What is the evidence that sound travels as wlhk (je5 /tx4a wave?

What is the evidence that sound is a form of enervpk ja.p18 ic)1gfw v k-ylfv5936oitgy?

Children sometimes play with a homemade “telephone” by attaching a strinq7wao d 1-cjo+c0i pu,g to the bottoms of two paper cups. Whq 7 0oica ou-,pw1j+cden 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 into water, do you expect the frequen,unf l d08a-vzcy or wavelengul-,zdn 8af v0th to change?

What evidence can you give that the speed of sou)v2 oj5c-lptwil3mm8y j-yl. nd in air does not depend significantly on wvot p3m 5lim-)j -2.8ycyljlfrequency?

The voice of a personb5 m (7hw0:r za8+wwvwqm1bfn who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of ol9 wacoa x* :rxs:h8o8rgan pipes?

Explain how a tube might be used as a filter to reduce the amplitud1fo p*z(w yr.3 retj49ygyxd:e of sounds in vaex:. tdprgyw *y yo91fr3( zj4rious frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) r tqn/f((w + xix)yyqn4yu8+wspaced closer together as you move up the fingern+y/)8iu(wx+ytyqfn(x rqw 4 board toward the bridge?

A noisy truck approaf cr nro0v7 nrza8u6w 8s*u21kches you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-freque 10rna uonr2 uzvk6r f*7c88wsncy noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfer,dt f gl28+; ; /+aufpllxersqence in space,” whereas beats can be said to be due to “interferee/ l ts+f8d 2f;q;xll+ga pur,nce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would 1 +4z*pu*q we)i vodzythe points D and C (where destructive and constructive interference occur) move farther apew iu4pq 1*d*)vzo +zyart or closer together?

Traditional methods of protecting the hearing dpm.gylk 67tiw/o* l0of 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 which detects the noise, inverts it electronically, tpw6k l07t y/g*lmdi.o hen 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. Each wave can be thought of as a supnv p-a9i1a c3wuncq68 h ae94merposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) oaa vnp199h8 u6ca -m3iecn4w qr (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sou)b d.-* tk,0gtwions yrce and observer move in the same direction, with the sam-, ig0 tdnwyk.*s tbo)e velocity? Explain.

If a wind is blowing, will this alter the frequency of th c/w/lxj.ylxg,jvpq v; 8nei68b 1qo6e sound heard by a person at rest with respect to the source? Is the wavelebgxvej1ynq/6j;qlp6. cl 8/8wix ,v o ngth or velocity changed?

Figure 12–32 shows various positions of a child in motion+inongq8ken j/q5bl4 w; x*a0b u,b0m on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound ofb+xnnb/i , k;e 4 lg5mq q0bn08awouj* the whistle? Explain your reasoning.

  A hiker determines the length of awnr fe1nu1a46 lake by listening for the echo of her shout reflected by a cliff at the far end of te4n6f 1aru 1wnhe lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the s6082 /*qu n zeowt0ppfadrh,pide of his ship just below the waterline. He hears the echo of the sound reflected from a ptpdoh0f0q p8e,*/6 n2zruwthe 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-br bc9at wq-+ $^{\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 boatq*skgnx0 5dh u- kgv+w o93tk( is drifting 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 befoqo - ng90k3t(sw x+gdk*uhkv5re the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top ou 1c6fjp0k- f :y*obijf a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is th10p:fj-jo 6uk*f iybce cliff?    m

