l( ;ss8kv (1a(ytvxgpkvz pled, (a) by what factor will the intensity incas3(xkk8v;t y1 (1psgl z zv(vrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenlr2cq)ymzr9sdqd3 (x jgp zu8/,sj5 )t amplitudes, but one has twice the frequency of the other. What is the ratio of their 3 g(2) x,9ymzqpdd cssjzur8r/l qj5)intensities?   

  What would be the sound level (in dB) ;h.3 w i*r)z5tt jzperof a sound wave in air that corresponds to a displacement amplitude *5 t;riw3 )tpjhe.zrzof 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 10pb:yroy fwf+kn.5b;j4 c/,yxz 05 zzr0-Hz tone that has a 50-dB sound level? (See Fig. p+w0 xz jf okry5zz/cb:r. n,b5;yy4f 12–6.)    dB

What are the lowest and highest f0g mz0 2s;v(u-xu vjecrequencies that an ear can detect when the sound level is 30 dB? (0excz gv0 s ;m2uv(uj-See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound laaf bj; k*0gm v +8.( h0z8mq0a kaleczgs-,ibevels. What is the ratio of highest to lowj0eq80bfa,;+gzvlg(.i8m bh c*0a as - kkmzaest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of ta4zbs+v8- ra l-ct5n mhe vibrating portion is 32 8cr n b+a -5szmlt-4avcm, 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 ad8,t do28 -f kewew0phnd first three audible overtones if the pip 20 d,fo8dht8ew -wkepe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing across the top of an eaj am5hm (jps yf0l /51gn9qg*mpty soda bottle that is 18 cm deep, if you assumed it was a closed t a5fmj591p (s/ *jmqnhag 0lgyube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe orgphwfb+j -4h n(pc ;gp0 qq+(( q;wr4b ul1nvmban with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? 4mcu- ;h1hr+4 gnbqjp; qb( wqppb0(n+l(fv w$L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third h2 mx,u8 g*t inovzug+:sjg8v *armonic. What will be its fund8vi+ug * g2mgjotvu,8* sxnz:amental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 3mylqruj*9c ; m long and is tuned to play E above middle C3*;9c julyqmr (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open o j+x7nsisnmus-. txv) me7** vrgan pipe that emits middle C (262 Hz) when the temperat v *xsxmn7-sn *+ vu7si.)jemture 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)te,( b 2usfasm,+s yr 20 $^{\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 should the hole be t0puf zpy-by7 fdp.0 z/( qgdt:hat must be un/bg(up:.f7pfdp zy0 tqd0y - zcovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at8fd8wh gu agndy9u8 83 any 898agdgy nhu8dfw3 u8other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tub o ,ou)m8ncuj ; e1rwub d4vr8,ju4m+pe 1.80 m long is open at both ends. It resonates at two successive harmonics of frequenciesdmc1 4); b4u8rre,8pjom uv+uno ,uwj 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 *;df7, z2nnyelz i (gb$^{\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 fo 8iihw 03fw/nlr a 2.14-m-long organ pipe at /n03hiiw 8wl f20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal v4szpt)m(ds fz0*5vx, v pxw4 is approximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible rang5t ppxmzv4zd,)40swf v* vx(se) 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 txk bo1-5b2+ poomg(z irying to adjust two strings, one of which is soundingbiox bkpgz(5+-12oom 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and cc z)k3z +iawst;;.lf $C^＃$ (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 )ksz 4v -. ghud0pg7;f mmx1gwX) 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 tux0d1 w7fg-mz 4vm;k) .ph gsghey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/z txbp o87h03ks when sounded with a 350-Hz tuning fork and 9 beats/s when sounded wi3bh8oxkt07 p zth a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tenbtyj :6w: )ncsfo-t2 n zdg(e6k +xe+fsion in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. weksy dtc+6j +onn-zx)f2 6 gb :(fet:11–13.]    Hz

  How many beats will be heard if( ub) ktm5aawupn1o3qqm,uf7+q7/b d two identical flutes each try to play middle C (o 7ak7uqbuawfmu(d,3+5m qp/ 1t) bnq 262 Hz), but 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 frequency of 48: a bbjc8d0bh+cvz34ci6i u u41 Hz; when A jb 8vi8 zihccb+3d0:cbua4u6and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the 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 persone4xvucz( ako/y-z j-r t2*k.l6h a(rn stands 3.00 m from one speaker and 3.50 m fro*axrohny-/ta kz(.j6kluze - 42( rvcm the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz*wgy a3 fme en9uy86/x, but a piano tuner hears three beats y 6yxm /e9nae3w8f *guevery 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 mu r3 x/4 lv-3ishztmw9t ,et-d in air. How many beats per second will be hear34m,lu/d 3- t vetsiwx-zh9t rd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is ez :* y+ 5-nf6fke5jwx+twcpm1550 Hz when at rest. What fm5cny+:- 6ex* f+f5ketj zwwprequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you xwf/mhx sb1 xv,;aa0p ; w6xr.nr9a4bdetect if a fire engine whose siren emits at a4,xwb/rm9ar6.x nfsh0x;;x1wp avb 1550 Hz moves at 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 sot8 n7bv myn *:ygtvpvhr) 2d13urce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies ex7 *bnp2vvy rym nhg3d8t1v:t)actly 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 frequencs btb6s)0g.m ty 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 emit? Assum b0t. bs)m6tgse T = 20 $^{\circ} $C    Hz

