What is the evidence that sound travels as a owj*fw(uc+hx 3u*n u -fs*i o5- 6ggkewave?

What is the evidence that sound g4nu8mwv9v a5e(7 ucc is a form of energy?

Children sometimes play with a homemade “telephone” by attach8m3lgd0g ycf weks42*ve*9 q)xmz0sa ing a string to the bott8eef * 4wdgm3qz *2mylk9)0 0acx vssgoms 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 other.

When a sound wave passes from air into water, do you expect the frequency or wav +:hx*5xbz sexbj nj24elength tos5 x4bjbxnxh:2 *je+z change?

What evidence can you give that the su8wyyld 84um5x zg0utb+9ymlsm ; g52peed of sound in air does not depend significantly on frsggl5 yz;889umx2w +uldy 45mt ub ym0equency?

The voice of a person who has inhaled helium sounds very high-pitchedoljfm-vd0m) sfj - 1bkxl, h,0. Why?

How will the air temperature in a room affect the pitch of o xev9k1q1j/ d n af3rrwltd(:8rgan pipes?

Explain how a tube might be used asfoyenoz22 a01b ,c02hzq 7fuz a filter to reduce the amplitude of sounds in various frequency ranges. (An example isu1z7bq2coh2 fy,f0z2o a e0zn a car muffler.)

Why are the frets on a guitar (nb j)z0r,/m bp6ptb6 m,g6hvfFig. 12–30) spaced closer together as you move up the fingertjm,b/,)hp6fpb r b0n m6g vz6board toward the bridge?

A noisy truck approa 7 ok6n7yd8 qrad*1bimches you from behind a building. Initially you hear it but cannot see it. When it ek 6ybdram1*d7 78 qnoimerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beat lce g4 +5*o9l7wzr1ii5wxkois can be said to be dui 5gi5+4w* roci1wzl97x k oele to “interference in time.” Explain.

In Fig. 12–16, if the fe 43inxi 7v:tirequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer together?i ni: 3i7ex4tv

Traditional methods of protecting the heari8zwc1f.9i/ddxkq .el3ef /uwng 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 sound levels reaching the wfq1fuw i .8d3lce/k/xed9.z ears?

Consider the two wav(mjt-ea ugx3ma/1 fxo e)fa8;1a jnm; es shown in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In m8 ex3m;ff (t ujoaa ajga-1 1;/)exmnwhich 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 eu;l*x)v5la17j bryej a .)j pmove in the same direction, with the same j1v*jj ey)rl7ul 5pa.a);b xevelocity? Explain.

If a wind is blowing, will this alter the yf ;( +anlt+r*;gf kkgfrequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity +*;gf;g rnatlfy+k( kchanged?

