What is the evidence thatcz0 d+sfi-vf9 sound travels as a wave?

What is the evidence that sound is a form of ener+e5:8wrfbtor gy?

Children sometimes play wity/fj9 w/ tmirfo. d,sb/3d0 qvh a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, thewtqs39 mvf.dj0r,/o //b iydf sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequencyue-2g 2x gu8tx or wavelength -g22u xg8et xuto change?

What evidence can you u484 avmz-ja dr.p1/ ifv63g vqiupf;give that the speed of sound in air does not depend significan/1.- ug p ;azripfijfvdv 8vq4am3u64 tly on frequency?

The voice of a person who has inhaled helium sounds vl c dmsmu:y2:z,7 3ywpery high-pitched. Why?

How will the air temperature in a room affect theuui03cl;sx)m f,o1/yaok.r va j5p2ov-x( bi pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundsk81w rb;7 r9xhtz r l0k+q +svsb)lur/,2ozjc in various frequency ranges. (An example is a ca9k xhv7r+01z)crrrs j o ;2wlb/l uz+s,kq8btr muffler.)

Why are the frets on nju./kk jehpvl8/io+:qak6 7qp9i;c a guitar (Fig. 12–30) spaced closer together as you move up :+ a;le/.ih/ uqo c7k69j qpkvi kpj8nthe fingerboard toward the bridge?

A noisy truck approacheb5tnu8 npyfad ;089ets you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound i ;ny 8uatf95bpt 80edns suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said tqhga( 984 ocw5cyv h;eo be due to “interference in space,” whereas beats can be said to be 5y ghqhw8;94ec o c(avdue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the s.kb ss5w 8nbadgu3c- r;;u st7/ z8dhypeakers were lowered, would the points D and C (where destructive and constructive uubs8 sz8r.3styk; 5gd;/h bc 7-wadn interference occur) move farther apart or closer together?

Traditional methods of protectr,juoz 0i/b7+1d bpx dqrd 5n8tlhy*,ing the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used whic1 btnuxo8*zr,y jd+,i7d0/dhr pq5 lbh 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. /twt0h8xm+a- etg m.9n c+cun12–31. Each wave can be thought of as a superposithctegt8/u na.c+mxmn-t+ w 09ion 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.
(12-31)
(12-18)

Is there a Doppler shift if the source ,xcbuj un/g (o3t++qfnu8g t,and observer move in the same direction, with the same,uujtx( +c g8f/3noubqtn+ g, velocity? Explain.

