What is the evidence th*buz1es/ v/vxf7 0nbyc c3)uoxpb,. hat sound travels as a wave?

What is the evidence that sound is a form of etw 68t a-vpr0 2l4uegnnergy?

Children sometimes play with a homemade “telephone” by attach,lppsk 9o am3 n.5awvz;9pe u7ing a string to the bottoms of two pape zes5 muv.9,wa7plon3a ;9ppkr cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air int s.;pt nrph0r/o water, do you expect the frequency or wavelength to ch0p/ n hrsrtp.;ange?

What evidence can you give that the speed of sound in air does not depend sign-hc;4o y7jt* tifcf)u ificant)cjti *fy7u4 c;t fh-oly on frequency?

The voice of a person who ugr7ub kk- .1c;mk zb)has inhaled helium sounds very high-pitched. Why?

How will the air temperature iu6de, wq5qdb vy0d /+kn a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude j)9 *dapm(-7juxl/ t ji8ahcwof sounds in various frequenct(pj /7 mu)*cjh la-aj8i 9xwdy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together a3.a brwcc, x*cs you move up the fingerboarcac3.x*rcbw ,d toward the bridge?

A noisy truck approaches you from behind a building. Initially you hwh-rb- +:nk:2zrra wu ear it but cannot see it. When it em-uak2-rwr:w bn: +zhrerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be qb: -jk;g3* 6cpwjugy:; eko jsaid to be due to “interference in space,” whereas beats can be said to be due to “interference in tim3gcjj uow qjy*6-;:e:gkb; pke.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pou5k 8qux/tfewch+/ 6nints D and C (where destructive and constructive interference occur) move farther apart or closer tog qx6+fcuewt8/5n h/ku ether?

Traditional methods of protecting t+nua2 )c6km w,w/ musku,.b cdhe hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. Ws 62m.k ,ckbauu,/wundw)m+c ith a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Eab7yy 1w. wcf *6k8/ wgcdly-ewch wave can be thought of as a superposition of two sound waves with slightly different frequencies, as ink1cbd /7e. www ylgyc*8-6fwy 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 and observer move in ts p,y*xrmq2 -c:g8kn)e1hv8po + pe zlhe same direction, with the same18:yhr+x8m ) epkop-s * ,znvcpgql2e velocity? Explain.

If a wind is blowing, will this alter the frequency of the solle22 e nnbb+1 h mn 8+fna)duvh8p0u6und heard by a person at rest with respfb02mup h8b)nn6 +nnhe8la2 e +1d uvlect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in m 88atgnfe.tj6 otion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, win g.tfej 86at8ll the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of ar7srsbi z/m,8 lake by listening for the echo of her shout rei8r/m 7bzrss, flected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline.c1fm0 la5/jfy j,kaxd ob;) ow(uwv2) He hears the echo of the sound reflected mow5cj ,)o jf(b;2dakuy)/ aw1vl0fx from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 s+x-8jp zo/gf*qj7p y$^{\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 dh)2lepuk, 0ipf * *aw k1lpeh.rifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befo u),f.1phh0kepkp le*l 2 aiw*re the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top o(xgx4voz.w;8pdoc6) s b9knk f*t,h zf a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hoxg s6,z h9. kvpkwzb dnft4c* o8x(;)igh is the cliff?    m

  A person, with his ear to the w8o;+a rsm-mx ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard 8;x+moas rm- wfrom 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 m nj8f q6msk1:-gkxw +dade over one mile of distance by the “5-second rule” for estimating+mdkf8k6 g:wq1- jsxn 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 0mow3e cxm2t:-w/b+gp 3 ye bisound 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 ii ;xoi4mm507 ij y3xyhz9ckr6 +cwx7sntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when bby7x8hsfate.ka7 (ee4nx + 3j4+ cflfired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, x e+f k 384x7eajth4b+ fncs(eb.l7ay not dB’s.]    dB

