What is the evidence that soun ,u hrs v0ya+r-zov7u,d travels as a wave?

What is the evidence that sound is a form of x j1-ymryub, 6energy?

Children sometimes play with a homemadeog/ , apvmv./j u8l)y/q6 wlsg “telephone” by attaching a string to the bottoms of two paper .oau/v/ p/w,vqlsj68 g mgy)l 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 frequency fp:a4t wn,k-r/tym9b or wavelengt-wm ,a9f r:pk/ytbn4t h to change?

What evidence can you give that the speed of sound 8er*i9 tdox7yyv6+az in air does not depend significantl7xzyd ota +ey69riv 8*y on frequency?

The voice of a person who has inhaled helium sg4e d29xr ugv4ounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipeh j l/8bdar0glh18qv:hb 8a 2ds?

Explain how a tube might be used as a filter to reduce the amplitude of so8k dug8 9uz3hvunds in various frequency ranges. (An example is a car muffler.hz uv8g8u3k 9d)

Why are the frets on a guitar (Fig. 12–30) spaced closer together astf0.-d64 zewg* dkud1lj 8 owh you move up the fingerboard todw . d*l84 ew-udf61zjokt h0gward the bridge?

A noisy truck approaches you b*pz8 2mqah6t.ykmh7 from behind a building. Initially you hear it but cannotyapk6 zm28bh.h qm*7t 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 diffraction.]

Standing waves can be(uj x57ye+b)kd t-jfb said to be due to “interference in space,” whereas beats can be said to be due to “inejf5x(- j b7b+ )dytukterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wouldhxu5jh yl x xqkz+fk,/;nuxaf w1y (9q+z76-g the points D and C (where destructive and conyx7jf -fnlhg/16x95xhq(, ;zk q +uu +awzx ykstructive interference occur) move farther apart or closer together?

Traditional methods of23vlxjnqf/dmc72o n ) protecting 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.) 2cl/fqx7 3jnovmdn2 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 wave can be d*1h lgd.2bvnthought 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), are the two component frequencies farthernhv*21d. l dgb apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if *ff95e)hv:ktmk2pqwj, v 8vr the source and observer move in the same direction, with the s5*,:mq kjhfp2wve8v9fkt) r vame velocity? Explain.

If a wind is blowing, willt8-3 huck;l en this alter the frequency of the sound heard by a person at rest with respect to the sourc 3uncekt;8-lh e? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a c +d gil.38;kkb jk,euphild in motion on a swing. A monitor is blowing a whistle in front of,b3 +lpkui 8.k;jedkg 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 shoutuba- l bb jhn q:)-a2w12m8mam reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Esti qmwb- bnj:ml 22baa1ha8-) mumate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears(ix)lz7fx vtb+4c 7hx the echo of the sound reflected from the ocean fl( z+f )vxi7t7xchb4xl oor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 r-a- .ipvjx 1b$^{\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 j p z ross:hg-vs;c)+1c oaw*s(ust above a school of tuna on a foggy day. With *sv(w :-hsor;cgp+ocssz a) 1out 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 the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes wh1b*bml,si sy 9en striking the water below is heard 3.5 s later. How hig,ssy91b l imb*h is the cliff?    m

