What is the evidence that souapam:vibcm7b3q o:g ) bw+ x+/nd travels as a wave?

What is the evidencej(.rb 8xu( ele that sound is a form of energy?

Children sometimes play with a homemade “telephone” by attad f9 vl2cam1.es,jyhebcad.c ,55-c eching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into o1 syabca 59me-djcc. 5hefd,celv,.2ne 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 w1zpn8 ;z*czl into water, do you expect the frequency or waveleng 1z *n8zzpw;clth to change?

What evidence can you give thay,6 t6ssw as; o-t2bk0z 7t;cjezwak+ t the speed of sound in air does not depend significantly ojb c ,;2ya-w t ;ssz +k0kwe6t6astz7on frequency?

The voice of a person who has inha8f1dj y.s,gmc9ysf3 *w .0iwtg*edv yled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitchb qysr+eikni v4w+6y,egl4bq*1zg3, of organ pipes?

Explain how a tube might be usedg(afbyn up38 j 1gz2t1 as a filter to reduce the amplitude of sounds in various freq2a(gf n 3by1 p1uj8ztguency ranges. (An example is a car muffler.)

Why are the frets on a guik vb19j4t:ycwtar (Fig. 12–30) spaced closer together as you move up tkjt1 94:cwy vbhe fingerboard toward the bridge?

A noisy truck approaches you from 3b/cu3 t 81ef 1gufkamu+er7dbehind a building. Initially you hear 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 Section 11 7fuufaertd c 8gk/+mbu3113e–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bexijs( iv;rj vj+y*i.)8s* k zaats can be ;8(s i.z +jav* is xyv*rkji)jsaid to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, wo lsvff)k1f ;3msek79;bb c) kuuld the points D and C (where destructi1k;3bf vf9 )ck)7 ml;usb esfkve and constructive interference occur) move farther apart or closer together?

Traditional methods of protectingy; gp 80vs uhaxs8wx1( the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. 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?a 08v xywp18x;g(shus

Consider the two waves shown in5 jx hrlm7j bp)57nlo6 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 which of the waves, xlmp b7 lj6ro5)7 nh5j(a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if t lwr4 pv/yxwk37e1wuun* )j6 nhe source and observer move in the same direction, with the same v)6r/*j1n3eul ykuxww4vp w7 nelocity? Explain.

If a wind is blowing, will this alter the frequency of f fa .z9; trktn3dugxit+05)athe sound heard by a person at rest with respect to the source? Is the wavelength or gir 9+tfan5t ; ukd.atzx)3f0 velocity changed?

Figure 12–32 shows vxv3w9dov4z:g jtd1z 3 arious positions of a child 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, will the child hear the highest frequencz3vv:1ow tdx 9gdj4 3zy for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by liss jab5 vxve;m/a9o h9 ylo8/q,tening for the echo of her shout reflected by a cliff at the far end of the o59yjeq 8 smla;9/vhxv/b a, olake. She hears 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 juste z4rf;:9sw wwdfx eug-,shw s:x(2v, 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 or9-2,wfsww;,::xzu(s4d s e ewx fghv cean 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 atv;*22f oyp1acz tjf8q 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a sd(so)y; zgad* 7ahj0i chool 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 d0 y7h)jszoad*ag( ; iis heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a ci m d/u,zhf 8i.0sn;nqliff. The splash it makes when striking the wi, /qsunhnf.d zmi8;0 ater below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the +vjy 5fa-ky5p ground, sees a huge stone strike the concrete pavement.p5yyv fj-5 ak+ 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 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by themo/ x,u8s;0eiysoo /w5 g+wgm “5-second rule” for estimating the dist wseo8,im5yuow/m+ 0oggs/; xance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB 9d.pjz9ez +pl?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whosia9lw ;al;s6 ue intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sn *nr2vrf/* d ojy1he7ound level of 95 dB when fired simultaneously at a certain plach2*vfn1n7eyrd */o rje, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distpv766lx lx fo/1 n m2y2iawt)nance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add w7x 6/n1loiml2vf62p) txn ayintensities, not dB’s.]    dB

  A cassette player is spdw-ip hoc3eqw o( 9/3aid to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eac/ odqw9i 3w-ohc (3ppeh device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound 1 ruokzu piht/ )l0, +qtw-n(dfrom a person speaking in normal conversation. Use Table 12–2. Assume the sound spre)ltu+n drip (,htzwk10quo-/ ads 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 eard7c3x.tqvg htjy g +tj7lp5h:(rum 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-bwp+b mm-5o 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 fro -b- t+wbopmm5m 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 in front jv3 *3s xo+lb yiu5gnb1k.nv 1of a loudspeaker on the stag s1kn1ybu3j vx+n3*v5boi.lge.
(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. What ict)muokl8i5: h5njrw 5 dy4-a s the ratio of th rik8 mj:hn5ldac) -y4tu5o5 we amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave /c j2foyp/a .qw,we u8is tripled, (a) by what factor will the intensity increase? Increase by a factor w8/aeq/ j,2pwu fyoc .of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice th*ud7:jbic1 gs3b0ykve frequency of the other. What is the ratic 3v us:kd0yb*g7i1bjo of their intensities?   

