What is the evidence that sound z +z: mj3u(vtetravels as a wave?

What is the evidence that sound i ; q-btulax n3tx+.qggg3 ;k5fs a form of energy?

Children sometimes play with a homemade “telephon m)6:6 *z6rd u m8mufe-ipodvme” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the dmfmmermuz6o- i*v ):d u6 8p6sound wave travels from one cup to the other.

When a sound wave passes from air into wanmsc9/ geay *2z5rjpb4b6 2ol ter, do you expect the frequency or wavelength *y9l5g zb/4ncparbos 2 m6e2j to change?

What evidence can you give that the speed of sound in air do p do o86imra9gz,)g)ugu7/bbes not depend significantly on freqgdrb/ , )8iob 7u)g6mu apg9zouency?

The voice of a person who has inhaled helium sounds very hw)d0(fgjhj9y9,t d sgxk z26ligh-pitched. Why?

How will the air temperature in a roo3uejgknn cp1l.7 b)9u41jmrxm affect the pitch of organ pipes?

Explain how a tube migmy(newi - 0s rq;h1o,u8zd5is ht be used as a filter to reduce the amplitude of sounds in various frequency rangesy0- 8,qdsi(swh ino; ru1z5em. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you mor:k88(kr vcjg srpn 7*2zq-d zve up the finger r7*28sz qd -cgnkj:pvk(r zr8board toward the bridge?

A noisy truck approaches you from behind a building. Initially you h ak403x,di2ibr ttlb( ear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 id3k 4b(lb,xt t 0ria2on diffraction.]

Standing waves can be said to be due to ;3at p:.xvugv )xw2fy “interference in space,” whereas beats can be said to be due to “interference ipu;:xg v3vx2).yaftw n time.” Explain.

In Fig. 12–16, if the frequency of the speakefk-nnm:-l5y s :b xg4krs were lowered, would the points D and C (where destructive and constructive interference occur) move farther aykl:k:mnf bnx 45- g-spart or closer together?

Traditional methods of protectcph ztk gk+(ize j; 2;e35zq-king 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 which detects the noise, inverts it electrone+c;5-zjkkeph(iz z3gt k q2;ically, 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 s b 60,; w.hs6sou qjp-ozark7nhown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly differ,h6r -su;sw6 zn7p qjb.ooa k0ent 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 tq9u2wxe1 ftwa +k0q bi 2dd9n4he source and observer move in the same direction, with the same velocity? Expldi+ nxt4eawu2w 09q kfb19dq2ain.

