What is the evidence that s n8z1c.wrcs 4fln )3djound travels as a wave?

What is the evidence that sound is a fojdyom .vm 5;3.ba6aoxrm of energy?

Children sometimes play with a homer m-0m+i-2 pm9 9hrjyzawf /dsmade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cupf /hrmmd9 yr-jz amsp-wi+0 29, 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 frequency or w0y gj 2ons1e7n6r:u+sz wcsn 6)yj:fxavelength to ce7gns :y6ryfc+ :zx6sun j0j)ns2 ow1 hange?

What evidence can you give that the speed of sound in air does notjjm 9o6oq.+d d depend significantly on jdq o+m96. jdofrequency?

The voice of a person who has inhaled helium sounds very high-pitchep dy in)x r82-d,4plztd. Why?

How will the air tempera hq/ymc4 11 n2awm1ckmfpn1b5ture in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude +w astr3k+p 2iof sounds in v ir+s3+a wp2tkarious frequency ranges. (An example is a car muffler.)

Why are the frets on a guk54* yc)dnmjnitar (Fig. 12–30) spaced closer together as you move up the finger)yj c*n 4nd5mkboard toward the bridge?

A noisy truck approaches you from behind a building.uq,w. e z:3u 80i,zwq9dppcr p-be 2dp 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-frequency noise. Explair.qedzu2:bz -e,pwdwu 8 iq,p930pc pn. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interv(z28mc0ovfky .d a)a+cy.v+ xl *xfo ference in space,” whereas beats can be said to be due to “ vy f82vaxocmxo+ (*zvy.d+kc0fl ) a.interference in time.” Explain.

In Fig. 12–16, if the fre-ixbhl:6 zzwmex(79ly 1q fs2quency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or c z:b 1m9(2qslelx hx i7z-6fywloser together?

Traditional methods of pr 3l eijctz0g 0em/kkaz e()q/y-hl 9a7otecting 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 ga3c(t l-eh/ikjzq ykez am)l007/9e 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. Each wavaa.9/4g jl kjpe can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), areg9 .jak jal/p4 the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obsel7d5*ml)fv90frh q ff rver move in the same direction, with the same lffffr*dl)m7 h5q90 vvelocity? Explain.

If a wind is blowing, will.nare)dt: lbhwb n,0o ):m2nh this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocityn) lme20,)hn:bo wnba ht: .dr changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitob+)r5s rp f7dyze8bw:r is blowing a whist)58bw7 fsdpe :br+zryle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her m.x4*ur qohl-shout reflected by a cliff at the far end of the lake. She hears thho*.u q4l r-mxe 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 belowlp0u / 7ftjc4 s3omjh.c)f lm8 the waterline. He hears the echo of the sound reflected 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) an l3lso m4uff )c/htjpjmc780.d does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at zsirm1drk7h2f : pe.e0bp: o+20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. z1;i: (eegtbt Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How muchz : ;ttei1(bge time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frto6:/jpf 4s+lpqdtf 3om the top of a cliff. The splash it makes when striking the water below io/p f: +3tlt6dqjps4fs heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strikav7)pn,osom 3 e 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 away d7ap,)os3vo mn id the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ovs/s mc9l0*r cuer one mile of distance by the “5-second rule” for*lus/mcc 0s9r estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain 8az/c:h n)d w plk-9pilevel 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 *fhuo-e .,fyc a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound lev a 9p0pbe gjbo6j*dgyy.q 32d)el of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hin09 .pae o dypggy 2db)63*bqjjt: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplvdg w c+; ) d-q/94yzoulbwr9uane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the c ug+9;)y-dd c/4o9q vbluwzwraptain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is sgr+6 s; idgw8faid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities os rdi+86g ;fwgf the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power u 4wgzz0cqa.e 6qo e1(output of sound from a person speaking in normal conversation. Use Table 12–21uoeaecgwz4zq6 0 (.q. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whos.+8hw 3gubcg g8v3dtyzg yhc i+g,9c );co s(pe 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 )i *azf ic.4) y(ytrkjmore modest amplifier B is rated at 40 W. (a) Estimate the souniykiy ))f.ar4*ztcj (d level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in qrdh3 e;87h :tyt+lrz front of a loudspeaker on rdzhl7ety +8hq tr3;: 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 so k lnbl j q vc,7aftj6+9-7w8nh5ls6pyund level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount?ck-lypb+ 6jntvls, jlf76 h 7q95n 8aw [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trip pal +i-( /g-pgelsxfci,s1(nled, (a) by what factor will the intensity increase?+fsl- ,c1-psp/aigl e xin((g Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacementoh/ 2w)fyk:su amplitudes, but one has twice the frequency of thw2kfyu):os /he other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds wut9d p;5ad /bto a displacemed;wp5tub da/9nt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what soay1x (m sxs:- q.,rm0f+nq zqpey e.(sund level to seem as loud as a 100-Hz tone that has a 50-qq mf0rz.:ypenm xse +x y,qss(a .(-1dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that afrf( l3:6myhjh0 t25leg byz. n ear can detect when the sound level is 30 dB? (See Fig.6 t ( he53 lz2lm:0fr.fgjybyh 12–6.)

