What is the evidence t ,3lq dnn1z2,nzj hpv-hat sound travels as a wave?

What is the evidence that sound is a form o-p i07fkiz5lc9oexit :o:r al5wi)+ ef energy?

Children sometimes play withtdj q+g t2 ,rb qx9jz0p7,/z eibf)-nb a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wa z pz,b9bd20+)ijfjqtt e7,qbn/g xr-ve travels from one cup to the other.

When a sound wave passes from air into water, do you expect th x 8ou::q 10yqrufzlq5e frequency or wavel 8 1:zuqoqqfy50lu xr:ength to change?

What evidence can you give that the speed of sozj.8e4 q ipgk+und in air does not depend significantly on frequenc.8 i4j+ eqgpzky?

The voice of a persoty)fb) b. izz*n who has inhaled helium sounds very high-pitched. Why?

How will the air tem e6soex( +ok;jperature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitn s/:a*:t8eslt sxanq,9x 95sk pk tl*ude of sounds in various frequency ranges. (An ess 9s x,tnk8*xn aql:5a:s9p/ tetlk*xample is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced 0vik5/l3q i iicloser together as you move up the fingerboard toward thi lkq 3i0/vi5ie bridge?

A noisy truck approaches you from behind a building. Initially you he cam;ycu8k(b( 4vkz+nar it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sec4 vauy+ bk ck(8(nmz;ction 11–15 on diffraction.]

Standing waves can be said to be q:uw) 2qgr6atdue to “interference in space,” whereas beats can be said to be due totqgqur):2wa6 “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsyem(n r.t-(hs;k m/uq:m x5fx D and C (where de 5sqt.m;/m xmkf(n-( h:erxyu structive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the he6.eobu;lxugt hb4)i4 aring of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sou4u ig.6bl4; xobeth )und levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sup x+ug8v,,glo q /e9qqmerposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of t,mq l,9v8qx/eug o+gqhe waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if tthz+473 fq1aahtwzd oc a /e)cjq:h*,he source and observer move in the same direction, with the same velocittw 3o/e 7 a)af,z*qj :c1+4zd htahhcqy? Explain.

If a wind is blowing, will/xj n t-pn4t)co9:*ao2 hc m+0wsjafl this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or ve p fs9la:a)o4wjt 2+-hmtxnjo*c0n /clocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mq5ol(c 2b7ipnyp gt25 onitor is blowingi5by pn2tl7o p2gc( q5 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 reasoning.

  A hiker determines the lengthkt3gb41 q0ts rkx 5fkqsp2s5* of 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 the lengt qbkqp04*5srfgst 2 3k15 xksth of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He h 5f,oc+ lgizyb;ed6e/ ears the echo of the sound reflected from the ocean flo /e,;fl6d+cbz oe iyg5or 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 202 aty8a +ezy qkj,d3ke:l d e4/sxw6g8 $^{\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 schzane,la370p0vz43qh4urdn r4 hoo- hool of tuna on a foggy day. Withouhn4a7o 0,vo r 3uzdzah0h p4qr3-el4nt 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 yev*osr83v*log:* s lsplash it makes when striking the water below is heard 3.5 s later. How highs olesv r*v *3yl8:o*g is the cliff?    m

  A person, with his ear to the ground, sees a hugemg a+633v eyxw euu4a09 +ozi(k, waze stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in tx9me eoai y36u uwe( +av0z+zwka4g 3,he air and the other 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 oveos5 1(0hst yhor one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (yst(01hs5 ooh a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a4,q b zty7f9 fh3soi)n sound 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 4/o4i0svp*qot 2cb bi a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB -+ff*sgz vo0e when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add z +veff* gos0-intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally fgy8mo71u qf1,gfw63tmk 7 ol 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 allf 73k 71q6 tfy8olf mw,g1omug but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ra9 )fk z)7/w:/rsllfroqssap + tio 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 for97r)wlz r +:afsok/p sls )fq/ each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of prg;6(i+mn)z ls,0vp;pu7/ tff legh sound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughlmpsp 6;7 hufgr ()lz0fp+tn/v lige;, y 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 earxok)5.a:tx di,c le syzg: u:;3tfo o,drum 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 a8ovdla+0v e +-felk.2kxw gts dm85 z*t 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected inkde-sgva w8fmztl2l. 8* +e0 k o+x5vd turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whn(c;n3;wpzj)vj2v n5b./eptxq + dy zx*n4yjen placed 2.8 m in front of a loudspeaker on the snx 45j )nedwxc3;pnj2v +bnp/z.*z( ;y tvqyjtage.
(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 lm(o :fd dgdx*5ee6/ zdB. What is the ratio of the amplitudes of two sounds whose levels differ b dx(eglm f5dd6*:zo/ ey this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by*m698vjvx 4 y -ddndfn what factor will the intensi96 ddy4vj nndmfx8-v*ty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, butuew e6b)o5r1zi .5t ck one has twice the frequency of the other. What is the ratio of their )k.zrbe itw 1o65ue5cintensities?   

