What is the evidence that sound tr74m;la6q4bex elvqs+5d u/q mavels as a wave?

What is the evidence thax ;4bpkvo+ kv8t sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a strif/ pv ciu4wp1*ng to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the o /1fic4v pw*puther.

When a sound wave passes from air into water, do you expect theo 4g sib0now2f1k0mmazex; kuu) g5.8 frequency or wavele b4ag 0nmxz5o2e)s u. kiuo01m ;w8gfkngth to change?

What evidence can you give that the speed of sound in air does notn+ 66 vf2ak5ncqr;e hc depend significantly ofav2n6 +kc6ch5nq e;rn frequency?

The voice of a person who has inhaled helium7 -/ddkn:sz b*rak:k kc jlyon h/o:+3 sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of orga.tv a;adwfp2 :5do l6on pipes?

Explain how a tube might be used ap p *3vh4po+34y hixj138 de1cicuqgxs a filter to reduce the amplitude of sounds in various frequency ranges. (An ev84 h y p31 *p14xxgucqe i+hcdp3ij3oxample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you movem 4 ,o )1fb pzs+dxh-7oec0fdrx zjw*3 up the fingerboard toward the bx d 0e3f*,ho m- jxcz 4o7brsf)p1+wdzridge?

A noisy truck approaches you from behinbj.35xy yxa i4d a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “bright53 xj4yabi xy.er” — 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 space,” whereknku7m;y /cya4og 9 x4as beats canxm cy4ny;ua7o/94kkg be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would th;ih2h y;oeel3 e points D and C (where destructive and constructive interference occur) move farther apart or clos;;l o hy2ie3heer together?

Traditional methods of protecting the hearing of people who work in areas wa-s:a xb;/is:- zq mi8 ci:nyaith 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 it to the headphones iniaisbz s:ia/nc:- -y xm ;:8aq 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 as a s-*xnvel .ruh6b7 gua .uperposition of two sound waves with slightly different frequencies, as in Fig-.ge. rx hnluba7 *v6u. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the spisy 7 3u(g65tkj7o k9ox p4usb+nbi: ame direction, with the same n:pto y kp(+ksi6bg4xu9 7u3i5o sj7b velocity? Explain.

If a wind is blowing, will this alter the fc,b t 8wdt-8fqrequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changt8 td b,f-c8wqed?

Figure 12–32 shows various positions of a child in motion on a swing. Ad 3np6p hu22:9 1rhh svqbv9ir 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 the sound of the whistle? Explain your:vp9 9b2s1hhv3r2pqh dri 6un reasoning.

  A hiker determines the length offf;l;ux7i w5+3 b jxbdc*tl8 y a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate thi7w fj+xd;tcu5fbx3ll*b;y8 e length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below thqbog,+7s 83n, fz qiohe waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and dno7bzshq,f 8q3i + ,ogoes not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng281/adccta o jo y +bope:;n)pths 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 tunam-x6avx;f2t a 0zn1xd on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses befmvd2x-a x0za;1tx nf6ore the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. T szol,59qpl6v)o1elz k mj-f6 he splash it makes when striking the water below is heard 3.5 s l6)zlvo ,klsp6f5 j9l1 zq-emoater. How high is the cliff?    m

  A person, with his ear to the ground, sees b y)d 6nluqs.8a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the othe86).l synuqb dr in the concrete, and they 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 the “5-second rulep)twp bq):r-qr:.wukn 2dd9eks0* zn t pkdqn - rqwusb 0::rz2kpw.))nd9e*” for 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 s,eylkf t/9g.m* yfwa .ound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose ing 3+b*c(ow vzrtensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB)likdxl :k3;3ua sfo.x9s-tl when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hintls) il3-ktsflaxd :k ;.39xou: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equall1 u uzwdsj0(l*se6; ocy noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Ad; u(z10cljoue6ds*s wd intensities, not dB’s.]    dB

  A cassette player is said to have a signal1- psd)qd q3pe-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the - q3)pedd1s qpratio 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 from a person speaking in normk dkq 112i,wxzal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a ,w1 zk ikx2dq1sphere 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 striko6-r ndq+qy/jes 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 rated at 250 W, whi/oxfi ab,6j;yvg )j 5dle the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connectedd;6) j/5xfvga o bjiy, in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 d/d6eyjt6 5pd cB when placed 2.8 m in front of a loudspeaker on the stage. 6dp65dejy/ tc
(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 differeno6erb5 5gl a;mce in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amg ;brm6ea55l oount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound 6nak0+6 v7h t plb8ndfwave is tripled, (a) by what factor will the intensity increas d vlf80+pn6a67hbtkne? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitud+ *pk/fic5g e lef:tf9es, but one has twice the frequency of the other. What is the ratio of their k+c tlgef:fp/f5 9*ieintensities?   