Figure 12–32 shows various positions of a child in, ly-ib+a70 ka5xvsqc motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E sxk0a,c l-iavqy5+b7, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the 91 xhjru+z 8 6yynie8tlength of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears8n6herxj y19y+ 8zut i the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He he mccif 8t6utrpnepdd v+qg: +3jq0,76ars the echo of the sound reflected from the ocean floor directly bel0+egpqq+r76 cfjp: v,dmcdn t3ut 6i8ow 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 i4jkdqi9n ,fa/ 3ll. :vy3t mlen 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 jj2 0 zvlxb;r7us6t7ja 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 heard (7bv7js 6 0lxjrztu2; ja) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes wh3 f :xt:wl*aoten striking the water belol 3*wx :to:aftw is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concy:d 2 2yaqdc 44b:vthmrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concretbdy2y dq2c : hv44ta:me, 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 zqno(nv84 x1rmile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperaturnvqzno8( 1x4 re is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound w/ - jeqpm3i9ur-tm1qat 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 a1u*o (g*jj k:bvqx7 /hh(wn;tn; usc x4bp2ol sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simp9zh 27;iz--izf, k -l ilq8nys cy.quultaneously at a certain place, what will be the sound level if7k;ny9c.z,- 8 y zzpfhul2 siilq-- qi only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certqp2hw9f,w qilylft,qe+1 )jfvx-g 51- kqc b3ain distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. Wha fk-,1t, y 3q1hl)gpe qxwbqi9jflv -wc5+f2qt sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said abyo)d/h)s 7pj,yr8lto have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the rarad phj8),s7yb /oly )tio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powerpds/ xa+oe58b9 ek*pi17k.g4 emdv if output of sound from a person speaking in normal conversation. Use Table 12–2. Assume+ak/7x ido5 pfikgd9es8v1pb .*4eem the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose a1 ne5:ztkfl+maj a q7:rea 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 6mvqasyw. v vwiz7t0*/ 3;djomodest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a/.;v*d 7 aios63t jmwzv vyw0q 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 1 rgs1m os8kdj/gvp61(30 dB when placed 2.8 m in front of a lou 6g1gpo kd(v mrs81j/sdspeaker 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. Wmh4 bwif9 d m:njnw0v3s(o9inf3r9 ;fhat is the ratio of the amplitudes of two sounds whose levels differ vs :nwd f9ow0j 3hfb3r;n(imn4mf9i9 by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tript shmn:rhgdd*3 7 g05uled, (a) by what factor will the intensity increase? Increase by gt *7sm d:u3hdr0ngh5a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal dispqe /8(katic, u*twqb*7kqs1 flacement amplitudes, but one has twice the frequency of the other. What is the rati7b (i8ctk,t* q/kqeqw*auf s1 o of their intensities?   

  What would be the sound *x*axj )cczst, 7a4w fcdf j,-level (in dB) of a sound wave in air that corresponds to a dispx 4 sf)d*7,wt,jx j-f*czaca clacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what so0 epox*o( q3scle11hsund level to seem as loud as a 100-Hz tone that has a 50-dB se hql1e cs0o13xs*o p(ound level? (See Fig. 12–6.)    dB

What are the lowest and highest 6ca q*/l-w m9trifa)w frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6lmi*a) ftwq9c -/wr a6.)

  Your auditory system can accommodate a huge range of sound levels. What is -jkm0ygmgb w r73k/e-th59lyj7 u2ag the ratio of highest to lowest intensit - ky79e/b7mhg03-5uj wgkm2 jgtalryy 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 lengths 8 0o vpv ejdzp0ye:4un;-/r 2plg)vj)y-w oi of the vibrating portion is 32 cm, and it has a mass o-:-zsj o p2nyv0)ei 8pj0reo )p 4du;vywlg/ vf 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the+k87qnmdpdyk5ql5s h9h 9s m, fundamental and first three audible ov+, 59nhky5pd k l78sdmqh mq9sertones 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 frequencyx6 bh-7+ hgo,+mywy bsck.m7l would you expect from blowing across the top of an empty sbg7myho -ls7w+,b. kxch6+ym oda bottle that 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 pip zwte-cq,j 7i,e organ with open-tube pipes spanning the range of huma,t eqz 7,-icjwn hearing (20 Hz to 20 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 ity,sdj( n:x 5eas third harmonic. What will be:sxn5y e,(ajd its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tung. 2 vr+h0x;3 uhyckmled to play E above middle C (330 0+hc;v gur3hx2lm.yk 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 qd*fil*rycyf yw69 -npvm528 Hz) when the temperaturednp5f*lwyic62v9r m8q y- f*y 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 a +: tzt- k5gzkf/fl9gwt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute icj:p6iyjrp- )n,xmo p(06o i on Example 12–10 should the hole be that must be uncovered to play D above middle C at 294 Hz? pm6n 0i(p:o- j)i,yxoojpc r 6   m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not ats/ m+lk-v 56hss tih,w any other frequencies in betw,+wk 6msl s/ih-h5tsveen. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It re(2n+o gytp)u1 r4h vyam6:ntc sonates at two success g6u2y:4y r n1aot+ncvh)(tpmive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 4wos 8 k ax7zf1vr9s fpzxjy dxv7ln):9wk872 $^{\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 u)n y-s0tu +(pfuk5h ethe audible range for a 2.14-m-long organ pipe 5 nesyuu-pu+0hf)t(kat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appro 1x i3n6en7yefximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardr x6ynfe3n7 e1ium. 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 a --lq.gn2el vxcf*x9ty3txk3djust two strings, one of which is sounding 440 Hz. How far off in frequency is the other str.ln3 2y9 -e*gq xkfvxtlt-xc 3ing? ±    Hz