  A person standing a certain distance from iu zxm+*z4*b(og yrb)6d*ghvan airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound legdh )obmi*yr4*6v* zgzb+x(uvel would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-tokt6cb ;xt6 -flkhv:h3-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 backg h3vkt fc6hk -l;b6t:xround noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powep*cre .mfi ,0lr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly ol0.i*, cmfpe rver 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 stri*tvz1;kf 9tl tj 2-zsbkes 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 mo,a q hydk: l,4j8dtn*vdest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loud,, vl 4d*dy 8tj:anqkhspeaker 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 i8)gc l:vbv2s 2.8 m in front of a lv2cgvsl ):bi 8oudspeaker 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 dekvuv.yg 7 1vjsk;(g(9i ifh b0tect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds wh( viyi 9f hg1jk7k0(vs ;g.vbuose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, thkc, tz(.;ej (a) by what factor will the intensity increase? Increase by a fact je(;c tkhz,t.or of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one hc.)y9oev7o wx jn q98sas twice the frequency of the ws98 jx) yoov9q7nc e.other. What is the ratio of their intensities?   

  What would be the souz*v2ecg1 u hd0nd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating aez2dcg*u1h 0v ir 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-xst4 w.0h6johxnyy-, Hz tone that has a 50-dB sound level? (See ony,jxs.h60hy4 wtx - Fig. 12–6.)    dB