  What would be the sound level (in dB) of a sound wave in air tha;ir1g+6bhf :1 z hdlqqt corresponds to a displacement amplitude of vibrating air molb1ihrzq1 lq+;6 h:dgfecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound led, .t*r// hov5i hd9bekno* lovel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Figbnr,59l. di/*o/ dhkvohe *to . 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the soun.tdf)q +g ald,3 ko f5rub oit*71k3jad level is 30 dB? (See Fig. 12–6.)1kjf+ rd fkud73bo.qi,al*og )5 tat3

  Your auditory system can accommodate a huge range of sound r, cbj9)uvhn ; f)l:lllevels. What is the ratio of highest to lowefj:9n ulv;r )b llh,)cst 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 length of t uyrlv2 +k8j6 4rx3bimhe vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be pla x bvijr4kmu2y8+6lr3ced?    N

  An organ pipe is 112 cm long. What are 2lk-z-:wwhhtk2yo(/p h8 8pxauycv h s3w)5dthe fundamental and first three audible overto h(p58yxzww-2d8o uh-wlyhkv/ hs3tk :c)p2anes 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 expk et7r7c2c j m2bo*j4iect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wastoc2 2cr7ji*7b kjem4 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 organ7w 5tx 6s oii-mzfuahzmn 0pq4 p-*-8n with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what wouldxi z w0nof--tum-p*q pz4 sin5a7h8m6 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 harmonic. What wi*c z mng dvmx,t2+;eg8rc8cm 2ll be its fundamental frequency if it is fingereder+t8c8vzcd* g2mcm ,g;m2xn at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned sc1k9vj3vef;6l 1sido1 qqx, to play E above middle C1ek9qx1 s,si ; 1clqjd6o3v vf (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) whe ,nwi6/cth1slsntu jd(j0* l8nun6 ,1 0sj8/ihjd tlltcw(n*s the temperature 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 2j wo7wprf 4dqqb t8qb.x5(l3+0 $^{\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 th0sau17w3iuu v at must be uncovered to play D above iu0s 7ua1 uv3wmiddle 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 reslrm .);ugw *ajzy 7)lfonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other freq*7ylgau)m f ;)lrw.jzuencies 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 z fks, ;bjyz+/1+lr* cgi6acv both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is +1 ,lcrafjb zzs*k ci 6v+;y/g
(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 p2u - g2(pcv zjn/.pkc$^{\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 w+ d;zs-y+ rrklqu4f9 4bq(fn 2.14-m-long organ pipe at 20qk( -lf4n; +brd w+yrs9qf4 uz $^{\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 to2z8a qa 2uznr bj6()np the outside and is closed at the other end by the eardrum. Estimate th2 ( up)zzbq2ra6j8nane 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 every 2.0 s when trying to adjust two sb cxgc17vmc* (cl6/a ltrings, one of which is sounding 440 Hz. How far off i6v1m /cac7 gc*x blc(ln frequency is the other string? ±    Hz

  What is the beat frequency if middle C (269vx;m9+ibfnhewf6 9(us pm s)2 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 (bran2 unmu) mhybjizbc)m1m(- 15j d X) operates at an unknown frem1 (zub- 5imc2)1nmhjy) jm buquency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tun)3 6 uzw oro4bxu6qb7k.qytl .ing fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vi3 .)o 4rq zw7tbokqly u6.u6xbbrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to th p69l:rm2f3 1 (pdi/ar dbayvoe same frequency, 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 t: 2pm/ i6raav9 bl pr(od31yfdogether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two ident4b8e0gm l;octxt*r6pio 1lw - ical flutes each try to play middle C (262 Hz), but one is at 5.0°Cb;-ec 0 to4wm6o x8ltlgi1rp * and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tunin 4 tcb1(ishza.qnci,x2dk2*kg 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 frequen2* dcc1nisk t24xi.k(zb, h qacy is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person staq tju8bwy2me 4; x ,o-j3.bffands 3.00 m from one speaker and 3.50 m from ufxo;8 bj3e-q.m 2,ytfab w4j the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a swyi)6wm4t9ez30lt*nz 1 : hx(ih pbrpiano 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 frequ1ystzwb 3) (mw0i nx46:h* rt pihl9zeency 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 andt(75jnfq le*bqi 8tt 7 2.76 m in air. How many beats per second will be heard? (Assume( tfbq5*nt7ltej 8q7i T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sir)x8/0 ibl88 un0ljxuv.i lo;t h1njgg en is 1550 Hz when at rest. What frequency do you detect if you move with a spejou8xgix /8)gnvlh8tl .j 1i0bn0l u;ed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency 0.gqk r:niavho ,g h7*do you detect if a fire engine whose siren emits at 1550 Hz moves at a s0g*: ogh,vikn .h7 arqpeed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a a)f z30mu+v9x; dgja wny2vz. 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freqzwaamd3 v9yj .2)zngvu0 +x; fuencies 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 sam0 .chm1pebfc+y3k+jtgh n .g 0e single frequency horn. When one is at rest and thep0.cngk mf+h13g0 c jhbt.e +y 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 T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ret safook2:pegl 30la 52urned from an object moving directly away flaso 2fl5g:ea k30p2orom 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/sl- a roedm/4h9 As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequah/od9em r- 4lency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, 9 ce+p h:qvwd*;hpsw*x2;hyy a tuba was played on a moving flat train car at a frequency ofh; c+pyhh 2p y9*xsw*dwvq e:; 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. Supposa; 2p)6)jjvnbuy3 fn+nlx/z j e 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 expecn6bnvuzfyj) ja2 npx l+j)/3;ted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usij+l )j-rc8xtuy 4i8jcng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 d,xhg 7j(y-4mdnrf6 0qatpczuz, :0vHz. When the wind velocity is 12 m/s6g-ut0ddh n rxqvzpjfcm04, :y,(7za from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speiqr*qq )h4w s-rz,emu* yda j)zv: +k62fxq3e ed 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/1flu4 nagt/1 ds (a) What is the angle the shock wave makes with the direction of the airplane’sa 4t1dfn/g l1u motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the b. qzhmpv8 +3k*soko-speed of sound is only about 35 m/s -.mhos*z8o q+b3kpkv
(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 travelin(xi j4j5r dweu3tk1g ;g 8500 m/s strikes the ocean. Determine the shock wave angle it pk j5 4(wie 1;d3rugxjtroduces
(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 1 l50,be eq y/nqi 24bzbytw3h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and sj uwi1pt;1; tfee 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 a horizontal distance of 2.0 km. See Fig. 12–34;1i ;wft 1jput. 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 devn qei5v1jqx tc9r98;w ice that 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 pulse5w ;ni98q rt1je9 vcqxs (in fresh water)?    s