  A person, with his ear to the ground, sees a huge stone suy6us tfu/z np.h (uoc10*i;y trike 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 theysz p;y (oi0/h1n u6ut*. fucyu are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by t yxhnb4 q/df+ymw+r5 (he “5-second rule” formd4h + +xy/wnyqbfr(5 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 level of 120 dB?h;t u .3 -. n2mgai;n0nsgbogu    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 4l syg( :kzr ,vpm:he5j4tby0sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers prodapr (lha,+aa((w3fn cuce a sound level of 95 dB when fired simultaneously at a c,aaa(a3p(r +(cwlfh nertain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dis nfh k +/-3n;jlktl2d qbb/jy)tance from an airplane with four equally noisy jet engines is experiencing a sound ley2d;bqtjj/ 3klb +k-nlfh)n /vel bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is swg1n95:c c)m fk+qedwaid 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 of the signal and the background noise for each devin 51wcc:dge mqkw +)f9ce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversagn:+zzjza0 b 5tion. Use Table 12–2. Assume the sound spreadsjb g n:0+az5zz 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 eardruh;fpp/ z f0p3dcajjbx(+:rs3m 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 r );5; d sa1k:q,/1xq i+ rgpyfgzux:aswn d:rmated at 250 W, while the more modest amplifier B is rated at 40 W. fqrw)dpk;5xi,ud 1n/sq1y+ gz: gs;: r:xa ma(a) Estimate the sound 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 regicl acpuc-xm/1 z- 7ww7stered 130 dB when placed 2.8 m in front of a loudspeaker oxlczw m apu-/7- 17ccwn the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 d)ydu +vltm;n-B. What is the ratio of the amplitudes of two sounds whose levtm+)d v;u- lnyels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave il f+j(dlwfooxd.:0 ;:mwf2 bms tripled, (a) by what factor will the intensity increase? Incrdf jfdb fwl;xm:.oo2l w+: m(0ease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twrj;od)c m a54d67rtk) agwz t1ice the frequency of the other. What is the ratio of their intensiwj7c5r 6att1g ) o)rzda4;d kmties?   

  What would be the sound level (ii 5(x vm9/a rkddn9f2wmx b5my* i7vq-n dB) of a sound wave in air that corresponds to a displacemenrx7bavqwk d5-i 9n(vd y9f5immm/x*2t amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sqd;lb2l f8yc8ound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. q2;ll f8y8d cb12–6.)    dB

What are the lowest and higheqn qn(qhpq9 m hej/:0 rc,1n:co)f qw9st frequencies that an ear can detect when the sound level owc9 )p::n 1qhj rqceq(q,f0/nmnqh9is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommobdo *8gs8/ b ,vnj:tap:wwjf*date a huge range of sound levels. What is the ratio of highest to lowest intensity a8 *wn:tb dgba*/s o8jpv,fw j:t
(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 * pa q*yo)+idp440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed**i p)qa+odyp?    N

  An organ pipe is 112 cm long. What are the fundamental and first three auu2dm9y(qk1y a dible overtones if the pipe i 2qymda9k(y u1s
(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 the top of tu5 a); kzl+nsan empty soda bottle that is 18 cm deep, if you assumedz )slua +nkt5; it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ withu 1fh8)hkf+2v rmb;rqkj+ yq- open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz),rrbkyhqkqhf- ++j;fu m8v1)2 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 of 540 Hz as its third harmoni0cng4g z9e4 hpc. What will be pgz4 90 nehc4gits fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0+2i)gf:4vc,ybx+k /obp rqo lyrn1e/.73 m long and is tuned to play E above middle C (330 Hz). g,lkof/+ibxyqo ry):1b c+ vr4 n ep2/
(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 pip5 ob b24afbne)e that emits middle C (262 Hz) when the temperatob) 5ne bfb24aure 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 e*e.n-kp) +;o+jdz) mkuzqwk,rlu6gat 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of t1zkjvvzqt*;qv z t(, 3g em/(che flute in Example 12–10 should the hole be that must be uncovered to play D above middle C at 29/kj;*zvq c,1z(q3e v vt g(zmt4 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, 44 / kucxwaw3 pok /-le 1akr75-5ao-pob0 Hz, and 616 Hz, but not at any other frequencies ikxo- k/ko5oc -e auaa7 -r1pbww/l53p n 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 resonates at y0tg /9r/(f )efylolt *qgi +rtwo successive har ty/lotg f+)l q90r*i/fg(ey rmonics of frequencies 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 mt:m5;8pe zic$^{\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 auk6 h+- xfx *gp3sklm3cdible range for a 2.14-m-long organ pipe m3sk*p+x k3gxflch-6 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 and 29qkweozdf(f wd8 q *2lm1o+d is closed at the other end by the k8w2oq9qde(m fl+of*d z2d1weardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat eve kmwsnxai,a m2peu0 ta9a8+( 3 t2cc9kry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How fa9+(8ie,k93acxu tnat as0 mc2w2ampkr off in frequency is the other string? ±    Hz