  Your auditory system can accommodatex(n7:ld24;o fzo xxsm;/uy tp a huge range of sound levels. What is the ratio of higx;;4xo7u2y( o sdf tp lzm:/nxhest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440hx0f x .vyre66 Hz. The length of the vibrating portion is 32 cm, and ityr x06h.x6 vef 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 three audiblem-0-cd+p ca xr overtones if the pipe is mrdx+ac c- 0-p
(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 woulg x-*8nxxtolb 4 i8t;md you expect from blowing across the top of an empty soda bottle that is 18 cm deepi-x;xn48o xttgbm* 8 l, 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 pi6vf4mpx.o 3s tpe 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 o36.xm 4svptf 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 harmonic. What w)vg 0w0yb2nwi y g*)oeill be its fundamental frequency if it is fingered at a length of onlyinw0b)* gyv 2)0e wgyo 60% of its original length?   Hz

  An unfingered guitar string is h aoc75opkoypp3ady0768 9fc 0.73 m long and is tuned to play E above middle C (kocyp76d0o358cyafa9h 7ppo 330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) wheno0gl-tgse/.o,b 3cmqpw 91u t the temp ucptsegq ,mgo3 -l/ 0.1t9obwerature 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 attdbz4+m t5i w0 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should theh5lr;l 6wq:k2)i gz:cyy*- i bqeqge( hole be that must be uncovered to play D abovbc*ig2 e5 hl-wg)zqkqqr i:l6;(y y :ee 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, :zj8*8er, 1xe5;giafg 3y)5 wpb4 zpdqa qoeh440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closed ph;x,wj ep4gd3iogb8 fy:z z1q5 apa85r e)qe*ipe. ----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 reso2a gy- vwf1+ez yv+8bknates at two successive harmonics of frequencies 2758-k +ab1w+ z2ygvvy fe 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 d0 psg-qjis.7$^{\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 presetfgnm;5od g l 2cn3)2hnt within the audible range for a 2.14-m-long organ pipe a3n2g ;n)dtgh 2mol5cft 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 outside ds.wza20bqt(b l5g n7 and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the2w50(banzq. gtldsb 7 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 beatzf7c cr58lx 53r4r nez every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How fa5l 8crz e 4cznx75rf3rr off in frequency is the other string? ±    Hz

  What is the beat frequ):vdn0;tw hhri+zr3 a ency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates at/xq:;,d an7p4 iqd-s i.bqfyq 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 are played simultaneously, estimate the operatin:yaqn.di;pb q d s/f, -qqxi74g frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 3503 w+n hgggej57-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your r3ne wgg 5hg+7jeasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The y.s*b loky glr;,.xa 97j(dvn( ra1fttension in one string is then decreased by 2.0%.. t(1l n9dvxbraa.rgj kf(ls,7;y o*y What will be 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 identical flutes each try to play middle C77w,s zaf*ue2uxc4 pc (262 Hz), but one is at 5.0°C and the other c*fu7 c4, 2exuaw 7zspat 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, + ,7,undpa 9p6d x, pvdox9x k(jke4kfB, 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. W,dv4,k+9adkpn 96(jd px eku,fx7x pohat 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 stahwj3qw 28ig1rrf fz03nds 3.00 m from one speaker and 3.50 m from the otheh1 2rgf0w3 w zq8fir3jr.
(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 ;ears,cne idca7o:// tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency o,7 sca;/:de oan irce/f the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many bpiqv;p ;g cq*,jrmh23eats per second will be her ;cqm qjpi*p;3vh,g 2ard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enpd,a,8sn qiwxo+ :v 6q* qojm; a)il:ygine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with adv,js;qlq+a ,p)o6o8ixy a: mq i:*nw speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequenc4zf7nj ea.4c,j - *8 jcpmfoxjy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/sxja84z, jfe jc7c jm-.4*po fn
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2 zb0 r7 0fp*dne:ns+swhjj(a7000-Hz source is moving toward you at 15 m/s verzsjj es0 bh(*7 nafwpndr:70+sus you moving 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.slptf ; p :-wv;k-*5rqt+pwpt When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency w*-wp:-ptqk5f +vstr;lp t ;p of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasoni3i7jpzx :lx/mj z4z2bc sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is2 x bxzmz:43/ljjz7pi the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, gx ltvp31sliiae8 e 0; sry947q pw.s.the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequqx; .i4 1s0 p7 va.etl3w9srplgyies 8ency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played oblhbc 9p/y40 pn a moving flat train car at a frequency of 4 lhb0cp b9y/p75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure )ataxg ql6zm ;m7m y;*blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is) ;xglamqm6m7 ;a*tyz 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 using ultr:b+z2qz1 d ypg3 ,otmn/ma q2easonic 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 Hwnv ,8(y:z.ml n7 jkntz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who wn.( k 7zn:y8lv,jntm 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 sp*e,rzod vb71sv9b z( weed 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 q;ot (axxi85gspeed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of t;itgx a5q(ox8 he airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed ofj+dzoi1giub: f1e,t7 sound is bo71tg 1i+jief:z,d u only about 35 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 the shock wfk l7hj32 3a f/jfjkk7ave angle it 3 7 f7h jja2kfkkfl/j3produces
(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 n.ar7a q mgg,75i9s kcs re7y6$/theta$ 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 1vy ql8ke .wt.pb 28zm*.5 km above the ground flying faster than the speed of sound. By the time you he.ezq.kw2mvtyl *88 bp ar 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 sends 20,0e/+qf7mbg n8)5h )tv; 3xkkab)ay fqs00-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth fske)q7q3y5av+n ba)tm/g f )f;bhx 8 kor 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 iwp4vdk s+f2 ur1hcjzy zc7-p2i674e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a/n ynx: m8ski; sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open os;8i/ xkmny n:n 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 flsp d:g/ d-fej /7ivio*bmf++rom a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? /:o+ d+edfpf gibsij/ vl* -7m   dB