If a wind is blowing, will this alter the frequency of the sound heard by a perk7)g(s8v y .d4yy/ fgwudgaw5mrs o +,so.gdfs /, ud7y8k+ywr g m(vwoyag5s4)n at rest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion l +cyw2g*5e qcc3vdi 3bvm;tt 2;r. veon a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the cv; 2t*e m .5;3t2cqlvwrg e3iccv+dby hild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening ar) le8,ynms rxh77nwl0+ yk8for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the la)8+ nwya7hnresx08y rkl,ml 7ke. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below knxul,mt8 j x.+ag/ d/the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is a/8ku /gt,+nj m. xlxdthe 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 3wmn:melbjd)u4ww az *-8zj; 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 fo dq44xy68jgx xggy day. Without warning, an engine backfire occurs on another boat 1.0 km4y84 jxxxd q6g 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 spkyai x4d1,h6olash it makes when striking the water below is 4 dahk6oix,1yheard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stonew 4 t(bux5y3to strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far aw 53x(u4wybtotay did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by thek0cmh: yg8e1*qnnvff +9g/tsyv0;q u “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 3;mvkyn9:gfc0+8gqvqsn e 1yu 0*htf/0 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun33sv,vyt r*mra ;fib8 pwz*n4d 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 mz mw-;6j,+raxx;m jww4q zb6 whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firez.,hnsei+)uiu-w h6 e d simultaneously at a certain place, what will be theeuh s-iei, n)6w.zu h+ sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dist 9a:4gvizh8s aoym1(tp4itjo 5 a z)n*ance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level waptzo(5 i asgztjmv4 iy)*84an:91 ohould 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-to-noise ratio of p1 ggn r5a7 :wfc0fd6n58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eachwa0n7rcn56d gfgp:f 1 device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the poweq k**nbrpnunh(. 8 d6lr output of sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformlr k * 8h6nbdpunl.*q(ny over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose xkm0zhyi .kxpf0kt, 3;d./owarea 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 a)sbe-qui ygo24g n 5;xt 250 W, while the more modest 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 loudspeake i o4q5yg-2x;bn ug)esr 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 rvpkc. k0lub)q3ci m-1egistered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. c umcq-bi )1kvl.kp3 0
(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 differeeecfo 1zk6d3qj +d(od no*80knce in sound level of 2.0 dB. What is the ratio of the amplitudesqf6 *18od+kedoz no 0 c(jde3k of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will thk .(lu9 gc*f 4t(ruhnziirk.( 6nym6ye intensity increase? 6c tki6n(r. l*fgyh.n i(k( y9r 4mzuuIncrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bu8i1d )td-3fb9fgnhlm4 ,an 6nw2qei st one has twice the frequency of the other. What is the rae l9it-nffnid )3 mga,s 1dqw4h862 nbtio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corn: : ug,9cku/ ub11gtxl 2ticmresponds to a displacegnmx1ku 9ubct:glu 1 , :ct2/iment amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leveo gvdm1+k1d/ bdu,pa2sm u+j /l to seem as loud as a 100-Hz tone that hm1uk+opdddv +a,g /s/2um bj 1as a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest.g pby1vv1sxq z9v (w1 frequencies that an ear can detect when the sound level is 30 dB? (See wpb.v1 vg(9v qy1s 1xzFig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. W2;bmn5jagcf -l1 r +kv 4bir+/sm)juyhat is the ratio of highest to lowest intensit rm5kri jsb-bay4f;nmu l+j/1g v)+2cy 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. The23x(rq+njbdz length of thj(+dq2 xbnr3 ze vibrating portion 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 long. What are the fundamental and first ( 8i tdo*hx i*u3wp9 ge6tm4lxthree audible over*8tgtxw4idu 6 loixmep9(3 *htones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from:w*qg 0pzk3-o m 6qcsz*gc8kxdjv1 h1 blowing across the top of an empty soda boqkdkhoz01 6zqxw -: sg 3*mcv8*1pcjgttle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spann9r gl7n0ft; r2ddjme 7ing the range of human hearing (20 Hz to 20 kHz), what would be the rangetr dm27r7;jlnf9g0 ed of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harm) e8 +u * 4mhuzjjt3lcbfj1tx7onic. What will be its fundamental frequency i+4juz* ucfxt h1e38m )jtj7 lbf it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is h 9w24+7xogvy-gi efk0.73 m long and is tuned to play E above middle C (330 ih 49 gy +x72kg-fewovHz).
(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 openvu /f5w ) s*.pwf:(e jfm3 7tnvbfu3aq organ pipe that emits middle C (262 Hz) when the temperatefuu)(7m w3q *jtb:vnp.5f3vf /wsf aure is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2:o fdn-6us,zd0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example g6ka+m w ndl3g12, ten12–10 should the hole be that must be uncovered to play D ab mk3a2nnd 1 gg+6wte,love 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, 44lb:c;f)(ie l5 o.nsqg5s: iz *8vqns f0 Hz, and 616 Hz, but not at any other frequencies in between;eicosl8 5 n:zq .:v lsnbq)(5sfigf*. (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 ezrj cjyn; )/2resonates at two successive harmonics of frjr) ;cnyz2j/ eequencies 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 u61l ;3+2q ziavcrpwi2l vo/v$^{\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 rangxxhy n);0un izkzf k 2gr-9ue112.clhe for a 2.14-m-long organ pipe igh ;rkcnyz- x9lhk1zu ).u1f2 0x2n eat 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 outq xy654 th;yweside and is closed at the other end by the eardrum. Estimate the fq4yt;y6xw he 5requencies (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 wh3 mx/gclhnso++o0c6 w en trying to adjust two strings, one of which is sounding 440 H /hs3cmgoocxwl0 ++6 nz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) anx ws 6u;zpj/h-d $C^＃$ (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)x5w7. 4ph:iaktnt9nn: z jr;x operates at an unknown f p:.w 9rtj4azxt57;xinh: n knrequency. 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 beatcx z7app :m/p+s/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain you xppmzca7/:+ pr reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one4rn9zqqo. l+z cmu72e string is then decreased by 2.0%. What will be the nem.7olr z4 +zq9c2qubeat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two idtwxyu8/v k/f 0y9 q*fjentical flutes each try to play middle C (262 Hz), but one is at u 9x8/v/fyy0fqw*jtk 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B ha/cb2k;o *4g owei xt.fvx: e7vs 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 fvxk* 7/x.fwtee4 c voo2:i; bgrequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one spe0s stsbv : ix-,*sw,tuaker and 3.50 ms sv0 :sisbxt,uwt*-, 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, but a piano tuner hea 5 zc (g-gsocjxn9;5yu c0ejl6rs three beats every 2.0 s when they are played together. (a) If one is vibratingj jugo96s l5 05cex (-znc;gyc 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 wavelengthsw.i ,o:nrasxi3 ,kwq ) 2.64 m and 2.76 m in air. How many beats per second will be heard? , ,)oi:wwq3asin x.rk(Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a c uhqg 1qiha.,7o+lbs.) +4 hhqish9 udertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if iduq4b.)s,q+h h9h.+qih o s7al 1ghuyou 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 vr72x qw*m-x;s j 3oqwsvh4x: c,j )kwdo you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of xkw7x;hm* ,rs qv2wjxw)s3q4v o:j-c 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a9w-a9 hst6 cdlnew:z* 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exac h-ezswc*a: tn9wl69dtly 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 sd ec.1*zb1 pe,/vkp sxingle frequency horn. When one is at rest and the other isk,x /s.e1 p1pe*vz bcd 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 re7 8 0aw34hcs2e-0vfpcid f galturned from an object moving directly away from it at 25 dapgi 00lsaec 4f3c2 f87-wvhm/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wallyt,.v jxnv0nl-39 wpa 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 reflected wxlp, nayj. wv3v-nt09ave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moftv q btr *1n9:ozr:0jving flat train car at a frequency of 75 Hz, and a second idenv 01:fq*br: joztn9rttical 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 waves to measure blood-flow sp7t+17ene bt-avyb +s beeds. Suppose the device eme ne-t +sb v+ybt7ba71its 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 away from the sound source?   Hz

