What is the evidence that sound trave ce le35d6u:nnls as a wave?

What is the evidence that soundvca/z2ys huax b) qm*z c:4v*7 is a form of energy?

Children sometimes play with a homemade “telernm7ebp le+ i/:9 ges0 (,pbkpphone” 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 sol0ime+:e(g 7k9e/bn ,bp rsppund wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o:q ,/kc eskuvp;fx8i)89leis r wavelength to chpl9 c iqeivses,;k 88:kuf/)xange?

What evidence can you give that the speed of sound in air does not depend sn;d/y9nu r r1nignificantly on frequenrnr9u 1;yn dn/cy?

The voice of a person who has inhaled helium sounds very high-pja2jfe+r y j 4z9s20s(szi-jritched. Why?

How will the air temperature in a room afv5 xxygbt7w81t kr/(o fect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude 6i,vv3 f.z9jah gzl*k of sounds in various frequency ranges. (An example is a carzv,j6fl9a .h *kv3igz muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together agtj6 a5agvx3 d084 eofc 87kkpeg5j9ks you move up the fingerboard toward the bridge? c8554 egkxv7g9t6 eodag3 fjkk8a j 0p

A noisy truck approaches you from +tq9y dp: e avj/+(nagbehind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you heae(aqpdan+/9+ t g yj:vr more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due toejmkbup ..;) z “interference in space,” whereas beats can be said to be due to “interference in jzk.bme) ;.pu time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the p0sat hr9x +xc6oints D and C (where destructive and constructive interference occur) move fa9 t 6a0sxrh+xcrther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with uzbrq,:tr/h5h3 mz-; ti,. nwuu s8usvery 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 noiseiub,w hut/q mz;zss5h83r- :t.nr,uu . 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 fz5c-3)0,of f uq yu)d 1oxcnsbe thought 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), aru1 50o) 3sqf-cdy, )fuczonxfe the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if *g;9s-jcszr0/kubtn ky 1ldmt 2z )bvp5l t 0.the source and observer move in the same direction, wrgd -t0*2 jlp 5tnczbmsk 91)y .;0v z/tbskluith the same velocity? Explain.

If a wind is blowing, will this alter the freo4ald 2fu30z qquency of the sound heard by a person at rest with respect to the source? Iz3 d2la uqf0o4s the wavelength or velocity changed?

Figure 12–32 shows various positions of a chil2( xa(ie0l xc*u.p 3gxgdvco/ d in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, v 0 apgixxu(g3xl cc2d /o*.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 ,ykp6g,k5ll g 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. Ek6l g ,lg5yk,pstimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of h hw--)e 6u)w hob.tzejis ship just below the 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 )ou e.bezjwh w)-th6- 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 5qzddpx/z.hfb75yl/ iz 8p x,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 isq3l4k suqnk* 6 drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is sqlnkq6k4* u3 heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splas:a+e)e vv40hnpaz kq ;h it makes when striking the water below is heard 3.5 s later. How high is the cnqve:aa ehv 0;)z4pk+liff?    m

  A person, with his ear to the ground, sees a huge stone strike gys0r1q)g)n9 0(ilmwbw waw- the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table rw gqg1wi09a- (n ) wwl0sb)ym12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error mj..xqbo 88dtp+ntr86v 2zten ade over one mile of distance by the “5-second rule” for estimating the distance from a lightning strxt8.n pnt vb+2 z o86qj8ertd.ike 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?ze/)qodnal- e92mh 7t    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levelped,i f 3sh9n+ of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of wj 6;b uib h1p,j7ddu;95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intenwb6ijd j7;;uh1ud ,p bsities, not dB’s.]    dB

