What is the evidence that owv+i rw+.n/;0 qjnsb sound travels as a wave?

What is the evidence that s. yo,e c-)qvgbound is a form of energy?

Children sometimes play with a homem ( 7 .a16tajtf) ;gpji5vbu 3arbi8egeade “telephone” 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 evf.eg(bj3t u1;aai i8t b5 6gr7p)jaother 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 fre1pv4ty 61ppydc y+ q0equency or wavelength to changepyyq6pd +1pv4tec0 y1?

What evidence can you give that the speed of sound in .mb4j ,k8 ghkvair does not depend significantly on frequek .ghkmv4j, 8bncy?

The voice of a person who has inhaled helium sounds vero)iie:- :+icogxlzjb w w043*-e t1wl onq4usy high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipes3 zzhy/ky ,d7b?

Explain how a tube might be used af23v(btw gx2);pf pgzs a filter to reduce the amplitude of sounds in various frequency ranges.bz p) fvg2pt(w;3fx2g (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you ,,7g k4gn qsgbmove up the fingerboard towarb4,gk,n7sgg q d the bridge?

A noisy truck approaches you from behind a buildo/1ygulfw . -zing. Initially you hear it but cannot see it. When it emerges and you do see/yg1uwl zo-f. it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in rqpgj :( qd.23r,f/m)p qbttz - mfe,gspace,” whereas beats can be said to be :-tpfrqef.(q,jm3pb,gd/ t) gz r mq2due to “interference in time.” Explain.

In Fig. 12–16, if the frequency xawo9)+3 bnzgz+ y: ov7)cdihof the speakers were lowered, would the points D and C (wc) + o3xba gy7owd9:z vnh+)zihere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectqh00fnt:b)sy5/k niq ing the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds i/0h)0nnqk bqiyts: 5ft 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 off;;l+( rrtjy9b;nxf * vtrj(r as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In x;rvl9ytrn ;(t(f*brj r;f+j which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shir*:(3,n hct-t1v xcw+qyzhyh+a ng4oft if the source and observer move in the same direction, with the same velocity w+naz1t+y3gonhy(v c4 h-xrqc: t,h*? Explain.

If a wind is blowing, will this alter the frequency of thr5l e+e/sk4a 9dnnmj0 e sound heard by a person at rest with respect to the source? Is the wavelength or velocitym/ a+ 4 jel9nkds50enr changed?

Figure 12–32 shows various positions of a child in motion on a swin n1s zrdc+36yqg. A monitor is blowing a whistle in front of thqc6r s31yz+d ne 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 sho;4j3vfu o oe5zut reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. jvf;zo3e 5ou4 Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. H7w j73v(vsctvw5ff l5e 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)s cl f(375wvjw 7vfvt5 and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengtx,tl ijcb,lh4lpl/.qv b 34.bhs in air 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 trf7nn, 5i0kgfuzsq5u *-fxfnke nw; +):0iu yuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the5n)n :f0iiur+ ,f egkfkunn w5x7 0q;s*uy- zf fish,    s (b) by the fishermen?    s