  The Doppler effect u :u n9mv1 r0 gtth1wzyof*(5cvsing ultrasonic 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.3/e uw3f-x ov*yudu x, When the wind velocity is 12 m/s from the north, what fre3dexuuv y-/xfow *,u 3quency 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 movingflbs8jee )buk*6 5vv vby sn0379d xt) 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 wheq b-mk*t(j 5kvgdt 9k1re the speed of sound is 310 m/s (a) What is the anbk1 jq tdkkmt5gv(- 9*gle the 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 planet whe0 ld- g1:6n hug;oocwjre the speed of sound is only about 35c6ug0wgh :1d-ol;nj o 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 zoqi3 4kvl2 *swj: kt:ocean. Determine the shock wave angle2jz sk:ilowkv q43: t* it produces
(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 )2kg5 av kq 4ephg4u6i$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead w+a.q* 7 v+v witks:kcand see a plane exactly 1.5 km above the ground flying faster than the speed +k7+:k svivtwac*w.q 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. 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 x0*x i:* ftv d d.fcujjg(m-s9sends 20,000-Hz sound pulses downward from the bottom of the boat, and then det :c m*fgvx u0*-9s(d.fdxj ijtects 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 zy+j5 sog6q8crnt 4 qp6ee4v7audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It co0 r0wrkl.q.fk4;6fe/5(cnurk ge nmdnsists of many plastic pipes of variou 4(eqcmg.;nk/k0rf5rluf .0kn e r6dws 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 :nxe ;xsecgcd zukpy 5)25pz*1 )x1caa sound close to the threshold of human hearing (0 dB). What will be the sound lev)zxkdu ycs2c pxacxn)z5g51 *ee 1:;pel of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-2y* 9h-o fug)swhuv;t dB sound and an 87-dB sound are heard simul9-;2) tuwfg usv*h hyotaneously?    dB