If a wind is blowing, will th-qio iyw028 aris alter the frequency of the sound heard by a person at rest withaow0 yri-qi82 respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a sp75e; a qv(fzzwing. A monitor is blowing a whistle in front of the child on the ground. At whivf5;a epz z(q7ch 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 byistui, ;v juo1*l5. b sdr4.oi listening for the echo of her shout reflected by a cliff at the far end of the lake.,;1ldu s*5os4b.roviji . u it She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hgr2 2h+r i2 jw-yjk*zpears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assurhi*2 -kjgpy2r2z+w jme 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.r*avpgc3r0as.a x,g.d d+r f 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 foggy dr9f1if 2yor- 79f;keyvdpn)u, k8i bv ay. Without warning, an engine backfiiukb91rkd pf8ofy;y9fvi ,ev r )-27nre occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The ry *2p (r,t 1apdc (3*4lpc5x zitvdw+4rhxsisplash it makes when striking the water below is heard 3.5 s later. How high is the hacry(wpcpi sdt t4 5zp*+x 1*l,4 2ri( rdxv3cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concr +;aheb3s fs-m.ymj0lete pavement. A moment later two sounds are heard from the impact: one travels in thsmm0y 3ba jl;-.h fe+se 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 distanc a z/pyc hp/bh,*;trdw9fjp23e by the “5-second rule” for estimating the distance from a lightning say9fdzt; 3,2 wh/p/ c*jbrphp trike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound . c3iztx35/ l7i/.inwyudq ao 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 int 0q-efhmer.j(zek9rml4+.u r: ztp (uensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a s d(er d +yocpz)o .nit(+gs12cound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is +sr()oc icde1to+n(z 2.d y pgexploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane withga uewp,9 :*; fhey*af 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 *gf,yea *9ae: p;fhwu down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to haap3m1lb6to z8sx:hd*5kv v6 tv uuw87ve a signal-to-noise ratio of 58 dB, whereas for a CD player it isz v5lad8:tp3khxoms 8 b6vwv*61 t7uu 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 frox*n69 hv skef0m a person speaking in normal conversation. Use Tax*9 nf0ehvk6sble 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 strin 0gd0esv( 6 mzw-zzp0kes 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 2 o 8sganml0twsk2 015x50 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a poixmsot0wa8ns0 1 5 k2glnt 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 sd hy+4iqok o23fz +x7meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stag+zhki+o7s fq yo43xd2 e.
(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-rcv3;o j *gys1o9cbz.0 dB. What is the ratio of the amplitudes of tyoj-9 rz*bcg3 ;o1vscwo sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soun o;b ike2x bp;f+)d0cld-a4 cr0sbqi6d wave is tripled, (a) by what factor will the intensity increase? Increase by a f2f;iebca+co-0qrbd) b6 ld; p4sk i0 xactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplit ga/5-gseltgnr (.ae29k. jciudes, but one has twice the frequency of the other. What is t5-2 jia/ elgtgr. (9 ekgcnas.he ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air u:gbg3vp9/utk ry/bv ipdv. 1 .uj:(bthat corresponds to a displacement amplitu.bgu:r/v9k(pgivy 31p :butd /bju.v de of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have w 8n10tk6ighu) tvu)z bhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.kv) ) zth1ut6uing08b )    dB

What are the lowest and higu 4ia1i8t 3nl (olbv,h)gx1;wug kr+ lhest frequencies that an ear can detect when the sound level is 30 dB? (See Fi 8auolh +4ulvggb )l1k w3;(itnx,r1 ig. 12–6.)

  Your auditory system can accommoda6 )axws- nvw7 u s0h zuzt9jy9eq0+qn)te a huge range of sound levels. What is the ratio of hs07vqyquh) -)wzs9a tun+w6x zj e0n9 ighest 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 violi.phrdter q/e1r*u v,0n has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what te/v*,1ep 0drr.tqurehnsion must the string be placed?    N

  An organ pipe is 112: py*5ut0hcp to7akae1 a ma9q)a*g/ w cm long. What are the fundamental and first three audible overtones im7oqg uky1):0a*a wahctp*9a p/eat 5f the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect fken/)p l42 qyprom blowing across the top of an empty soda bottle that is 18 cm nk p/qley)4p2deep, 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 x)acc:9xyyjpa( wc1 b usu:+ 9or1h86hk+yhu a pipe organ with open-tube pipes spanning the range of human hearing (20 H ao989sxch1arkhc(: y1bc wuu yup)+y:hj+ 6xz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as - 29 2bxl-ka,dmvr k wo)5yrcoits third harmonic. What will be its fundamental frequency if it is fingered at a lengt r oa25 -x -2olb9)kcwyvdmkr,h of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m ( g5/(kood pdvlong and is tuned to play E above middle C/5okpvgd o((d (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 ope.+qgxv mj( 492w eirt xcgz f.oc-(+:0tqjf bkn organ pipe that emits middle C (262 Hz) when the tempemfoqfc4q9zcet:(+ vrx..- j 2+ 0(ixg jtbkgw rature 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 a-kp8i poj ,6gut 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 Exa:2s wwe4 mp76vf14dbvdm 3kyo mple 12–10 should the hole be that must be uncovered to play D above middle C a op3by2:ve kd vd76 fw14m4mwst 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 m8ki16pa3 i l hhjkm4kl(8w*c at any other frequencies in between. (a) Show why this is an open or a cllihmk *8mal4i h8 6(k1cpj3wk osed 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 bo s2fc8, wb39s4hommhh*ie ab16lh4x0/i fwyoth ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What 80 wo hc y/hi96 ow241fishb shfe3b*a4l,mmxis
(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 ek;a5 cwn/4xg2f 7fom$^{\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 2.14-03qx7 )kea byt1)+1 iyaphs sym-long organ pipe at 2 )hy pb0x73qay yktai1ss+)e1 0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsxim) eq roxd,9rd8 5ej+2qu.cide and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is thei,r5dqor 8xc2 ee)jm . q+9udx 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 trying to adjust two st7ixj26w/lo* *o rsa errings, one of which is sounding 440 Hz. How far off in freqe /jwarx*7 6o2 *silrouency is the other string? ±    Hz