  Approximately how many octaves are t2nwrrq4 )yd -mhere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer4 g2i6yep9rvi pipe symphony. It consists of many plastic pipes of various le yeg49i6ri2vpngths, 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 nu4dmzvph (0ujgo/ h2 pki.fh+883 cx sound close to the threshold of human hearing (0 dB). What will be the sound level of 10nh/3 ppfhujuo c 2k8 4igzd8mh0+xv(.00 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound acsjnad,. i0u,1rw(alj .0-o ok2mlnrnd an 87-dB sound are heard simultaneous kj,m0id,ascn-rao1on.0 .w(r jl l2uly?    dB

  The sound level 12.0 m fro,wyjcqbgto +:84 wa1m m a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (Wcw w4jg+yo,t bm 8qa:1) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at bl4eibme5hy ww (/ 6v1150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What im e5eb1( v/ 4ih6blywws the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective deviokf+ x18v-bb:ltg p*y ces 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 c*pl bxtgo1-y+8kvf b:m. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain,:gwyn vbh uolcrp35 i, vui.a.;,h)k3 $\beta$ 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 frequencyku4wn.lb om 68b8,psbt.+b (hsax1yi 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 ewwz qe1,25ulfundamental frequency of 440 5e wz elq,w12uHz 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 +/i 2fz bvj m)x+4twvf3jc i7mopen tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. x)73 wvfi bmtfvi/+z4m+ j2j cAs 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 near a tube that is openg .g3ktakn83s*uc bm9 at one end and a3k8b3u k c*.tg sngam9lso 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 ob)anu/tcw ms1 u(i*bg )u3iw6kserved 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 comingu 2zma (;ftb)n from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency i )aznum 2;(tbfs, 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 whistle/vi ,v6u 1hintaiiu8+;m)pr6ux-a8 qjuqb 2gs. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the g1qvh ia/xu+b 88i)u6 iv q p2n-uaju;6rtim, moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. After q8 kzxk3y8x.u it passes you, its frequency is measured as u.q xkzkxy38 8486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you c 6ii0z v63.wiokzxqx,q2a/f, irx (ahan estimate the speed of cars just by listening 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 halvedq 3ii r a2/oxw xxf.,q60z(h,vaikiz6) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togeth1j/ bm+nej i/(ujo53 eecj:gd er, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is e/5e bn(3 gjeijdj+: j/om1 cuthe other?    m

Two loudspeakers are at opposite ent ;do/)7 4ghoqf2 pyllds of a railroad car as it moves past a stationoogyq74t 2)lf/l p hd;ary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) 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 e.konk75uh u:wj6lo6 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 waves travel with a spk .ho5 6nulk7 :o6uejweed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while thwzk cwab/+ 2e7(o1 omhe 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 moth(ea/ 7kchzoo+m 21 wbw?    kHz

  A bat emits a series of high frequency sound pulseg)vmfr e0n9r5 z. +fdhs 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 one chirp returns h.)fnev 5frd09m gz r+before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to senu +o(4,w2o if m 1kxhbwjmtzsc,/1.fz d signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m 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 cf 2b ,tofzwo/u wi1.(m4z1m+sk hj x,open tube.

  Room acoustics for stereo listening can be comproqis -)ihme*:6hu r*z v2yi*somised by the presence of standing waves, which can cause acoustic)su*e i 2 hq**-vy6 rzsho:imi “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,9tl /+y xiggj(iy68f5zot b9e” involves a long, slender aluminum rod held in the hand neayt8yelbi f6zj99o t +( 5i/ggxr 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 of hearing ojjb ln:f: m4(for the human ear at a frequency of about 10fj4m :lb:n j(o00 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 thexp7 f +xk.je4x ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? xjxfx4 pk+e7.   $ \times10^{4 }$ m

  The wake of a speedboat is 15 - 3i ic6bk;dy0ayp. dm$^{\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