What are the lowest and highest frequencies th+h68ksw +fm; xka) ckwat an ear can detect when the sounf)w86kmka +cksh; x+ wd level is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate ax6:v i,-2 ge1j*e sw,mq hlub1ey zej+ huge range of sound levels. What is the ratio of highest to lowesezyl,2jbee+: u m1 w,x-1esgqvj6*h it 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. T;a) p;id yy5fphe length of the vibrating portion is 32 cm, and it has a mp p5 di;a)yyf;ass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental an)l8+rl;r bpffv+bf*(:a9 eia j 7 itugmdc//nd first three audible overtones if the pae/bpc*/ra7lv+itm )j(f 9 :dfrn8bilgu; f+ipe 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 blowizc3 jp5ko73- 1w djfsbng across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed 3pk5zj1-s d bowf73jctube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube poh6-8rvshe2,k xg e.shmk 0y7ka-)kripes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the l,eh 0.e-k6h hk2a g-srvxy km 7r8)sokengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency5)l9u j* j jmwgh12i7yv+houu of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of onljmjuug5o w 1+l ij9)2 h*7vyuhy 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m lok z5p1z2iahd;r/)dkgomo6,i ,yupi+ p(g h x4ng and is tuned to play E above middle C (330 Hz). ii21(5o ypr,x /ku,p)z+dgka;g4zm6o hdpih
(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 o4-tv mqff*7/hovx w c,pen organ pipe that emits middle C (262 Hz) when the temperatfwh-vqv ,o ft*c7 4mx/ure 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 cu:()hakuj d -p b-i2l i+a,pcat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpi+zvi ea-qru) ibrl5 fg((hx9. ece of the flute in Example 12–10 should the hole be that must be uncovered to pla( u(i air.gfevxhz)ql -b+r95y 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 at arhnvu*7x(/ek i5x z6rny other frequencies in between. (a) Show why this is an open or a closed pu/i5zr e *(xxkr6 7hnvipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open xj 0+ x kuhnb wj+u61)rxrt4d0at both ends. It resonates at two succu x t46h)0rxw urdn+ 0+bxkjj1essive harmonics of frequencies 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 ugm km ey;x*wq ,9k;9m$^{\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 fauf zio ze(4*6or a 2.14-m-long organ pipe at 246a(zi *fzoeu0 $^{\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 outside andxtf lo szudq3cn -;5 r/qpp(.* is closed atr ls q/; -3c*nox(futz.q 5pdp the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two strings, 2 ;,pkjo1(a izue 1 ecn4c;wkrone of which is sounding 440 Hz. How far off in frequency is the(cj c1i; w;e ,pe1zakn4r uko2 other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) and vc6;f cl/e 3jq$C^＃$ (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 tuy yc7* cf*y63*h(l7cz afdoat 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 ar f t7 6*yo*uhfc3cyl(7z*cyade played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuy74m ffan19lcjzc, t2ning fork and 9 be,c1f92camjt f4l nz7yats/s when sounded with 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 tension in o.wz,t mj,3v 8u lxgn/nne string is then decreased by 2.0%. What will b /8zut,nm 3gwnlx v,.je the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicaanqw 8mel(* 6d0 bfqk gswd xdd3(n-c6,yp*n7l flutes each try to play middle C (262 Hz), but one is at 5.0°C and the other at, m qydd dn0-*8 spbxaew7fnk3l(*6wcdnq g(6 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency ofziup :ngz 3e +l.d18hbe1et m8 441 Hz; when A and B arzpg m:el8but3 he18i1 zen+d.e 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 person+shdza 6f/ s.h stands 3.00 m from one speaker and 3.50 m from fh+. szha6d/sthe 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 vib0. vmp znl3/1qb lny1grating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togeth z .ypl g10lmvnq/13nber. (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.th 8+l zr 44smi5wdm1c76 m in air. How many beats per second will be he wscmizm 4 dr4+t581hlard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wov56 yyv (0kv*6gztt qhen at rest. What frequency do you dettt vk50g y 6(zv6*qoyvect 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 detect if a fire enginer bs2(9ljj2o a(ti,haf -gvb,ac(z) v whose siren emits at 1550 Hz moves at a speed of9 z r,(of)v-its(abgcab(lh v2 ,ja j2 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequencyf/uv (03o )f113tvxtepfotq9x e( ,trx8rtt z if a 2000-Hz source is moving toward you at 15 m/s versus you mq( ,u f(1) fxrzftoe9vtxtp380v1 tr oe/ x3ttoving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When on bq+gxr7 syf:8e is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat freqgr: q7 f8+sbyxuency 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 receives them hihq1 plt5(8k4fxln1 returned from an object moving direq(tl1 l n814kixh fph5ctly 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 e;2mg7ib.v )jngra 3 himits an ultrasonic sag.;nmi7)rb3j hi2 vg ound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exj-wwza4 sf+6q n8r-t fperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the szfnj- wa4r- w+ tsq8f6ame 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 ;fy w0nb oh(rw3,fl,uwaves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is takenuo3 w; (rwfh ,,fy0bln to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrv9se6lq(* dcn ) hzrdl: ;ts b-ve3y0iasonic 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 frequency 570 Hz. When the wind veloc/k :hwabe5(gn.),xgdr4 ,zzr ogc l8 qity is 12 m/s from the north, what frequency will observers hear5g:rge/.zwr zkh,x )bdl qc , o4(a8ng 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 objec bi zk y*kq;j4em-p8.ybg3a 5zt moving on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (amuh /v ;ppb :wks85jxu 7yd.x7) What is the angle tpwk7vm jsb7y u5hx;:u8/p x.dhe shock wave 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 a planen6kshof;:m0 g0rjn 0w +r sen2t where the speed of sound is only about 35 m/sr; ohkj+em600 2nss :wgf0nnr
(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 strf-r: oxp+ltc.s0j,dna 3 jc5rikes the ocean. Determine the shock wave angle it pro :dj rf5-xcc l.s03n,j +raptoduces
(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 oswl-,2bv- xs -/-cu+0st ma+gzcd(oh.nd ep$/theta$ 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 m8ui ul:ri,4s+rcc( kgb 2s6x above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. r6 ( uis:x+8m i ulgrs4cckb,212–34. 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-Hz sound pulses downwa jbqoy, 4xo 4f.kzzg3/rd from the bottom of tz .4fogkyq,3/ xbjo4zhe 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 th -21ajwv gdzak0d-b85k/hvope human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consist-;xuc4alkr3b)+-uuwy 2 vxg s s of many plastic pipes of various lengths, which are open on xu3c;24g+u sb v-r lua- kxw)yboth 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 clos238sim n;tnwgr6 dqk 9e to the threshold of human hearing (0 dB). What will be the sound level of 10n ; 3gs82r9mdw6 itnqk00 such mosquitoes?    dB