  A person, with his ear to the ground, sees a huge stsik55wwfb phn -; 6n1e r5r(drtbsx5* one strike the concrete pavement. A moment later twe(1h*d5r 5ik t; bx -brnp5w n6f5sswro sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made o:yuk2b;h3l ya ver one mile of distance by the “5-second rule” for estimating the distance from a hb;2ual y:y3klightning 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 ve*qvh7l81 hyu w6l;l120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound leven 6oufao) k o00u kywe;yc8 0g;hf,wzpvs7)s+l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously1 e1esfc(puz/n lz7j- at a certain place, what will be the sound level if oz l1j( -nfe 71pscezu/nly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplanj1c4 ).68vgzp )nxju h zdogw)e with four equally noisy jet engines is experiencing a sound level bordering8vw)jzpdxz).4j c1u 6ggho)n on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to3-a 6yuv3v :wvi9rczf 0 -fyxh-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each dewv0rhv3f9v -azx 3y fi:uyc-6vice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speak0/7u s xavg zfp(uu7n8ing in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mou/(asznf7u 0u8 gpxuv7th. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose area ( wmcum:j//m pis $5 \times10^{ -5} m^2$ (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 modest amplifier B ilf8 oac,7lj3xs rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeakeo j,al73lx 8cfr connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in /* sr f(.aala0 soe0pjfront of a loudspeaker* 0ssp(fa j/0roal .ae on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. W 7b)7gdkzsrl: hat is the ratig7b7ds zl: kr)o of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, l(f ra,m)bhmicr g2wb 1kr 68;(a) by what factor will the intensity increase? Imkib 8ar2 lrw;fm,1r()c bh 6gncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplituejfb v1lk.2 t-des, but one has twice the frequency of the other. What is the ratio of their intensities? -2bk tv.1felj  

  What would be the sound level (in dB) of a sound wavcbz.uil-( pdt(j8bd *e in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 8dp.bbd-ut cji z*( (l300 Hz?    dB

  A 6000-Hz tone must have what sounod +x.o:e1ol bd level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 1.eo d+b:1xolo2–6.)    dB

What are the lowest and highest frequencies tha*z jkjp;4jb 1at an ear can detect when the sound level is 30 dB? (See Fig. 12–6.)4j1j*j bzpka;