  What is the beat frequency ifqd+eb zvlfmq)z+/sj-yav ( *. 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) operates :tps3m*n08 zldya8qa4 0qnet at an unknown frequlm e8 dn:ay4 pqa30z0nt*8stq ency. 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.    kHz

  A guitar string produces 4 beats/s when sounded with ab,-/,js ej a/t xle35gdf5zw i 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational3j/db5 l gwaiefze-x,ts /5,j frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the :opsuj7 cc*(ay18h+tiktz 5t same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings(7 t*c tks8a1uztcjy 5 po+i:h are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if 2 es9q2jt8l lptwo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othet9l2sj82pl eqr at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. For .zofq)*cr1s. xbj)ppk B has a frequency of 441 Hz; when A and 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? Wx1*sfcqbjp r)op.) z. hat 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 onephc 0 f,1v)h.8:rh rjglz hx7q speaker and 3.50,h) c vh:r7pq8x f.0jg rzh1lh m 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 132 Hz,d)3 entkc)wz , but a piano tuner hears k,)n3wz etc)d three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. H,b(2evlky cw3 ow many beats per se(b2e cwl3v,ykcond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 5xn v--vw-nni0 ; eepnHz when at rest. What frequency do you detect if you move with a speed of 30 0nvpnx-5v;e-wnen -im/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a5-j 4mrjfcr x1okby 0d99 (rro fire engine whose siren emits at1bryfrd cx5jm0r9k-94 rjo o( 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 soybhryfy:02t lr, : aks1xb.m/urce is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the s rxfmy.b0l/ k:s:tyhr12,by aame? 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 freqb :/ dgbbvf/(i8o)qn f9,9x(jkaj kds uency 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. What9/(( obk8fjj9gfxiaq)b,s vd:n kb /d 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 receives t1i emrm6iayi c;mzdo :(03+ 8yrtxw5chem returned from an object moving directly away from it at 25 m/s What is the received ri 8 y:1i0+tcricaw; 6ozm(5mx mdye3sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward aeetidlf4 *5e 5bxqn30 wall at a speed of 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 re4bex 5t neq*l30ie5d fflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played0anl/qxl+m1:* - nryx2 z lwms on a moving flat train car at a frequency of 75 Hz, and a second identical tub lysn 1l*:2/rlamzmwxn+q 0-xa 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 measure blood-flow speeds. Supposgc pty0(h1 .cge 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 awgtcycphg1(0 .ay from the sound source?   Hz