  A person standing a certain dih/qfdyqpeig q/7 m4/8stance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pg/pd8y/qh 7 m/4fqqe ierson experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have; mg/.the3pv(to o ,sr 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 device? 58 de,otp; /h3(.gotv mrs B =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking g4.nary7 na 9yin normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centeanr7nyy .g49a red 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 eardr35v qbl ;7 tbu glsrt8lef,5q6um 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, while the more modest amplifier Bttzf368t:brf x/ s gz* is rated at :fbstttz / z8* gf3r6x40 W. (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 registered 130 dB when placed 2.8 m ug 0vsa*il.( kawr cra.0zk ,;in front of a loudspeakerc.,iaa*r0zav gs0. (lurw k;k on 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 dB vu ;am: sqybc: taa11m:+nty4. What is the ratio of the amplitudes of two sounds whose aytata:n1s ybcm +;m:qu v:14levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave ie vy5mb s -k-atbj w spx.)+nc8z+*x3os tripled, (a) by what factor will the intensity increase? Increase by a fa8 evxs3)ka.w+-m 5z cxb p-nt+j*s yobctor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement ammn0wslzy,r l: )1ry9jplitudes, but one has twice the frequency of the other. What is the ratio of their intensitie ,n1z9rj :sl ywm0yl)rs?   

  What would be the sound level (in dB) of a sound wave in air that corresponds to ubg (:2z(qzlu a displacement amplitude of vibrating air molecules of 0.13 ugq z((z :lub2mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1h9odq.jkcyd /6/*xue 00-Hz tone that has a 50-dB sound leu/x9/6d .yqjd oek*chvel? (See Fig. 12–6.)    dB

What are the lowest and highest frequen 0da adhm2 c)*7 zgw)yk)mbkh+d*u q8fcies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.) 8*b dakz* c)d7+f)2w mga d hquky0hm)

  Your auditory system can accommodate a huge rf/)yt (o) ckjky)vbcc)iy 5:nange of sound levels. What is the ratio of highestcnoky jc )y icb ):/y()tfkv5) to lowest 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 fr8)ctbt9a5x) 9 szbgciequency of 440 Hz. The length of the vibrating portion is 32 cm, and its5)zb 8t)t igc ac9b9x has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cq7a- ;bvm1ws ;7 xbzavm long. What are the fundamental and first three audible o;w 1 7bb7sxmvq;a za-vvertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acrossdmj4ricpp4w j9yayl ;7;v 8i2 the top of an empty soda bottle tha74 riv;ywypacimjd4p8j ; 9l2t is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanni*owmr(ezai0gy yoay )y+pw43f 4 +en/ng the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? fy0 +n z oi4ye wyae3)ayo*mrg 4(+/wp$L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz :l2 3ng6e3(zy9wp*y zm zf* tgjglkx3 as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengl:*z(k z9w ejpzf yltmg32xgy3*63g n th?   Hz

  An unfingered guitar string is 0.73 m long an,hqm 9* ocaygmtx,:h.d is tuned to play E above middle C (my 9a cx*qhtm.:,o, gh330 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 (2cp u 7f8s4zu:k62 Hz) when the temperature is 2uc7:uskp4z8 f1 $^{\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 a5jq/i .(d fbs2vek+ovt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 shout-verdrazv6w 4 .65 agld the hole be that muw 5g.r4 a-e6drzvta v6st 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 can resonate at 264 Hz, xk l/l6g13fdh:ou zggep 2lvn 6xa/ d47h2l+m 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this ig/3lnkp+gh6gze6fdmlxuv ol h da :/2 xl2174s 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 y 8fzn+cm 3pp onb)e+5jur1 -. k:f )jci5bgimis open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz-jieofrkmpf5 ):gbj1.) 5ycn cumnz 3+8i pb+. 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 0/ 4x-yx pcrre$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-4a u+hnp.z-yv long organ p-4znha+yv u.pipe 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 g kwf+xbqt tj. 59,qb9khs2*dq3 v/osand is closed at the other end by the eardrum. Estimate the fb dbf.3q*k9k /w+h 9,oxg2q vsqj t5strequencies (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 tv 8voxem5 3v4ae30qzy wo strings, one of which is sounding 440 Hz. How far off in fmve o5a v0v 3eq3yzx48requency is the other string? ±    Hz