  What is the beat frequency if middld ;:hro;d6kguu 1z 3oae 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,d5i, ou5fmi0fpe bj)yfo621chq:(hdzj 4c f1 while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans wh6:25id,u4ij pzf)e(bhofy j 51fmhq d1cf c0oen 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-Hz2 x)p;z(etml a tuning fork and 9 beats/s when sounded with a 355-Hz tuning forl paz)( e;2xmtk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fovwwm0 5+ eup az/ze lq-78vkl/*k3vjrequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strinvu w-z/kpwv+e3 z/ae *7580lkqvo ljm gs are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eaabx0y/ikvg i6nz:g yz716l h2ch try to play middle C (262 Hz), but one is at 5.0°C and the oth l/b6 iiygx:vyk1 2z7z60han ger at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B h tvph4ehag)-;e gbaq :j48dk9as a frequency of 441 Hz; when A ah8g-4a; 4tbephdgv9ke :jq a)nd B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat 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 stands8:x+)wd ( kj sfb4 oxgz*i3y8bok6leo 3.00 m from one speaker and 3.50 m from the other. : 8*wfg3ok)ey8zb 4 +6xid( okjlxbo s
(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 arowj lh y/. yl-)x+1r5huoy1a piano tuner hears three beats every 2.0 s when they aoh)y-+y o51r1 y.xh lluwa/jrre 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 2.6/ - m;e+jfrlq2ynic8l4 m and 2.76 m in air. How many beats per s;cnq8 ylrm+2l-iejf /econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency vo k /ig jpzwu1r7whmub5915/ 14xbwdof a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move witip1/v1 5gwj/o7 1rzw xum5k4 du w9bhbh 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 detectrch)51w p0igp if a fire engine whose siren emits at 1550 Hz moves at a speed of 320p1hic5 p) wgr m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source i 1xmm,;kxe l enlfg)5/s moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the xmxm/l5 ;gfe,nkel)1same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. W 5mc1w.q3lo hjhen one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency omc j1w3l h.5qof 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 recei5i:w y y9et,rvctn0w:ves them returned from an object moving directly away from it at 25 m/s What is the received sound fri,9c5tvw yyrn::twe 0equency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall 4xya *f7 ikim7at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wax ify*ia74 k7mve with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original rz0iwny d rp7a8t9 w*.bl+o ,jDoppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard yd*arit7po9.z,+j8rnwwl b0 if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wx:pyr :ef,y nyw e06q.aves to measure blood-flow 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 experp:6y 0q. :xnyyewef ,cted beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves oe98v;q ,ev zlr+of+ fif 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 soundts7bd ver**7xdp;1j j of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency wv*;s*txd 77jpdeb1 rj ill 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 lan l fj0vmrdy-h+zp84w-y/52g -b yyy nqd if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/4 sc8 l1vf,)zgf(hw3eyn+ ydx s (a) What is the angle the shock wave makes w, yzywfc(gxs nd1v l48)h3fe+ith the direction 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 entersfs ps*6fhgy.a b( ta93 the thin atmosphere of a planet where the speed of sound is onlya69tf3ss.f*(g bh y ap about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine thefds+zr;1t0kv x2p7wd+bpup: shock wave angle it produ0p+dt1u p xwd7p :zs ;+r2bfkvces
(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 epwn )ojh -fvfu(n-(/$/theta$ 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 exactly9jgqhbmo h*lw c)47 d ebx39vrx. fp0e/pp,z5 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic oh4wvg/9q9) *xz fdpee3hp,705 pbcxm rbl.jboom, 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 downward s0 hxd,29jae* tgcxs1 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 pulses (in fresh water)?ehtdj x9sx0a g,1s*c2    s