  A bat at rest sends xhv+ 3:h (ak) rb-rhnaout ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the+ka3 bxhh)vrh n(r-:a received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/wb*wb6d- rk2 ss As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectsbk6 ww-rb2*d ed wave?    $ \times10^{4}$ Hz

  In one of the original Dopplert l.biv -5f0oo experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s bf t0o-v5i.lo?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds 5 pu/ vjfu0k)4x5hrdh*j 9lmw. 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 90lm jrv4xd5jph h5 fw/u)uk*is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequef1kzqg m)d:,ux 7 +g cpab4.iancy $2.25 \times10^{ 6}$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 ezzqa*2(n iuk0t8zl9 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wzel8q0k 2t zzn*au( 9iill 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 speed at 281bh u fegy2u*0 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What i+cjd +vm.y5t is the angle the shock wave makes +vc.i5 tj+m ydwith 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 tha13helwiw ;ics6w6gn))dx )f99cre k e speed of sound is only about 3)cndwkgels ei 3a;9xw1c )f6i96r hw)5 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 travelingw(71r 8dxlpoo 8500 m/s strikes the ocean. Determine the shock wave angle it produce 1(pwdo r8xlo7s
(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 oq, c)64kdpk o$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andhmtra4ypf0 /9yack,d y) 8a1j see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has travele 8d4hrmf0jpcy1 a/9ak,atyy )d 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-H4l+t.2odu cgqz 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 time betweenog2 utqlc .d+4 pulses (in fresh water)?    s

  Approximately how many octaves are there syo03of 2kz4xl7kg;epe a/l)+ax 4dw in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe k uru9c 7kok5q,43wttmnvp/2 symphony. It consists of many plastic pipes of various lengths, which are open on botc/3k mpwu5 4,kqu7rk2vnot 9th 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 threshk4 i vcunru f,))03ndmxi6w; gold of human hearing (0 dB). What will be the sound level of 1000 such); f0 4ni,3curgu6xkmvd i)w n mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB soundvm,l1o13mz k;tu/b ss xa. f(a are heard simul(m/tzax;s f sm.ko au131v,lbtaneously?    dB

  The sound level 12.0 m from +2v5w8 a.zkzt+g +(jsmd ggkia loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) +8w2(ki+kgmtzsd5ag .z+j gvof the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power )70gye8cc uraxej7 /exynd1l0l q,7 r output drops by 10 dB at 15 kHz. What is the power output in wattsecend0g u/,rx x1)l0l qy87 a7c7ejry at 15 kHz?    dB

  Workers around jet aircraft typically wear protective de cbh cyx1:qf/,e)2( u8agek agvices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear ,e g12ca)ch(8 x/ka:bgq yuf ehas 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, the0mi4m9h9o-e; o:mrr pl1hpx r 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 jj jp7w/ 98v8ht7 znyeto 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 fdty )g/fo( ;hf tff54kixed points with a fundamental frequency of 4)k 4 ty ;do5ftghfff(/40 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertipdi rw81m4q3ttsv .t)cal open 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 tuning fork when the distance from the tube opening to the water level i tsvqit4d. 1)mrt3 w8ps 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 ntahv5xf 7 2y+ qnl:5bsear 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 fundamental mode) with the third bs+t 725x5hyf :aqlnv harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full l8g 7lc(pl2oo poop ($\frac{1}{2}\lambda$) 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 raqp/ s4x:8oyw0pn+wqmu*us c ls*8z/qnge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequencqosup/ w x s:n +pq4y/zq*0s8 cwu8l*my 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. 4mvg)l51j chy,rc1 6 oeotw51)fcdq t One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frj,c1dto)6cgyw5ceq1m f4 1 lr tv5o)hequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it appr;uw-m+mqbe ( eoaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinewb-;mem +uq (g (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening t*ufe*;r q;/ ufie t o yn47zj;jj6al:to the difference in pitch of the engine noffoay/;u :*j 6qjuj ee;4zr;tlin* t7 ise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce azz3 f)b7rzq7vk-s h ;e37etr z6 92cmq csf/ox beat frequency of 11 Hz. The shorter one is 2.40 mffo-3sk e) z zb32szhr/9qecz;xt6q v77 7mcr long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mzc)b+ gz,ue)k oves 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 th ),)kzgzcbe+ ue beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is,j jj8;3xne-gaki a+w normally about 0.32 m/s what beat frequency would you expect if 5.50-MHzx+j3aij ej ,kw8gn-;a 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 the bnz+c,al7 -v1xj5 y iimat at speed 5 m/s The bat emits a sound wave of 51c-5alxzii ,1nmyj7+ v .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 e rpm+5-uqab:high frequency sound pulses 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 su5eam -qrp:b +o that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) wasns() n 8 ibk7vj*-aukfihg6s / once used to send signals from one Alpine village to another. Since lower 8jn ii h7nk6-b/kasvuf (*)gs 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 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 the preseh) p kw)ds+q em x++ko./sc1jznce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate thqj.wmhx 1ce++zp+ k )s s)/okde fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involv,- o-l+jb kvcblk.ih0b 2vjcvkj4) :wes 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, t b+k-civhbjl ov,.vj)l4-kwkj:cb 2 0he rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing f g5a h1:bmcmo8 h7fui-5k .rllor the human ear at a frequency of about 100iml.f78kl c-:b5a 5ho hm1rug0 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 the sonic b3-g zoxhk ,wf(oom 1.5 min after the plane passes directly overhead. What is the plane’s altitudh gwz-3ox fk,(e?    $ \times10^{4 }$ m

  The wake of a speedbo irm1zb5d5xhp7sc j9 ,at 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