  The Doppler effect using ultrasoni) n hzob(+l;w05 vyenrc waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of fr5sf(rof qfam prrdy8 9*c( 4:jequency 570 Hz. When the wind velocity is 12 m/s fro9rjdro q4((ap r *:8fffysc5 mm the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its k(y y/z-xqprs z1s+* whp.f2wspeed 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 316b;/ weqz7kc l /nlmy(0 m/s (a) What is the angle the shock wavznc ylwe bqk(m 7l6//;e 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 aux2 ddw4m:yip0b* 0b jtmosphere of a planet where the speed of sound is only about 35 m/mxjb0 d:* 2 04wbyupdis
(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. qwx :/ev8z6bwpe k 2 t;mg8pg1Determine the shock wave angle it produces gxbq 8: kew 6w/g81vt2;zm ppe
(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 uucjkrb s2/a) +j. 1pk$/theta$ 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 grohih)r q :rx mh7am7ob79w;fj8und flying faster than the speed of sou87x;m:7 ) hmw hiqhjao9r7bfrnd. By 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 d/o9ogbv zy 7p*fsm /y on6d*2wevice that sends 20,000-Hz sound pulses downward from the bo9y2 dbf/o7 z6*wgynmoo*ps v/ ttom 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 between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audi5n-iunbd c cr9 nehtu6 u 85u2gs(,,nbble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sy-daivqzw x9*n*9 3lae mphony. It consists of many plastic pipes owxneai*v lad-z399 q*f 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 tqzu l )g7cu0p2o the threshold of human heari g )7qupu2z0clng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-h ko:es pt,c/(dB sound are heard simultaneoue okch/(pt:,ssly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1b80h:kmmxzl w461oahkog.h j+ o+ yo105 dB. What is the acoustic power output (W) of the speaker, assuming it radiatehamzkylm.j0 46w 8h1 kooo+:h1g +obxs equally in all directions?    W

  A stereo amplifier is rated at 18fg0 rdovh8t(,cc1 hh50 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? c,hgfh vtoh c0(dr881    dB

  Workers around jet aircraft typically wear protect2kj8gl 0i) s(w7pfffg /tm6xjive devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distag)jf260 (7lf wf8ptmxkjg/is nce of 30 m from a jet airplane engine?    W

  In audio and communicat (ja53,xxa,pg; wa1hx qk ng:yions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is twcrtmnff6 ;*n 58k+w zuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between*zbzk 4 s43sfb fixed points with a fundamental frequency o4b*sf zs3k zb4f 440 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 intol1/xqe tg6)5foq ifu ) vibration above a vertical 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 tuilt1e)) o f 5/ugqxqf6ning 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 massh 08mkzqy8x. b 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should qbxk8 0zm8hy.be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resdj:dj f+d:j* gmi(0 kuonate 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 r nz 9fvpj-6-ouange coming from two sources. The sound is loudest at points equidistant from the two sources. Ton zo-6p9uf-vj determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-ay8qo*r-z ogs 4j- m.xHz whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speedqs g oyx mz-8.j4-r*ao of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After i a4exw a-gtw/(t passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume const/aw(x4 -gawteant velocity)?    m/s

  At a race track, you can estimate the -7c0 o2pr sojn6xd l1pspeed of cars just 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 octav1npdocl6r2pjs7 x -o 0e (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togetherbo6e4 vo6a9cr , produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is th oc9a6be ovr64e other?    m

Two loudspeakers are at oppo84ab jzge:)bj 9 zc,kzsite ends 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 zz, k89j4ba:ge) zbcjfrequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0(xv7f9lwwod 6 .32 m/s what beat frequency would you expect if xlwvd(7of w965.50-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 16hhq.rl en-u6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after h-e 6q.lur1nhthat wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound rmzw6ompu bbt q5i e*bc;272 hm- 4c)vpulses as it approaches a moth. The pulses are approximately 70.0 ms apartmb)5pmu2mto bv bie4 *7czwh2;q -6 rc, 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 before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used tst:*:f1asw fot gh2o 4o 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 fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tub::g otwfs1s2*f ha4o te.

  Room acoustics for stereo listening can bezu cqx1+k7f(d compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundame cx(kq1du7z+ fntal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration,.: nn ko-fi0bu called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the ob. :k0nun f-oither 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 thr+p9af 3dsat3+: g-rok *wyxx ceshold of hearing for the human ear at a frequency of abouo+-*ypxarxf+s:9 kwtc33ad gt 1000 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 obsejluxv.xe ; +o52k8dau* uunxc e 95x6drver on the ground hears the sonic boom 1.5 min after the plane xavj+kxl.x9u u*oc6d e2x5euu 8n;5d passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15).f8hpauyd(d6:/95d kw lw ek fg.e/ivb8uh r $^{\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