  Your auditory system can accommodate a huge teg*-d 2w: klgt96zn drange of sound levels. What is the ratio of highest to lowest intensity at n :de- zwgtdt2k 6gl9*
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamentjp+:sqc7 a ;ptal frequency of 440 Hz. The length of the vibrating portqjt c:s7;p+p aion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm lonx*afn ni7eg e4nq ns w2t+-t0;g. What are the fundamental and first three audible overtones if the pipwn-gs40e* eqtxf ;i 7tnna2 n+e 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 f2;1lcb0exrjy4y2s7z so /s in x 7u*edrom blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed 4 ioxcus2e701b;e /dyl 2*7z yj srnxstube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipea:l/(5u 5ma e 5ifarnq organ 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 re( nu5m:f le5/i 5qraaaquired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itsw,p1m *ucu0 fb*5sfo(xk kxz8 third harmonic. What will be its fundamental frequency if it is fingered at a length 1 kp 8xbkffz*cm(w5 oux0us,*of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abovr usd6a9k/s z*e middle C (d kuas/s* r69z330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middiawka-e x6- bw +bs)d;le C (262 Hz) when the temai+)6b ewaxsk bd--; wperature 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 kj3lzkwx ujw h;-t(9)at 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flun1z g.d788orol a.wqv te in Example 12–10 should the hole be that must be uncovered to play D above middle C aq o8 .rowad1lz7 8n.gvt 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 res)tcxkv56o d*l 35o apyonate at 264 Hz, 440 Hz, and 616 Hz, but not at any l*6 3oy)d5ovka5ctxp other 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 tube 1.80 m long is open at both ends. It arwo,laqu:z 54 vr7: kresonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What ikzaar5rl:74o wv: qu,s
(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 ;vb u. oqpc) oh0+7qff$^{\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 an1d 52to r, (u/i0ptnzj 5b 6k.p/rcjks4m jrrange for a 2.14-m-long organ pprkjs j4 nbuktrm65 /j nc.1oda z5t,r 2p/0i(ipe at 20 $^{\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.x8v2 qa1i lien2a*gt(u 9bqb p(e3ho outside and is closed at the other end by the eardrum. Estimate the frequencies (in the .q au2qh *ab 12pti8( vigl(xeo 93bneaudible 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 qjxb4 xx,i. ;oto adjust two strings, one of whq .xxoj;b,4ix ich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hs b ,/o4phj7cvz) 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 ajfiec(bjl:;udn9 eg)*xm 8 i5nother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, bu5;dnb ulcej m eg8ij* i(x9)f:t 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 a 350-Hz6kp n 3sop4r9v tuning fork and 9 beats/s when sounded with a 355-Hz tuning f 6kv49np 3porsork. 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 iy-nimw f*, oam b+n4/xn one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playe-a w,y4/mm*obnf+xi n d together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if twr3tb d v96js1uo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and thusv 6jt 9r13dbe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuningx3y rd8mr/q( c forks, A, B, and C. Fork 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? What beat frequencies are possible when A and C are sounded tog8r3 xcy/rm q(dether?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are zi.ump ugei7u-7l1p9 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the ot.u1gl-uiu z me79 pp7iher.
(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+ jq. 5n+ger29bm:l.hthch l z be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibra+t+ lnj.chb :lem zhgh 2r.q59ting 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 s wqw(m yg,gz e8n83ya*.213 gysenjrwz p6(rm in air. How many beats per second will be heard? (Assume T =3nw wgy83ryzrp(e8 s6n 1ewqs ,ma2g(.yg*j z 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire envk sj,jk 7:xvvog, us,1jms7 /gine’s siren is 1550 Hz when at rest. What frequency do kv/v js:jxsv,j, s1omu77 g, kyou 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 detectm4q9 +fho0wfdk;aqo2 if a fire engine whose siren emitdq fakfoq9m2how+ 4;0 s at 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 source is moving towarcj c(0d8 n3tr4n rnb8id you at 15 m/s versus you moving toward it at 15 m/s Are 0id8tcnbnjc4 rr(38 nthe 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 one is anulk+u,v9i* - a qtwq7k )+qoqt rest and t+un- )qkilukqq ow 9t7+v,a*qhe 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? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ldz cy5z:/oa4zf gt ;j d;(s8kreturned frojz 4a z5dl(oz8;sd:cty g/; kfm an object moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a walnv-0 o+5 ngyimplq4i2l at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. 42yqgoninl50 - i+vmp What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on qefbl7u v/4eb ( 1x:0qpi7g rca moving flat train car at a frequency of 75 Hz, and a second identibulp7qf(v0b4c7 :ix qe e 1/rgcal tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound zy7+o1gc-v i* nt+y tdu (ug/fwaves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequ* gf dy-(uovg+cy n1t/itu+z7 ency 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 frequenc/ meo3)qle1t,vkkar 4y $2.25 \times10^{ 6}$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 emit(7xp,p e vjsw(s sound of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observer(,w7 (epvjxsps 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 spee-szh-n y/7 :o, lulrymd 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 dx) (s:old+1gc q5x ycb wt6)sof sound is 310 m/s (a) What is the angle the shock wave makes with thq56b )+tw1(dcxsl:y d)gs ocx e 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 planeb,9 rp a7c+cwef 1i8ibf b(gs/t where the speed of sound is only about 35, /fe cba9icgs+7 rbpib1( f8w m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the5 bjam i(qln;*z-s qw1 shock wave angle it pqi;5ab(l- mn*zs1q jwroduces
(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 ew m(8l0a5qg+u4em+ tn. b cxme21kdj$/theta$ 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.d qs3 /):q4qxclk lnuy.3kaa1 5 km 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. 12–34. D lq4s3c 3)qk: xa/yud1.na kqletermine
(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 downward fro zukc- dtp e(mj7 rt591hr0rsv:5h m,rm the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed s 5chmprh9t0mru 1,v(rz rdte5k-7 :jto work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there p(l 9,+o6:gj aninmib in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. o 0 7dyskwx;pf :pcu5;It consists of many plastic pipes of various lengths, which are opensd u ;py0w;:fp 7c5xok 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 fre x8,qlz 3cno)ly 5y9z;p6yqwom a person makes a sound close to the threshold of human hearing (0 d yzpz59 lloqnq w)3 6yc8e;xy,B). 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-dB spo8v nn m6o:7 dx4p5cyound are heard simultaneouspm:cnx o y6 o8d45pnv7ly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the k1 vh86t xgm-wuq4f -kopen, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?-6- mkhw ft4gux 8vqk1    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power ogpv d3,i -0cfjutput drops by 10 dB at 15 kHz. What is the power output in watv,i-gd 3 pcfj0ts at 15 kHz?    dB