  What is the beat frequency if middle C (2 q3j w7r,(.cp7iz vuxp83ldcw62 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 01eig52 dhc:h2nq0tsnrdhp / ile another (brand X) operates at an unknown frd2tph/h5g02 i 0sd: h1 nnqecrequency. 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/ p(u2ies5 5ki3i8sq jxs when sounded with a 350-Hz tuning fork and 9 beats/s when soundseu ii q5ski(jp532x8ed with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to t.z )2fgl 4p cztv-rmk1he same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. Wha l)m z.fgvr21-pktzc4 t will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will b0v/)/ gjj,3 wd4a j ipdqn+jgke heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and thjdijp jw+0/ga4j,qg)v3n / dke other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuningk,knsk l ,jf0gxzn6-h9iziv3i 5 ; v(i 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 is 4 Hz. What are the possible frequegi z 9kxsi0vlk,nkh3 ifniv;5,6(jz- ncies 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 kxw iu,i*jc4j70nax z nb(,,4w zxf*aand 3.50 m fijzbfczan *4 ,xa, w*w7uix0jkx,(4nrom 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 supp(9v.hpsx:7ef tah .nuosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s wheha.x (se fhv:79n .tpun they are played together. (a) If one is vibrating 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 and 2.76 m in aibq4u6wg0w 7lwr. How many beats per 67q0lb 4wg uwwsecond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz whktr)n- 9*.docj r ,cmbeq-s u3en at rest. What frequency do you detect if you move wij-)ckqd9ou- e .rm *b3 ,rsntcth a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire eng j+:wv/hqy 6fd2bpd5jed p; f2ine whose siren emits at 1550 Hz moves at a speedpwy/q;pd hj v2 jb52df+ d:6fe of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freque k(l ;onk5p(xuncy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 5nlk ;ouxp((k 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 frers zec n)vr;:5quency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears:nv;s5 ce )rzr 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 ultrason72.(mt zwzfu zo,;ej+bo*a nxic sound waves at 50.0 kHz and receives them returned from an object mo(ua*n;+m zo7wf, x2b je .ztozving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speln cv:if:w6wkfr 8am/7qa3 h;oer 5bl*p*-aged of 5 m/s As it flies, the bat emits an ultrasonig *hf* i8:wo/anq5rlk-m6ar; ef7lb :apvw3c c sound wave with 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 played -i 7muu6tw2oohb)r5r on a moving flat train car at a frequency of 75 Hz, an robhrm-u)2w 6o5tui 7d 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-flk*krwv1 v)tzcy1 2z9dcj s. h*ow speeds. 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 expected beat frequency if blood is flowing in large leg arteries at 2 cm/kdzhtj1 rkcz 2 9v* wsy.c*1)vs directly away from the sound source?   Hz

  The Doppler effect usiwi1 zj4h. bye8ng 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 Hz. When the wik7tz3djkra/w0 )(y zro t,wo e6g z06znd velocity is 12 m/s from the north, what frequency will observers hear wztk)dkww, r06rot6z0 o /7zgyz3e (ajho 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 movin a* t-vbb,b;ipg on 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)l q 2dbo5ji id++vq8w the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s mo b + 2wdj+5qdlq)ivi8otion?    $^{\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 annj6h 92+honlm g. iu, planet where the speed of sound is only about 35 mhu.n+jl nnigh2, mo96 /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 anj .ngp+fi( a3ip rb /;.os5zpagle it produ/+r b3pgaof..sa; i5pjpzin(ces
(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 7 )v93+x+aq+fq z p-ee3zlyi)ijmzyd$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactlyk-cw.xs1 etcniov/qmuou8d t 453 r,/ 1.5 km above the ground flying faster than the speed of sound. By the time5 w/u t-tv38osqm4ixrc./ 1dk,neuco you hear 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 rknjyd(w6vfs k 4q5(;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 5q((6 vsrfjkw;d ny4km, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the humaq( .,oyhk5h j9lvwf(xc q:n 1an audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists om7 tt h-a fy6x6uz7c*tc8g*eb f many plastic pipes of variouh a6 ymgx t-tbef*7 tcz76cu*8s lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold of hup9a(5 7qli cq0m yhu21x 6nxcp6ifs:gman hearing (0 dB). What will be the sound level of 1000 such mosquitoesquxi1qm:p2s( 7 6 9clg65 iy0cxah nfp?    dB