  Approximately how many octaves are there in the human ac.zggolp o w6qs8r6 dt6hn4+.2g3 o ipudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mkjlfl (+iqe2;any plastic pipes of various lengths (2;f klljie+q, 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 kbow 7ysiw7-q1 ( uyqd16hk;aa sound close to the threshold of human heariuwk-(dy o; yq71 6isab wqhk71ng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant b-a6 i;w/ymz qngu32e sound level when an 82-dB sound and an 87-dB sound are heard mze wyau-b3/ ;qi26ngsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opes.gbwfmmq5 *r az2 ;)dn, is 105 dB. What is the acoustic power output (W) of the speaker, a*q )zg am2mbswf;5r.dssuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W outp hi,7zzt ayymc 6blhb5z*j*. 6ut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in hy76tjzl** 5b6hy zzac ,. imbwatts at 15 kHz?    dB

  Workers around jet aircraf5otif w o+(cs+t 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. Wfs+ wi(5o +otchat 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 syste qjxs*07n8layhry x 9+ms, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequzca) u v-vos72ency 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 wi9y w yud5gv i*q)y(3unth a fundamental frequency of 440 Hz and a mass per unit* y3quy)nvg9(dyu i5w 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 i *d8a4vi hc+s/ubmadv;h 9/dx nto vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning forh//i9 bds*x ; dmachdvauv 4+8k 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 opeeuy7 b) lc 5gr2+f(gjxpy0s0 olpn -5en 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 third harmonic in the tu( )p5exlb lse nr0fgyy2o-g5j 0pc u7+be?    $ \times10^{ 2}$ N

A highway overpass was observed to resonatedn)x2v7th,n 47zj4gtl w0 -m2wxl mmw 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 5p8zb/xaa 1 hb700–1000-Hz range coming from two sources. The sound is loud8zpba hb /ax17est at points equidistant from the two sources. To determine exactly what 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 whistles. One train is stationary. The conductor 9yxt /at /svb 5+-gpxj :ihsa9on the stationary ts bxy t/9-jx/s vg at5:a9hpi+rain hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steamei cz7rg; tfxs/jt8.8 train whistle as it approaches you is 538 Hz. After it passes str ;/cgie.7 8 8xtfzjyou, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeni)j2woo is5 ac17kf- siggob4cw w029txmyc +;ng to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain cw msc1)92y2owi o45w-sc k g7oj;igb+txa0f 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 e6 fh zsrxo f+4m(13bt5v9fxf, produce a beat frequency of 11 Hz. The shorter z fob xeffvhs9(1r543 fm6tx+ one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a ra, h2gl0b:ng wuilroad 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, (bl:g b,0hu w2ng) 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 d y+2vp.c20v/e0 oejo stinf8about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the rfvsy/+t.c0o2 viep eon82 j0 ded 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 while the moth is flying towa8p ph8 rg /izv*t*3zeprd the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wr pv /38*ez8 itphgzp*ave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high fmg(. nm(rvc2j;;k+u(xb rc kg requency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and eachk2cxc;;b rmjg (r+g(( .mnvu k 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. 12–38k(nu+ w:xmdu3t 6nf e*) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used n k(:twfn+x36du *umeto 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 open tube.

  Room acoustics for stereo listening can be compromised byxpx1 skhqgmk1u .)l4u :;r hk6 the presence of standing waves, which can cause acoustic “11lhq skhrp k.4k;6x )g x:muudead 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,” inm9+ 6e n.-dv sedv;zclvolves 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 rod can be made es vd9-;e6z.v dln+cm 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 hear/b1mwu lh: zh,;mz. luing for the human ear at a frequency of about u,w.zmbzu; l:/mh1l h 1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground he,8 ypczx:lirl9w r *vitywc 8p(8a /p4ars the sonic boom 1.5 min after the plane passelv/8 w8p 9i,4p8z*:tywy rxa iclp(rcs directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1k. cfgt; .p;ob5 $^{\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