  What is the beat frequrl q)unn;.r9 1ppy5i tency 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, wh y p7oshvya qykwz,2h6 6,qdbx35fs s ):c)nh8ile another (brand 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 h2qkhy:66ys38fd,z)ob7 ,c) yxw 5qs avps nhare played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35wknbef1b . j.*0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the v1 .*f.bjekwbnibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the sri) g:q5e9r uuame frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard ir u)er 9:qug5when 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 C soj (vo2sxysifo; .x ( 1eu2h jbv5-.n(262 Hz), but one is at 5.0°C and the othjb2sio1sv -. y(;oj5(vhx2fsu.noe x er at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuningia05w 3 v9a6 *p kl, 0 trfi.+oyvkcl:ii(vbjc forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency ipiotk30(bj. i 0kai w9lclfcvrv*+ 5 :,avy6is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker and 36nwoq mn/ 6j183ll5e-s mjp wf.50 m from the1mj 5qew3-66 fsnnw/l8 m polj other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a pian*tokel+3,wavbx , nd1y.+vcjo tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must t k+1j+, lbdcywv e*3ovax.,nbe 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. How mom-h g c/gb5y1,ugp4ln2l q i6any beats per second will be heard? (Assume Tm bcg16hyg5uqg -4,no2l i/ pl = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ces:jkjnp+au wi qd+/sq11 -b.b rtain fire engine’s siren is 1550 Hz when at rest. What q:-j bd1a/1i+s +kqnpwsjb.u frequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you de2o9z l5p6mnhg6e6 0-ch rsueytect if a fire engine whose siren emits at 1550 Hz oem he6r69lug5 -60nh sp2zycmoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yokw8j98ali brz l (.d.m )u:3eci v(megu at 15 m/s versus you moving toware9ue( z wrv:d8clg j.k a8m().limb3id 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 i* mwim(etudli71;)cs z1kf 6as at 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 hot1f (uwc;l 7i6am*) idzes1mkrns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz an+tkvw6nps 94q d receives them returned from an object moving directly away from it at 25 m/s Whaksp q v64+9tnwt is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fhsf6,gj /ze ,mlies, the bat emits an ultrasonic sound wave with,f 6emh/z,sgj frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was 5.y3r+ydfxuwc7) fk /qv:y-3 es-rd*ilzy la played on a moving flat train car at a frequency ofse wfqrxdy- fk+uaz7r-3.yy5 l iy*3/vl: )d c 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 of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. 8,3b y(wt z yf975)ywivqlqsb Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the exis y 5bqbyw3z)wf98qtlv(y, 7 pected 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 ultrasonic wav ylq7 .)h(y*gb xm 7g4i+crfsze7kd6 pes 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 Hzat8yybkq 96 (a. f+lrz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loca.8qyay(r9 k+b a6zfltted, 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 ml5.f-d n7wr4, xpsmwm9ma. aon land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What is doyt)wy lb2:zc1. a/ vthe angle the shock wave makes with the direction of the airplane’s motioal y:v wc1z/2ybt.) odn?    $^{\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 t5ylz lq jww59 wi7q,q9he speed of sound is on5zlw , iqyj9q l79w5wqly 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 0u a-lgyq-g (tthe ocean. Determine the shock wave angle ay l-g(tqu0-git 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 7drkoz(irq:; 3 sorf( $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead anisggsl lkcl . o62 4t3.+-0i rgiu9hhkd see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hea 0llug2lohs+it4 c6 i kk.9r-gi3.ghsr 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 20,000-Hz sound pu4u.i ,ytv/2uju *p3q ezj zbm2lses downward from the bottom of the boat, and uj3pi2*bq/ ,t.z 4umev2 jyuz 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)?    s