  What would be the sound level (in d)://88tou jq v)wf ,ab qpiaakB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm vi qkpu:o/8)b,/awj tf)8a qa at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-sq d v1u2zix8o loqmfa4 *0ex+a:*; juHz tone that has a 50-dB sound leveao4*msd ;qu*1:l xxq f0av zuj8ei +o2l? (See Fig. 12–6.)    dB

What are the lowest and higc24om yi0dzh14 rzr4uhest frequencies that an ear can detect when the sound level is 30 01h r4rzmiyc44z u od2dB? (See Fig. 12–6.)

  Your auditory system can accommodate :h;q.wx9kv cj a huge range of sound levels. What is the ratio of highest to lowest intensitkw; xvh cj9.q:y 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 fundamogo49n o)o.pdk zw5t /ental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the .toz o59o og4wdp)/nkstring be placed?    N

  An organ pipe is 112 cm long. ev npfb;-j0o bg 1l(x+What are the fundamental and first three audible overtones ivbbj+xlfge1; o n -0(pf 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 y /9 sd+icq0hfibf xc 858*urfzou expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was ai zd5sr9qhf+ufccx f8i/08 *b closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with o.*lt8nl qx .bun,)kx bpen-tube pipes spanning the range of human hearing (20 Hz to 20u qtlxxbk*)n ,.8.lnb kHz), 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 h: ext/0d q :uml8hqgf5armonic. What will be its gdeuxlhqt q::f0m85/ fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.7lq+ rp+qj 2,fb3 m long and is tuned to play E above middle C (330 f bjq,l2+qp r+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 len66+wn )jw i8c pl:k wp,j9zhysgth of an open organ pipe that emits middle C (262 Hz) when the temperature is lwjp 8p nw: +z6h9w)ci,sjky 621 $^{\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 2q86f6beci(6 f lg6*3 v tefbbb0 $^{\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 bq8g - )xxa,.zhr62p ziq7n3 ybr;tqsge that ph rxxb2ztya ;sr3g-n. 7qg)6,z8iq qmust be uncovered to play D 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 4zs9vcl+2qtmt.;e iw w tw0-zcan resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequen qtt wie-zc tsw.49z0 +vm;2lwcies 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 iswadi/sy h6eql0 r6(3 o open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 el/isaw6 0oy3 6(hqrd 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 vut7*fhppz80jtujg63+r0zc j*4d n u$^{\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 mp9:ci:s w4g drange for a 2.14-m-long organ p w9s4m:cip:gd ipe 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 th04wtf6v rje*me;rmde 3t 3pw;e outside and is closrt 3mt 4e*;m3fe0jpe;vd w6w red at the other end by the eardrum. 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 every 2.0 s when trying to adjust two strings, oiphs4 o)8pn)hkb t8af:i(e -cne of which is sounding 440 Hz. How fa i )fc8e: os) pthbn8ai-p4hk(r off in frequency is the other string? ±    Hz

  What is the beat frequency 5 kdfaki(pxlo1a o11; if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates uxzq) g5 0+. skzsu3ulat an unknou. 0xqs3 z+su5kuz)gl wn frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beaomy mp en5yz)-vv+ldm9+c g50 ts/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz m0nzdpv5 cl m +9)m-yg eo5y+vtuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned2u3ybr2uz)j zsbp0( w to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%.2b)zu3(j r w2puz y0sb What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eac*j,t k gcsjj:3wcj :s+h try to play middle C (262 Hz), but one is at 5.0°C and t:j,s 3k*wsccj+g: tjjhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4utl 0ca; ep4 6tzhy.q)41 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 frequep.c t tyzlheu;4q6a )0ncy 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 stands 3.00 m from one speav ts,wjtrln(ub1u0230is: baker and 3.50 m from the js0nbwuvlt1 t3s,(:2rub ia0other.
(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 supj1z ;t1(l9 a:yr-3ry x 2gdz8;quwvutrwd vs8posed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vitt19v zsu y(2grr- 8 ayr;v w1ql8;d:w3juzdxbrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m /+/f yp.e, zoyinsg7.gg,yr q and 2.76 m in air. How many beats per qpir+/ ys7 ,oggy ./ yg.fnez,second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certaizj7wwc6t-1joum4cr /n fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you/ tm-6rz4wuc7wjco1 j 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 firknjc.5wp6 0)lmcr ab9 e engine whose siren emit6c nmp)5bc9jl awk r.0s at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in fre.m7qhk6 eoc teg)., npquency if a 2000-Hz source is moving toward you at 15qpet)6g , .m.ekncoh 7 m/s versus 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 wisuw5 ot1:ua s-+6dn;r ixdq0 3gux n;sth the same single frequency horn. When one is at rest anddq 6;3ds anuguxn-s;t51uwri x:o +s0 the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ult zsvkad225j b3rasonic sound waves at 50.0 kHz and receives them returned from an object moving directly awjb25 kz v2sa3day from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a spee az5d6aiuk1j//ztez hna,( )tt +wy)wd of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wyd)t,j z)kz(+thz 5u16i/aa eaw w tn/ave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimeye 3pt/+ -f6)y sj(p /dtpaiofnts, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a secfps-+dypt p/)/3 jfo (6aiet yond 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. Sup+u5xlu-wx/r y r5ts7epose the device emits sound at 3.5 MHz, and the speed of sound in human wtxr-+u7e xry l5/us5tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraso tk(2.s/wedjfh: zg4 rnic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity isp ; 73jrnd6uq:zf4jwm3w hoi / 12 m/s from the north, what freqd pqwn:f; wj7r iohmu6334z/j uency 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 itsgb5mx(e4 ur8d 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 atqz1/2qwf xt.r ds,g4u Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the dtq2,r z.qfd1x/swg 4u irection of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters th8r zf0uk7,p1 q 3gwmaee thin atmosphere of a planet where the speed of sound is only about 35 r8eqgzmfk,0pu a 37w1 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wave a/: elnnim( /kangle it(n/ /mkl a:nei 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 ew(zn8eq2 cc)$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane9gv)o hy ,h 0x8ndil0onk06 vj exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear d, h9vn 68oxnyhlgik)0oj 0v0the 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 pulses d kew7dm( g*lb57rh-n mownward from the bottom of the boat, and then detects echoes. b mnd5-7(rk l* 7mhegwIf 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 the3*b xyomqrlv8+ t2t2jcr f i99r5; juyg njw;8 human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sympho yaor 7n53;poia ef*p8os:l3xny. It consists of many plastic pipes of various lengths, which arefanrex3 ;l:3 pp7o oy5 s8oai* 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 msx3-fxuup(*2eob c+3o kaa( y from a person makes a sound close to the threshold of human hearing (0 dB). Wuaxf-oxp bcayeu3o((3ks 2 +*hat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an: i wl2h oih.fqjlw4le(48j3 q*yp2 sv 87-dB sound are heard simultaneouslyhqlisj(2lo fh 3j *44:pi8 vwly.w e2q?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, 8z8rknl8a 5dhx,8qsla6 *w cqbluk++ is 105 dB. What is the acoustic power output (W) of the speakk ,+8akwqc u8 8nl*8zsba5 6lxhrld+qer, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outp ly45xpegpj4*ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. Wyxl 4e4gj*pp 5hat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraf fb*yu- jgf/8zt typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine8z f-f/b*gy uj?    W