  A stone is dropped from thecl fp n(e,h+ m u5)9k)stwp9bh top of a cliff. The splash it makes when striking the water below is hehs +b)n99(f)5l ck tuewmphp,ard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone7xu(,(yu fj9oz m mhw8 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 away did the impact occur?uyzxmh,o(wf7m8u 9j( See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distan.( ya j. ctyqh+ygr )49sqq0vfce by the “5-second rule” for estimating the distancey 9.g0 cjy4 qs)qfartv qh(y+. 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 level of 120 fq0bi- og4d vry8/6roj: kq5 gdB?    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 whoseaoc)qjm,9h0++k 2s.spuuvv8f hznv; intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simz xle8jvq:f g4eug v sp;+:odibhx4+dhp ::.;ultaneously at a certain place, what wx4;o.gze+d: il8pd: 4bfg;j:sx+ve :hqpvhu ill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane./* myn5sv,u u ypw1js with four equally noisy jet engines is experiencing a sound level bordering on pain,uj5yy,.1un s *vp w/ms 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/bjy 9-i bhh5z have a signal-to-noise ratio of 58 dB, whereas for a CD p -h9hyj5/izb blayer it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound froocg-:9k/ fpym m a person speaking in normal conversation. Use Table 12–2. Assume the sound spreadog-:pcmy k9 f/s 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 stri 0r5)ki. o4d0q)ydgtvufpen)kes an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is ratkkwh-)*dnd(m xexe;s :xz .0ted at 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 poz) -mx:wdns tk0h(e.xkxe d;*int 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 r r;flhykrw.4zgf141f egistered 130 dB when placed 2.8 m in front of a loudspeaker on the s4hz yf4gl 1ff1r k.;wrtage.
(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 typicallhz9+/kn 8 pir3hq2bspy detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two soundsph9npi8+bqks2h /3z r whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is f9t,pq-(fze oi; mz6otripled, (a) by what factor will the intensity increase? Increase by a oiofmep; z(69 ztfq,- factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twic ;/le6 kb:1 lw(copm0fah7 bcj-z,vque the frequency of the othe/ lhw7m6eub cqb,ka o:0p(f ;lvzc1- jr. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sounda 0 f0(v03nsyrpm dvy uwdyv7ik*:90f wave in air that corresponds to a displacement amplitude of vibrating air molrw:nu v0fyfp*sim007dvv 3 9(y dk0yaecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to selhxv u-ewpgh) 0*/y5dem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–)uwxp/ -y0h*dgh 5vle 6.)    dB

What are the lowest and highest frequencies that an ear can detect when oapf,;o -,wwgp4w :stk;v b1m the sound level is 30 dB? (See Fig. 12–6.ovbstf kpgaww:p,o4,;; w-1 m)

  Your auditory system can accommodate a hg-* wfkf obd1 lg1rx+/uge range of sound levels. What is the ratio of highest to lowest intensio frlb1*+1xgkd -/w gfty 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. The lenglyx)-v wb19hf:; wr3i (uejer0lehz6th of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?h0x ;9y(libez1 ee j)-v6 uh3wlr :rwf    N

  An organ pipe is 112 cm long. What are the fundamental and first three audible efrd 2gqz,u-;rmseyi /2c1d 2 overto;q2 i22/sd- zumef1rrgc y,de nes 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 blowing across c,4flkt* d/pqeu d79z the top of an empty soda bottle that is 18 cm deep, if you assumed it was *9zd74/fqltd eu p,kca 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 spanninz11k hr /uxz- wnn*dh/g the range of human hearing (20 Hz to 20 whn*dz/nz/uxk -h 1r1kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency o)s rfvhu/45v df 540 Hz as its third harmonic. What will be its fundamental frequency if)54/ vvfuhsrd it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is8c- q+g: z1* fozcqf;kggkxu6+uzcs9l8 5rew tuned to play E above middle C (330 Hz)fc-8k918+5;c uqkg eo6gwlu:xz* czrsf+z gq .
(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 emvxi+0k;vf :nf 4:mop qits middle C (262 Hz) when the temperaturvk :i;+vn q pofxfm:40e 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 v 4w(i.eeny8.(dpexg v3ik)m 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 the hole be thr:nfc+or+m ( q .g/oe f*/bjmn2krn 4hat must be uncovered to play D (+o/gfrnr nfc + b.m4h k/2qoj:em r*nabove 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 rjd/06 z,6 muw:m njn*l6o dlfdesonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other freqn 6l d6z,w*lo0dmfjujn/:d m6 uencies 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 bothcb /os 2/lrwv+ ends. It resonates at two successive harmonics of frequenciblvw/c ors 2/+es 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 qno1,q yi0 0*3mbhqs b$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range skh2 3bwd9g a-.6r ds8i1vlurfor a 2.14-m-long organ psw 6i-.8hg2krbluvs1 3da9d ripe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.2.9nf2) iynpy ;jic fj:f:ep.sv *uhc5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of.jyp9u:i n2cscf i jyh.:ef *2;n )pvf 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 9bsle zu4dqtu0j 9-n--8 lcaqtrying to adjust two strings, one of which is sounding 440 Hz. Hol0 q8-ua- 9dzuq9bse4cl -n jtw far off in frequency is the other string? ±    Hz