  What is the resultant sound level whe5fl gc*tw;(qiy, . b rn2g)rp+of sc3rn an 82-dB sound and an 87-dB sound are heard simultaneoi3b)cgc;wgp.qtf rry f2nlor( +,s *5usly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, isw29eu5je32mdktgs: e* zt 9u r 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in zsrtw2eejmu23eu9t : k*59gdall directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drokkce. 1p-bi,sw dq/+bps by 10 dB at 1s.pw,i1k+ ebdc/bkq - 5 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over, nzkoqs)4r58br *sl w 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 radin wlrzsok)sq, 4b* 85rus 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, th8* 9mr(ctamg8 3wi- eaftic) ge gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency *ki8x z e(f 4ft,*nvcf1$\frac{1}{2}$ 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 fixed points with adom60a a+beq3bt ;s/ p fundamental frequens+;b6mo 3a/epd0q tab cy of 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 into vibration above a vertical open tube filled with wa,(dahs uno 7.oter (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 is 0.125 m and d,ohonu. a(7sagain at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 o+g;pug04d c.jng4j dg is near a tube that is open at one end and also 75 cgp+ 44 cg0du. jnod;gjm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate k 4opwtunq80ll)e5le d/ it)3 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-Ho2+z:v, eytf /5sdehk z 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 about and fin2vo5zkst, hd: efye+/ ds 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. m* ef3.;ycrcyOne train is stationary. The conductor on the stationrc 3 fy;.c*meyary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam trainzn7 hn4qh2h1/b 0bb1gj y hje+54wox n whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was thj hz7b4n /5yw0+b4n2 h 1hxoghneqb1je train moving (assume constant velocity)?    m/s

  At a race track, youjze( 4t etm-a, can estimate the speed 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 octave (frequency halved)tme4-zj(,e a t as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequ j3 8ri- 6(5yk-rb8hzzqzssc aency of 11 Hz. The shorter one is 2.40 m long. How long is the otq(zz 35jk s8ah8by6 -r sic-rzher?    m

Two loudspeakers are at opposite ends of a railroad car aso))4 i dt0ktik lg-;es 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 helgo0) skde;ii -t)k 4tard 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 aorpo1l 9ws.v8m -i+h*a.d gln frta is normally about 0.32 m/s what beat frequency would youg1 .*lo l.npwasrh m-+vdi89 f 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 while0 8jljuzp-/ybdh)u 57bs.ziw 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 freq .uj5zljsb wib 8)-/pdu7hy 0zuency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a mosrfdr*y d4au k4s,/h.th. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detecte*44 dr/ha ks. fyurd,sd 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 to send signals from one Alp x:rv-nxp8w/7.w d d6-isfiet ine 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 nxpr 6tisd/ w:8.-d -f7iv xewopen tube.

  Room acoustics for stereo listening can be compromised by the preseb7ii ba20 wci(c+ kc,knce 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 maci7 k+ci20bk c ,(wbi 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 “sin1j9-bjb zrpw0rc -gq2 ging rods,” involves a long, slender aluminum rod held in the hand near the rozpr 0r-gb1qw2j-9j b cd’s midpoint. The rod is stroked with the other 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 thre1r:e / v55,f vyrm;h0os hmtdbshold of hearing for the human ear at a frequency of abo svv:5mbho;,th/5em0 f ryd r1ut 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 traveling9mmzw/wb:v lk9o,v0z q2 zes6 at Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is thelezw6 ,/:kvs 92o bq9 0vmwzzm plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is svf.i.mc9lg ; ip30mq 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