  What is the resultant sound level when an 82-dB sound and an 87-dB z2 vr8je v*gtj l*/so3sound are heard simultan3gze2*o/l s*v tj8j rveously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1jn 73krb tp ,-wb)ygtz6c4p u905 dB. What is-yz 63cb7nkjp), tb w4grpt9u the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated m)2pz* w o)aa o/s+)ythd-pz cat 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the *oppoa/ )c-da+ h )tzm)ys2 zwpower output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their eae+*wuc ou3g p*b;/wjd rs. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, aw* wegob cjp* +uud/;3nd 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 communications systems, the gain, 2d8o b 1jvuhz3$\beta$ 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 tfqxtd: -bn/3 euned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fir1v;fr/ywrvq zsx.r:5c( +czxed points with a fundamental frequency of 440 Hz an cr1rr .vrz+ vzwcs:y(5qx/f;d 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 tube1(vfah+t9npe ; awvf3 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 isavaw (pfvfe3 t9n;+h1 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open s7be diu.yrr;-0m7k a at one end and also 75 cm long. How much tension should be in the string if it is tbadmury; i.7 r7-esk 0o produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observedlmd6.n p 3xt/p 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 tonei x8u5e:jnd994x5cs0gvbwyp in the 500–1000-Hz range coming from two sources. The sound is loudest at points equs cegy pi9x8:v5 n05j w9dbxu4idistant from the two sources. 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 whisfia +kwr8 2k(ntles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequ( fakwi8+nrk2 ency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches yoj1j rh cr5r 7s+shhv01u is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant vr r01h sj+ch57vjrsh1elocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dwl bbgo*kx2vuf 1j/a 2 +n5kg(ifference 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 thel kwg/aj b5k2*n 2o+1ugbf(v x straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding tojndfnn4k. t p5y7 r98cj /aam7gether, produce a beat frequency of 11 Hz. The shorter one is 2.7pn.jnn 8mj7 /kdtayr9a c45 f40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it m+so99bq pa 4 q6dlqqt8oves 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 q4qs9q6l8+9dap tqbobeat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aor9r mk7yk*ve;rb (x0ii ta is normally about 0.32 m/s what beat frequency would you expect if 5.5 rbv*7( m;0 ky9xkerii0-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 z,jb:x8 qqp1n.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave refl1qxjpnz8b q,:ects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it ap2 z/sdqrd6q wj0;vw0x proaches 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 wqvr6z02x ;jw/ds0 qdbat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38)bst0u01 ,zv cv 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 most popular alpenhorn is about 3.4 m longcv 10z u0,btsv, 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 listeninbn,+p s2v 1dcrg 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 frequencies for the standing waves in thibs2+cn r1vpd, s room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rovy 8skz(4 6,/wh bbv3 6w7sonmtze4vods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other k (vt,o8obw3he z7s/4 6m4wszny6bvvhand. 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 hearing for the human ear at a fr06fdfg9*d7s z(/ yjd mk l:qv7(snep nequency of about 1000 Hz i fv nfg7kezs(nj*/6y9(:dl m s07ddqps $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boojx/5, x8 a0(+zrfqauuz5fm fcm 1.5 min after the plane passes direc/x5fm5az cajz , u0+q r(f8fxutly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat*xgru 8lmc0i 1q:qv/s 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