  What is the beat frequency7kr,hd;( z o)e7qwskt 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) ope5k (f pz1 rhzjze+6sg*rates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when trgz 1( hszf5k*jpz6+e hey are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 5m/5/e ca /onyhwc-lh( ig7r2 bwdb; p4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What i o7imrneah/hbc(wl y5 wg5/d;-2p/cbs the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequeiqwt-njnw zq/g6j.0 f kdl8:j-e ord(k,zt 8 :ncy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played toget8rjg,nd(6j: jltzn.qwtfi /w--8q e kd0z :koher? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each t tnipo i/f)nt(,1e7 otry to play middle C (262 Hz), but one is at 5.0°C and the oooteif inpn7( /t),1t ther at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks,n 9((op tptqh- 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 a(o-t (9 nqhpptnd 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 perso9t) jwb2ke+ )uuo;jr2q ihk e.n stands 3.00 m from one speaker and 3.50 m from the oth jwb2+eto2jrhu e ;q i9k)).kuer.
(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,bp 8uceb9gm )5f6elz4 but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 13 p)fu95gembz4 bcel6 82 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. Hoci5 kprhhh hm1 * ; +(--oa0 x-dq/yz,xaemhtxw many beats per second will be heardqmhipxty+5xd--,c(ek hh -xmh;*z/ah 0 1ro a ? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at re wl6n4sga:j;z;ey(s gst. What frequency do you detect if you move with a speed of 30 m/s; aw;ggylsje :4z 6(ns
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose m1 d/lm8 h :vk 2cfdlrz-egfq.p*bn9/ siren emits at 1550 Hz moves at //-gq1*d: zblfdk vrl 8mme.f c2phn9a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000rnwb1: aj1fhe / zfs79-Hz source is moving toward you at 15 m/s versus you mofjah1 br: w1n7 /fsz9eving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When one is aw qg /kov9:yx5t rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume xyoq5 k/gv 9w:T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives thpcge r51e6 k 5vtx8,vsem returned from an object moving directly away from it at 25 m/s What is the receivvc,k5gp t5xv8r 1ee6s ed sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits azdw *71ec2ty9pavh ry4+c4p61wd w3 sq)l mfi n ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectpri2 cctsy fd 9 a+pz1wdwl)3hy6*4veqm1 47w ed wave?    $ \times10^{4}$ Hz

  In one of the original Doppler ox s)4)2mpekcexperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba pl4ckes2)oxp)m ayed 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-flo5fkkj(bz w:1* jh6eunw speeds. Suppose the device emits sound at 3.5 MHz, fzjuk(1e6n5k bj *w:hand 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 using rd9w my*yi2u f7w( fm1ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind v pkq29t)lhq f,elocity is 12 m/s from the north, what frequency will observers hear who are located, at l,fk)thqp q92rest,
(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 -t;p o5ys0a/yrqhi b) if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where l *ke t1f+xvwud,- on w0z(k,xthe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpl kx1f+w0 x*ltwz,d vu(,e -nkoane’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 at ,u 8i;fnud,9a2rb) jao we.famosphere of a planet where the speed of sound is only about 35 m/s e fdjub82 nw;fai9,.,rouaa)
(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 shoqh. 5wuy,8b9lm9mm ncc g6r;lck wave anglemnr ;cq 5lgm99h.l, wcy86mbu 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 ,7nwl2n 7kg kc$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above the ground fpu es f f6v:k2yn;6a*5fj5fqvc; qm z2lying faster than the speed of sound. By the time you hear the sonic b 5yszqkfmf a *25; p vq26:cnf6ufve;joom, 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 thatkatsyy1 ;u.4hj,d ;q)9rad al sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water))lt4daa ,d q kha.9ryju1 ;s;y?    s

