What is the evidence that sound travels as a wmr hodnu00-4+yg b3gt0s vbtz ( n*oi7ave?

What is the evidence that sn/ c(gd6f5c*gl zc8vsound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thefv6r ):ppw j3e bottoms of twov :pj63)p erwf 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 sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frh z9:i*f. eieuequency or wavelength te*hzi:ef9u i .o change?

What evidence can you give that the speed of sound in air does not depend wyry2uxoz: 3 *significantly y23 uxorwz *y:on frequency?

The voice of a person who hqdgz0 9x ;1hthas inhaled helium sounds very high-pitched. Why?

How will the air temperaturqmd) eun+(s -2ldtw g)k o8po(e in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce9drw v(y2b ic :qg. rmmqw u00m;xh1g, the amplitude of sounds in various frequency ranges. (yxqrmg (cgh .bw,:m9wr v du;20 m1q0iAn example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togei: dpyzgd(28lther as you move up the fingerbo:i8 (yddzgpl 2ard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but cv) o7 b52ggf es0rp2wbannot 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 on difgpvbbsfe 75 g2o0r2 )wfraction.]

Standing waves can be said to be due to “interference ighp 8xnf yf u;cvw)mvg;1: 7l9n space,” whereas beats can be said to be due to “interferency9xh;m pl:;g7vwg 1nf 8uv)cfe in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the cs5n lqxz63j 5fc o4u-points D and C (where destructive and constructive interference occur) move farther 5qz c5ojcf43 x -snul6apart or closer together?

Traditional methods of protecting the hearing of people w0ekhs m 96r)bhho 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 detectssh06hrb9k )me 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 wave can be thought of a4561/ yz h(ynywlbj8/q ehrqb s a superposition of two sound waves with slightly different1/y y(wzr6qle54 /y h hqb8njb 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 shiu05onxv ox2 cbcf-w 8(xbvg3. ft if the source and observer move in the same direction, with c8-u2wvgx 0x3xob5nv .o( f cbthe same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hearob xhha1r6 )va/sz5z; d by a person at rest with respect to the source? Is the wavel6)a/o5sxh;a zhv b z1rength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a sihka 9s.7-k .yk t-m01o phhhewing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for ti hp-em-t skh1yh.0aoh k7. k9he sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sh/pdf26 cc92-mutvyfu3g w )o f z);xdjout reflected by a cliff at the faf6w3v)2c;gx-j9fu f d/)tudczo my p2r end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the eca+h ou 3 1jtd*vfye)0xho of the sound refl)xju3t* 1v od0yefa+hected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavep5/ rz.xef ).a okf)atlengths 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 drifxcj3vdk :j,7hting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfirdjkv, 7:c jxh3e is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cl. mflumm5 0r*fh)lr(miff. The splash it makes when striking the water below is heard 3.5 s later. How himlmr( ru)l m0.f*fh5mgh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pa. t;n3ld0q vffx(ub;xvement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 0l;u3fqx ; .nvdx tf(b1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by txxlv6 mm m9zp(xq0,g +he “5-second rule” for estimating the distance from a lightni6xm,ml(gpqxvmzx9 0+ng 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 dBuads5 vb6; 3ude --tia?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose inten :;tu +v/1)vqwtfizb- f)i 2uu qgtj6asity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simg9yg( gjp5odibd40 qv nn,m ;,ultaneously at n 4v;yjqp9,o ndig0gbdgm5(, a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certai tn3 /n 1jxdcax4l,(f/mk)v nxn distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level wouldj tmfn/4)n a/x ncx (k1,dv3lx 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 ihg 2a 6f(3i m8,htilbhave a signal-to-noise ratio of 58 dB, whereas for a CD plf6thmig8ab,(hi 3li2 ayer 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 ozdqw)xt,1w g*nk qev,3zq 5l1f sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly u qkqwl5 q)znt,gwd,1 *1ezvx3niformly 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 anpt+ov.9g-qwz +he9cu eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, ,6yqcw( +-uz *7hz6qks dpwufax( y/c p 18ztdwhile 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 mw c yudxq6cpfy(huq*8zzt-p,ask(+ 7/z1 d6 w 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 metenamjvmprh 3 6g:ie( sfb52;6j r registered 130 dB when placed 2.8 m in front of a loudspeaker on nsfj6( :jmpar5 vim;hg 2b3e6the 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 i k)xyts( *xf9in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See ()ty*ksx ix9fSection 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, ( o)f1 yv)w)fixu w9dg6ob:fw,a) by what factor will the intensity increase? Increase by a fa,i)yvg6f :)oo )9 ufwwwxd1 bfctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but o8gmz4j nn)frla w;/8zh6 tac+ne has twice the frequency of the other. What is r cazt6ahn8 w+m )f4zg8;/njl the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds t p8)q: bsf:h)0l*vdx- jj*(z ye dvawao a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hqxylebvz :-v8:*dd*0a jfa(phws) j)z?    dB