  Workers around jet aircranlf7w u3x/9nj 7ty52s 5 sukyk /xvsc4ft typically wear protective 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 distance l5 32yxs7xw7k5csnkn 4/uy9v s/juftof 30 m from a jet airplane engine?    W

  In audio and communications o8c+h4npq*k-enwvd -m n,thqwz)y;, 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 tuned to o347;bu k k pqfjg/7mga 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 fixed points witln;h1z.z2o ,bz*xu kth a fundamental frequency of 440 Hz and a malh,zz z b;*2.t oxu1nkss 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 inkxz3t cl 1d6-.kwrv;o to 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 tuning fork when the distance from the tube opening to the water level is 0.125 m and again atx3 c-.z1ko;wd6tklv r 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar stringz4oq83 m .d8aex vz8bz of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (3 zz8dqvmx8aze.48 obin its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r,qj;n6ep1( r(kksxu mz kpwld ;bj4*,esonate 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 tj9 9hj8eakx m/one in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine8/hkema9jj x 9 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-Hz whistles. One train is sta mcsk-ausjdq1w9:v2 ) tionary. The conductor on the stationary train hears a 3.0-Hz beas-d9acj 2) kuqv:w1sm t frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as m qonp.0o 9)punp;e t,it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was then)p .oqo,p etmu n90;p train moving (assume constant velocity)?    m/s

  At a race track, you can estimate nktg2fz, 99n4n-y g pathe speed of cars just by listening to the difference in pitch of the engine noise between approaching and recedingnp-gn9kz2 gn4fya, 9t 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 a beat frequency of 1ujv/kkb 9u4qwed2v/6+79vu g 3 gonxy1 Hz. The shorter one is 2.40 m long. e/n7uk4 9 dou3g+xjv2b/kwyv u g69 qvHow long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves kbylw2u26d+ z past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers a6+bzl d22 yuwkfter they have passed him, at C?

  If the velocity of blood flow in the ad1 tspj:x+ r3ah 3/pxborta is normally about 0.32 m/s what beat frequencspp+ r a/1j3 xxdhbt:3y would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speelbv)6*zv8s age+n7q o d 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz7lbz+ o8v nvas6*g eq). What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it appms h++xyif ;3t3/c( wh-v zqtoroaches a moth. The pulses are approximately 70.0 ms apart, and eo+3i3 tq+z(;y xhf w -svmc/thach 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. 12–38s)m5 yj2an a buj35c9t) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The moca ba52 u5nm3ty9)jsjst 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 listeni/6umkbde/8 fk m lsz.h+ -r9pwxpfn +6ng can be 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 fundamental frequencifb.u mf+hep9pxdkn +-k z6rw6/m /s l8es for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “s e5tl9( m6-yq6smqn(qgyp2d finging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand.fmt 6l6( ymq-e pqq(5nsg 2d9y 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 threshold of he2atsl+5l wc*uueq w96e *t:ub aring for the human ear at a frequency of about 1000+u l weul5*tetu2 :c6qsw* a9b 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. Adsfne )dkrkb59i8 1/ixvd 0o)n observer on the ground hears the sonic boom 1.5 min aftekdi5xksd9/0vo )e)ri bf d18nr the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb6ks-g hu wa f7mwh *j105zud5xoat 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