  Approximately how many octaves are there in the human audible va .lxfe6x (0qrange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewerrlz ) rc+tvl5e4yx(e+6o/pxz pipe symphony. It consists of many plastic pipes of various lengths, which are open +e (ov/ltlp64yzc x+5ex zr)ron both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to th4ldeicm+ fq94 e threshold of human hearing (0 dB). What will be the sound level ofd9+ ilecfq4m4 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-x mbbaqx h0:w*8 x./lodB sound are heard simultaneously? bomx.lh w /0q:ab8x*x    dB

  The sound level 12.0 m from a lcsz),f .s tzz1n1 as5joudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?zaj).szcs fz11s , t5n    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpuy ).56 hmvp bx5o)k7w+s jdjqst drops by 10 dB at 15 kHz. What is the power outpu))op ykjd5m qvhsb75x.j+ s6wt in watts at 15 kHz?    dB

  Workers around jet aircraft typir 8 9h3njbnw)qcally 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. Wha 93rqbn)j8 nwht 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,g7l7 qlq,2 t llhrux;4 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 a frequencwp jd:f .c3n c/da8ig:y 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 with a fc ,: cg6xl:zuqundamental frequency of 44cc gl,:uq 6:xz0 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled ( txki (5xgrf6rajx42 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 rax (5rxrx kfgjt 4(62iesonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g isx :. 1um3)pmcptrfqek1h9k;m 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 (in its fundament3f:;mk)1.th cep pmxq91ruk mal mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop 4h.jhdfc) xq v :8z qkalo4*.q($\frac{1}{2}\lambda$) 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 two souxk*jy+b ax,0 trces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency yax *t jbx0k+,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 stationary. The conductor odwys+dst e;q ;5/im+fk,qg4 l9e -anzn the stationary train hears da- /e zf5 smn +9g4sw;;kyi,dqe+q lta 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After it u cxv(gsl.zdw*y69/ ,a toyv. passes you, its freque9ds, zwvovg*l6y(t cyux./a.ncy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you qrahn:9 1jd g;can estimate the speed of cars just by listening to the difference in pitcqhng; ra91d :jh 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 togetyx)6*,u f52fopb now96ish rnher, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thbu wfypxs5n,*o)n iofh2r 696 e other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves)4an-e 2oe joc past a stationary observer at 10 m/s as shown in Fig. 2) aonjcee4o -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 after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bej8g *v / )*vk4ziwn /fcukzd1zat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume tc/ zv*8k* v/zf1wn)izkgj4 du hat the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/kk pg h5ek97s./jcpn2 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 reflects off the mncps2k/peg.9 jh 5k k7oth?    kHz

  A bat emits a series of high frequency sxulq w,;yx*n,kf4( pe1y,dhwe9.o xsound pulses 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 the echo from ;9ho,*e sx, uxfky dx,lqw(n4ywep1. one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once *b 4 0a u0c hubi4yt,sf5osry2used 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 s b,byh40a fyr*iu2o tc0u 54s3.4 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 listen:8;b pb bn2zmging can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consim:8bbn;zbp2 g der 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,” involve x 7in vjddgr8 -fh/f:wsi6pg/9st0,zs a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a littf xh6,9 vg- /zd tdji8n0s7wgr:psi f/le 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 fo1p6edqw+,a h -kh2gf ar the human ear at a frequency of about 1wha+6a-kfeg pd , 2h1q000 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 atan0 ns afvoqel(3 u4: 4w)bb/x Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passesvbbn q o3s 40w:a)/en 4aufl(x directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedbc6ojoh) s8l g..us.b2ju1xl5m (y ldtoat 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