  In audio and communications systems, the gs 2 ehww(cpm6.:wcoldn .cfe7rl9q/m 4 -1naeain, $\beta$ 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 freqz,we1((kcii 0l+,u9tbmv1 fp dwv8pfuency 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 b4pzr(tg4u gyd5v , y/is 32 cm long between fixed points with a fundamental freq4dp5(4z, /tvg yb yruguency 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 . rh2jc0sck +gvibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so02hj gkcr.+ cs, 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 i8/dlbgxk) k x w8y7xs,9c8owb s open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonancysl)o x 8,7 wx kc/dk98bw8xbge (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one ff;/fq2pba bryyi 14: jps z++bull 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 dn .9 1b,mmukz.eo2fd coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves.od kd, 2mu1fnmz b9e. 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. Thx*02li 0w8x am)gijjze conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of)w*ziig02xmjj8xa 0 l the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftere7u-b xa vs(u+ it passes you, its frequency is measured as 486 Hz. How fast wa (aues-vxb7 u+s the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just bytyoyj,* 14ayim)t i;q listening to the difference in pitch of the engine noise between approaching and receding c41j tiyy,aimo q;yt*) ars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, pr oex k- byc25.7qnhvy:oduce a beat frequency of 11 Hz. The shorter one is 2.40 m:y2b7kx5vy c-q e.o hn long. How long is the other?    m

Two loudspeakers are at opposite ends of -mt8(u +zlur hhki.u.a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the ob ul+hhr8. zumt(i. k-userver 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 bloopf1 fjm ow6goy)a7w e4pq:8ddj6ga5;d flow in the aorta is normally about 0.32 m/s what beat frequency would you expect i:gp;fjmq8e d7fa4owd6j )1o6ap5yw gf 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/9punt.n,o9ex zt 0zae69hk4 ss while the moth is flying toward the bat at speed 5 m/s The bat emits a souno hzn 9,4e ns0p6exa9uk9tt z.d 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 sound pulses auyuhc *+ol9 /ifk1mf:s it approaches a moth. The pulses are approlmf* k+u h 9/1uyfic:oximately 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 fr3cwxluo + crv1e.;m b2om 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 12–31lv x;c+me.wocb2r3u .) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stac9cejtpg ip.y,03 ag( nding waves, which can cause acoustic “dead spots” at.(ai0, tgcpeycj9p g 3 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 demonstratioqwa(.ntc 8gq8 wtc9/00kdu z cn, called “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the roq /8n.zq duc08 tc0t 9a(wkwgcd 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 of1+. pw8uj; asacld;efwo 7kt4 hearing for the human ear at a frequency of about 1000 Hz + p4;k71t;aae8 .f dljwsoc wuis $I_0$ = $1 \times10^{12 } W / m^2$ 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 M/nm1r* wdp6qd u)rr6tach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes direrrt* 6q )dmn1r/ 6dwupctly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 v s.e460f iaq( ey*tfb$^{\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