  A 6000-Hz tone must have wo69cw pzso;x ,hat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.)px;c9ozw6so,    dB

What are the lowest and hijrkwn8oi 5mehp/- x4 )v* 6eodghest frequencies that an ear can detect when the sound level is 30 n )w *56io4ek ejvh /r-m8pxoddB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of soup :lw -re4bn3snd levels. What is the ratio of highest to lowest:ben43-w l rps intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The lengt7rw(2 u3se yrpcs3)pah of the vibrating portion is 32 cm, and it has a mass of 0.7ces s a2r)3pruw(y p335 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fun 4w.h nqt*o8s j)pc)eddamental and first three audible overtonesjs8 qn o pthe)*4.)cwd 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 acrov4m qx g5,j vigu4d:0mss the top of an empty soda bottle that ism 4 iv5,dmxguj 4qvg:0 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 orgau4npzk5- /p 0(lfsxaon with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be t4usxzpp f nlk 50/-a(ohe range 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 m +ni1zufyyd.dm5a)6 n 4v4h2ayd6vdharmonic. What will be its fundamental frequency ifnyvd5n+1d6yady v. m2h4)ma izfu4d 6 it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar stri33-nff1ulklw-qj0p;xs. k6 ;jai zhung is 0.73 m long and is tuned to play E above middle C (330-hif nzq 0a3ul;jsj61l-f .ku 3x;kp w 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 C5ibh 5 +j+pfmp gear2* (262 Hz) when the temga 2 pih5pe++m*j5bfrperature 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 20 dw/ *- tne;icw$^{\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 shoulxa) z+r,jk8ob d the hole be that must be uncovered to play D ,k8jobz+xar ) above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, oypz,: d5:ob4 y+er8 kq/j kljand 616 Hz, but not at any other f:r: b58p kzjeyoj4dl/,qk o y+requencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonatesq x52 :yhza 83he0vr1a/qkedd at two successive harmonics of frekr dq 5 :0zv/qeh haxy8a312dequencies 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 (4ycuv;,sn m0c90 e1hfdg til$^{\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 for a 2.14bo)2uk a ccx8ifbi1 xny*m 1*1-m-long organ pipenikf)*1c ox xb 1y18amui 2c*b at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outside ab1* 7k i 7ej ,vhm3ox9hyasso7nd is closed at the other end by the eardrum. Estimate the frequencies (in the 3y7o1 b9ha jihv,7*xkssm o7eaudible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trp,cpl g4+ki1wo;d r0vying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is tp0ck1w irdp 4vlg,;o +he other string? ±    Hz

  What is the beat frequency if middle C-ji )* zu *q1usiezzv9w oi3+bssij3, (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 ( cnlv6e22.; dtu;z haqbrand X) operates 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 they are played simultaneously, estimate hz;2uad.;n2c6v qt e lthe operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with ap qlg.x37ipwg:i87o3pw2 f kq 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 your reas3 .l2gfw78ip:gwi xqko 3qp7 poning.    Hz

  Two violin strings are tuned to the same frequen cow 7d7 hxu-ij(d.m7kcy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat freqm(dhuo.7 d7ic- w 7kjxuency 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 middlewdl.ce+9 nvztwy (z34 C (262 Hz), but one is at 5.0°C ac lzyt (9w3w+z.vd 4nend the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency *xc8 jb r.jve:(2cz48cs dw0z0zvhtjof 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat fr b z:0x0c2jh .jvet8dvj(zwzr*c 84c sequencies 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 onedp sad7i* ( sqf5qi c) r/,deot;0y-yo speaker and 3.50 m fqd(odeo /)c7ssafiy,*5y-i;dq0tp r rom 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 vib f 7wdwpr/)rb1rating at 132 Hz, but a piano 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 of t1wrpfbdr)7/ w he 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 beatsj( sc cr; .)4ag,ftb.juaf /ac per second will be heard? (Assume Tf t asg)c4./ (.b rfjacu;,jca = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginqv41;ar73wove kv u b4e’s siren is 1550 Hz when at rest. What frequency do you detect if yourvk1 37v; ebw4a q4vou move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whosh,c2awbc04t5/q-cf 7 ff w pdbe siren emits at 1550 Hc0h54f d, aq- cwtf/fbw cpb27z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source isze 6 oxeo3zx;- moving toward you at 15 m/s versus3oxeo- zxe6 ;z 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 frdauvxswxs2: )g81-af zznu 8,equency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears:s d aa8vu2gx )z1xz,wf8-usn 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 ucd- tbx.))ihbgs p,rp/cfo57 ltrasonic sound waves at 50.0 kHz and receives them returned from an object mo5p ,hf)b dr- /.7ixp scg)tcboving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat hdzy57f3b nq .emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat heard5fz ynqh .7b3 in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a 6qni6os4 hf9y moving flat train car at a frequency of 75 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 of6oyns46 ifq9h 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Supptziz k8 g9 p4x- (**jd:a+lz6bfohvseose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries akbfztgez +s zp9x:oh i*v6-jda (* 4l8t 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wayd:8,p :nz7cik kcz;fves 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 wi/ rxf*es.y7eg nd velocity is 12 m/s from the north, what frequency will ob y.*xf/r esge7servers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its 0nzy bxo( e5/p.bf f(r:okih-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 daz) (t8 crhi+ 8dy(ow2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mot8hz+ac 8d) oytwr((i dion?    $^{\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 o89pn(gmpqi6 pjft181da :rdxlgth* 3 f sound is only abo 8attpj1lrhq18gf3pxgp:m 9di* 6(nd ut 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 odds 7 x6/(dmnacean. Determine the shock wave angle it produces sd(/6 dn7mad x
(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 bi-/ qklujr 27$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andnspycbr uyt13/ x ih*7yz+x(*bt9xr( see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled hbxynzs /x ri1bc3*y7*t +(rpu(y 9xta 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 20,000-Hz soundvjo8pq i v,iy)z:z2 d j:elo80 pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which i:8o2 0d jvoiv p8q),jeilzzy :t is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves ark0k :*bb4p wlpts(k7x 4 cqd8ke there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displarvf 5j.ovvin 4yk d0v t.,g+c7y called a sewer pipe symphony. It consists of many plastic pipes of vy vf5dvtg .cv.74+0v orijn,karious 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 a sound close to theip6bw8;n+m: .bzt oydr*dn; n:.jjd a threshold of human hearing (0 dB). What will be the sou:tynr p86 n:ozb.;b.j na;*ddjw+mdind level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are helykbj2wd26lwvj cv0 z;i ( 0y8ard simulta8wybj2k(d jvv0l6y 0; iw czl2neously?    dB