  Approximately how many octaves are there in the human audil8 *yt.utdmta20fyi(ble range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a di6 g 33qikk9)q5s ;2wcc jlkgzvsplay called a sewer pipe symphony. It consists of many plastic pipes of k)c9kvi3 q g6zjcslkgw3 q ;25various 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/p :edw41*sg.kb6d-emceh l v m from a person makes a sound close to the threshold of human hearing (0 dB). What will be the so.1 l/g:e*s6wk ebd4 ecv-hdmpund level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB souu0/c k 74 /s;v;b kre1vypbr7laxvk9gnd and an 87-dB sound are heard simultaneous9p bc7k kyvx1as70rgu;ek/ 4rvbl /v ;ly?    dB

  The sound level 12.0 m frpd :5walqbk ;c8xsl )hd1 hh/8om a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all d8 x5plq w)8lh :aks/hhddc1 ;birections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drja,:l5a:;ffsjbtl sv 6u6 t5n5 6tdthops by 10 dB atsn556tf6; j6hfllu,5 t :vdbt:ja sat 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their 3 ntbds jg0d86jpd 49eears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average huma9nesbpdj8j 04 3 6dtdgn 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 communi, lvpj:d3 ti l,jntv:n1lv6m)cations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fr ;e l)8g o*iat*gttlug9oj+n9equency 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 cma4 96/xn ay5cuszb.qy :1gwc s+fq,ws long between fixed points with a fundamental frequen +9fg61/w,ysbsyx ans 45c.qqz w:caucy of 440 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 with sqey5 f 3d.d3iwater (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.3es.q5yd dif3395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tu//8 9b ons2w9 c lfwf;)luj1wtstq *rcbe that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonancjbqf9;s )/t 81wru cw*lcolw/9 ntsf2e (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obserces m4h9a ;p9hved 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 comins4*pilrg5glj(k 5) eyg from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what thesgjk5pe li4g l)(yr*5 frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor o+ml l91kdygc+n the stationary train hears a 3.0-Hz beat frequency when the other 9ldk+1c lgmy+ 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. A 3 pyp7sx 7r(0qxm+mu*eddo+kfter it passes you, its frequency is measured as 486 Hz. How fast was xpd xk udq7 3*eo +7(m0s+yrpmthe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lissaox)l: tpu.1tening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halveds)1t la :xp.ou) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soundiiw9dmg5 xnk-wv+ f6 f.rj,7e3dcuvs. ng together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m lo. f.e5kjvns7- i9u cdvwmdw f 36rg,x+ng. How long is the other?    m

Two loudspeakers are at opposite ends of a raiud294/hg1k-b tdzl oc0vb8ls,k o+d glroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencbglo d /khd bd, +-cstul02v19k4goz 8ies 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 t5zwfpfc+bu:.yjc ,t q -flmebry wk(8pe 3859he aorta is 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 m.tb, +jc9y wbule:8 -fk(8f5y3p5f wpqz ercwaves 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*k;qk g+* ni7jqmi9q ae3xr z3 is flying toward the bat at speed 5 m/ziner qkk3*m gjiqx;*37 a9+qs The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sv par i6s)03l89 v -emkn-uryiound pulses as it approaches a moth. The pulses are einli v-p s av9yrk u8m63-)0rapproximately 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 one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vill6 vc;wx; ng4/gt6xy rcage 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 mosty; rc6 /xg6gxctnw v;4 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 liswb r)5b1k a8gctening 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, 15akgb)8cbw r4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lyh)16 goqc(g0w/yd g-xlj5tlong, slender aluminum rod held in t/)o5-1 dg jqhx6t(y wc0glyg lhe 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 thre+ s1w clc;bh:rshold of hearing for the human ear at a frequency of about l1 sch+wr;: bc1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears t6jbae5 on 3e8phe sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s anopb3 aej 58e6ltitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15i*w 00guf cdfqoo. x 0ax1in/eo5h09v $^{\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