  The sound level 12.0 m from a louds 5g/u 2ww)l ikp*uoxa5peaker, placed in the open, is 105 dB. What is the acoustic power output (*5po)2a5iw xkug/luwW) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 xvyjs . kzv 4q/nk, kww,6 vuk63-wkw9Hz. The power output drops by 10 d/. ,vkwvuk3k6 wy4k-jns6wxz w q,k 9vB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviceaz5nzu mm75n2sj wthe zz;x:p75 s38ns over their ears. Assumeuszh:zz5m 8 n wtn njz x;2sp75ma35e7 that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communivlm.9t8ec.p;7s ci) w pr gf7lcations 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 violiin uc34si10l ii2djxn1/w f:bn is tuned 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 hwrxv )q0i 8vzri:+ 6u *tau*ois 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length oft*:u i 6h o*vui+var0xw8z)rq $6.1 \times10^{-4 }$ 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.b: el tf(qz5d 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 at 0zf(5qld . e:tb.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that i)*f lj,.h/ xzzdxr4ch s open at one end and aljf xh zr4h*xd.,)lz/cso 75 cm 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 5hiaos +x qq0m(arv6ih m8-m1observed to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from twabbz*65 ctyr e*nf3r4o sources. The sound is loudest at points equidistant from the two soa z5brfr*6bt4nyec*3urces. To 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-Hz whistles. One train is sta ( h:-orfs6 k1)mdkzesqoah+(tionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the+okhmr)((-ssf qdk1 ezh: 6ao speed of the moving train?   m/s

  The frequency of a steam train whistl- bt campe( az8e4z- h,hqwo00e as it approaches you is 538 Hz. After it passes you, its(q0ea -z4mpw0o-eb8hath,cz frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lisp.ison5 vu2 u6tening to the differencen uip2svu65o . in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, p6daj vt0 x;4v(4beai lroduce a beat frequency of 11 Hz. The shoe46x( jb di4 ;atvva0lrter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a ss hyy,ggo(8z :a/oj a6tationary 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) h6z8og/o(gay:s aj , yhe 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 qlpk*g4*o 3ob aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waob g*kpq3*l4 oves 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:3pcj ih(sv gdyi95s: moth at speed 6.5 m/s while the moth is flying toward the bat at spe i5ypd c:iv(3s:ghsj9ed 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 that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulsesr(qnyh, l;4uz as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that (zn;u lr4, qhythe echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from oyy xx+j .3 pvm5/fkh-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 instry-jmx +.o5hf vx3 kpy/ument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can b yatm(m1-6yjwe compromised by the presence of standing waves, which ca1m(t-6mw j ayyn 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 frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendecnvt5i44ab+xt93x c98 gfzxz:) px aur aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a c 4nufz45xbz g3x+ p99taacxc:8 xvi)t lear, 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,; 6j9pb.kb+o jpxd(y yb2 ivteshold of hearing for the human ear at a frequency of ab o yjp,y+j9bpvtbi.62k ;( xbdout 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 observer on the ground 3pc947y 3uso ziuf 8+nrq*wivm +l ;yehears the sonic boom 1.5 min after the plan+oie3; w8vfmn4uq+yy3z pu7sclr i9*e passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat-yex*9g dt je))zxz2 e 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