  The sound level 12.0 m from a loudspeaker, placed l7;dp0 ( acscnjk v16cin the open, is 105 dB. What is the acoustic power output (W(c c1svndj6 7p0a c;kl) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier i9bai8fdz n(p8qf59 m os rated at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts anpd59qa 9( ffmi 8z8obt 15 kHz?    dB

  Workers around jet aircraft typically wear :w6:gugl7 6xl t :haiek+o hz7protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a dk+i76 a hlhu:gegt 7o6:lzx :wistance of 30 m from a jet airplane engine?    W

  In audio and communicatiocssk0.5sda(4gmvi8) 5gao j lns systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is t 1e6yqd1y,xkh uned 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 violttmie8r6uuvfg583 q eno 8o( .in is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass8 i e(on5u teftm8v38oqg r6.u per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with t ;ac*6f( qr8m0m bejhwater (Fig. 12–35). The water level is allowed to dr 8(ct;mjm0f er*6habq op 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 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is neaa52m3yv3 bf nvr a tube that is open at one end and banf v 23v3my5also 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 obb1u+41 a blbaj8b8fdrserved 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 fro /igqi (yuzwq+6v)i- mm two sources. The sound is loudest at points equidistant from the two sources. To determine exactly wha )(w/m6 yiqi-gzi qu+vt 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 whisq(pkb4 c4rq5m/k( x*7p ffvfhtles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is thfx4kfbk4(qpv5 p 7( q/hm*cfre speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After jqj*hp, v;nv;it passes you, its frequ;p vqvn jj;h,*ency 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 liste eaidp;3unqpx9b yl1h3xp,) q8/njd/ ning to the difference in pitch of the engine noise between approaching and receding cars. nx/ dx89d,/ phpebn3qpl;i 1yaq)u3jSuppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. The zvh. 7/+ ejt5.eq mj5txmice3shorter one is 2.40 m long. How lo j7+ i/5e ct h3m.ezeqm.t5vxjng is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a st*piaxuo3 17w jationary 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 f w7uo1i*xa3jprom 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 dr9 a6g oyc0,bjyo i lu34mnx6efo4*tf5-,po normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the wavesor365y 9opf,fo ndo6e,lg*i4-4ab cyjutm0 x travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flyi y;dg)gn)4x, edvaq e,ng 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 aqn )dge 4xy,)v;,egdafter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as g,f9b 7f3s 46t5njgljy a xbr0it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms longf 675sg jtr4j,3baflngb9yx0 . How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once usr ui+0p)w0pq1n 2jbp pkv3 rxbw0a 4z5ed 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 alp2+rz 0 14pn 3p xpw5p)jqbi r00wauvkbenhorn 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 4bbj6g.p+z p6yao :eb listening 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 st:y66jp4abpobgebz .+ anding waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,l*rev tw 0a,ir.o,k4y” involves a long, slender aluminum rod held in y airrk,*l 4e vt0.,owthe 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 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 o1we0t z28iea nf hearing for the human ear at a frequency of about 1000 Hz 0azewn8eti21 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 gy9e (fsc216ejri p9 uqround hears the sonic boom 1.5 min after the plane passes directly overhea69ycsu 1ej(pf er9 i2qd. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb.unli5 0j pr)6 b-aeqx m3;m*hsqw-w koat 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