  What is the resultant sound levely9* tjdjc. qgt 5m 0,:na+zcd9ljg nrew* 0o;b when an 82-dB sound and an 87-dB sound are heard simultaneously? *j.dj n9z ;boetr5 dqwa:0n0c g+ *gtlcjm,y9    dB

  The sound level 12.0 m from a loudspeaker, placed in the or/a )n jd95icrpen, is 105 dB. What is the acoustic power output (W) of the speaker,acjri59 /)dr n assuming it radiates equally in all directions?    W

  A stereo amplifier is rated a i6kdo3*c5vamwq liqf3yp. *:j(+ wxat 150 W output at 1000 Hz. The power output drops by 10 dj:yw 33w.cipad*klm6 oq 5 +fix(vqa*B at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically we nyno0pk91y8d ar 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 o9ny 1pk8yn0dthe 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 engine?    W

  In audio and communications systems, the gain, v-9 wl7,ikx;o a.ch j6k b1rih$\beta$ 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 tunjl* ;i -fa2ycfed to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long betweeni 6d-hl -f rqs/ud; t9g74vet;z,5mqlrhe(vb fixed points with a fundamental frequency of 440 Hz and a mass per unit l6fdtvr d,4h g-/ ebm-;qlui5ztlq; (srv h9e7ength 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 witewt j3,0vqga9w .yzm 082)6 az+tsk e)qhbpenh water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water lehwz wm0 zqnt6v),qpa0.ea+b )yg2ee83 kjs 9tvel 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 mase: smhxl1p,/ ts 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the tt/,sm:e 1xh plhird harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observejdl1unc3n630 7z fltzd to resonate as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two so(,x/e cx(p+0q wsr8sustz l/u urces. The sound is loudest at points equidistant from the two sources. To determine exactly we /x,ts(swpcq/(zx0l8+us u rhat the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz z nw.z i(:d(dapes n96whistles. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. e9 inn(.zp:ds d(z a6wWhat is the speed of the moving train?   m/s

  The frequency of a steam train whistce7n3t-c 9,q dk,)pvio s+ ppule as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How),c cido k, ppqp+e-9 3ust7nv fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars j.ni pi:c :fv-kust 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 halved) asc .f ::iknpiv- it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. Thebp b8.mq.pqd3h 3rc*u shorter one is 2.40 m long. How l.r quqpb .p8b 3c3dm*hong is the other?    m

Two loudspeakers are at opposite ends of msx v,/a+ gar4vw n4(ca 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 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 afterw avxgs vn a/+,(crm44 they have passed him, at C?

  If the velocity of bloo :.g9uzna b7 mw:pdy)syw t-7md flow in the 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:z7 mms gt7.:)ydp9 uya-bw wn 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/s whilyu,p-+gn az)jjatj1 3ex c85 le the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency ofg5jzjn,yl1pj ce 3xta-+u )8a the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. Tll: l);h xq62gdaqz4yhe 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 before the next chirp i: ;l)yz gq lqx64ld2ahs emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine vil6 pmizf: k+x3knm2o ,japq* 3plage 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 lomkf 2 ppi3: n*6+p,qaojxkzm3ng, 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 listening canwo77pi5. 116hvt zlje7+/cvnya omku be compromised by the presence of standing waves, which can h t ypvu7ima+cn.677 jeo1vo1 w5z/lkcause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alxwie+hu) bu,uw6+1 alk *e9d guminum rod held in the 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 ) 6u1e9a+ueuwl,*ix w h bk+gdclear, 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 for the human ear at a -coi lel7 .d y7/ygtt0bj)4we frequency of about 1000 Hzt l 7eet-)/b y w.ciy4jg0d7ol 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 f((qff)pg,d c8 u3qb) krct ;qobserver on the ground hears the sonic boom 1.5 min after the plane passt) crgf3u;df8, b) c (qpqkfq(es directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ,j9/ exjjr0 mjiez+ b+$^{\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