  What would be the sound level (in dB) of a so9;gszxypg:/ kc. -irs und wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300kxszs/;gy picr-g :.9 Hz?    dB

  A 6000-Hz tone must have what sound levelke0 0*/hnns pf to seem as loud as a 100-Hz tone that has a 50-dB sound le fe0hsnpk 0n/*vel? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an etqq 0kk,yt t/.ar can detect when the sound level is 30 dB? (See Fig. 12–6.)/0 ,tytkkq. qt

  Your auditory system cau* e1 kp.:o2( ra.3itnzur wuvn accommodate a huge range of sound levels. What is the ratio of highest to lowest inte(v1.2 . ukuutrranzp*: wi3oensity 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 fu/s q8kedgh z9maxt87eu93v (mn-(tqv ndamental frequency of 440 Hz. The length of the visznetm h9qe tv3/- m8(97 x(vda8gu qkbrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audiblqeep;k7gft 83 e overtones7;fqg e3pk8et 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 atfpu8a(mpi l2d3 zggot9 9* i3cross the top of an empty soda bottle that is 18 cmi p2*pgdl 9tz3uiag (o9fm8t3 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 spanning the range of hu .gggy0 bt*t:xman hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes ggb.*0x :tt gyrequired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freque, 1ylpqa:m g-ancy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of opa1m,-q:l yga nly 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above /ul m4akts+t- middle C (330 Ht-l+tk4 um /asz).
(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 ipihp tvd96wx,8q..h middle C (262 Hz) when the temperdvxhiw6pi. 9q8,pht.ature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 2goe :)5k,f zir0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpieo7q0 6l91fz m-. 5w k ok,bk1xoihvmhfce of the flute in Example 12–10 should the hole be that must be uncovered to play D above middle C 61- kvofz5ix.0l9hmkh 1 7obw f,qkmoat 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 pfmq :h*+of 5s vc/:n8 j;r*)zyzgizagipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whsg8)m*hc f:j/ riaz 5 zzg+yv;*qon:fy this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at *v yd as2g.+s(96 mtadx04t v:gpik kvtwo successive harmonics of m:aaid0*4vs.yk9vt+(6d g v 2s xtkpgfrequencies 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 0ior*6*,i c/em d9o gwyanxp.1vu v)v $^{\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 ths 4a4or,tr(pe g 9zy4pe audible range for a 2.14-m-long organ pipe at49p,ez(g 4o4 pratrys 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 outsiy6ut e;9lbzix 1eq;2 hde and is closed at the other end by the eardrum. Eszil6y;qxeh9u b1t2e; timate 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 odwtsua 4p.7g4o;)spzt re 5;jo(k z;s when trying to adjust two strings, one of whr);7t g(doktz4a;wjz s u.opop5 e;s4ich is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middlwnpl 86 ytxvv.p(-y5ke 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) opera/1 etkd(a vob7: gzud.tes at an unknown frequency. If neither whistle can be heard by humans when played sep1/.:a7dug (vkztd beoarately, 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 sgp 1y11uyt yr-i5vc8u.mw nl,ounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequencyl,p1 m ytg 1c. 8uywyv51r-niu of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 t xiij 5i2y0bsl9f)7cHz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playtxli75y f)sj02cii9bed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be hfz9qq*igl4wdb 3 * wj3gng -r-eard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the bzjgg qiwlq 3rfw-* nd*g43-9other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Cwn ;5xt*mx kf.4d zw:z. 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 frequencies of A and C? What beat frwx;kf 54:tmdx.zzn w*equencies 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 onbq 2y-zhetj 4fnzys6;h3g ; +ue speaker and 3.50 m from the otherj z gh;hszu 64n 3t2fb;q+yye-.
(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 supposucxwx: wxnxw:s* k, z t14y-d1ed 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 vibrating at 132 Hz, what must be the freqdysxx* ,:- nu1 ktzw4 :xwx1wcuency 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 p0y nyii0dd8( ska5*t2.76 m in air. How many beats per *iyidd a085nkt0p y(s second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ofaei anv5o*,u58 h qbw3 a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move wit b58 au*qhoin3aw5, evh 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 engine wh dpo2t*zw:zx:fcr.p kqena 5u +848rkose siren emits at 1550 Hz moves at a speed ofu8zr +4t5.ke :2kfnc r:zp adp *8xoqw 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward yob w:9bq*/.p /vwvrs 6padq qv,z6ji4lu at 15 m/s versus you moving toward it at :6dw*j,v4i.qv / wqvlrb p/s96 abpqz15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency h 54t0+tntyrs(mkt7 bzorn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is t stkm47t+nt 5 yr(t0zbhe frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives themo8/dq zwv22owymstkh5dm 8f1 vu ;m95 returned from an object mm;o 8 wfdqyz8vsm1/ 2kvdt5 u5h w29omoving 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 speed of 5 m/s As it flies ss0e +zpl . r-*;mxx*mii(tmg, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected w*ep;l gxrsm*- it(ms 0i+xmz. ave?    $ \times10^{4}$ Hz

  In one of the original Doppler experfgm7gg yh.(33 zifn t+iments, 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 if the train car approached t ffy7zgn3g(+3ih tm g.he station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow spezmj0b1zn6ejodm1a 8 3 eds. Suppose the device emits sound 81mz znmj6d 0aejb 13oat 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/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic 6:4ft,xdkuei5 + xyw m8q xv;nwaves 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 frk 5 3gtuk qx.niilg(;e(gukp7z8 3d e,equency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,ix.d 5it,u(e8kk (lp n 3guek7 3zgqg; 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 onzlgle0e*7 m*ff(uy+h land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What inv2/s0n)im4nk-oh d0ns s +uxs the angle thsks/nv)+ 0m sdhu-nnn2 ixo4 0e shock wave makes with 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 enters the thin atmosphere of a plamkm* 5*7ny:.h jf-jarxuzeq j39 v iw,net where the speed of sound is onlymf, jy:qu 9j7zvhwj 5m3kaxrni* .* -e 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 the shock wave an3cnx)rv(z ,fo,: uqiv;- q5spq sncz/gle it prosv pu:xq3z 5fnn);zso ir,(qq c-v/c,duces
(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 bs xt5 :8gp4 f0o*wc ,efystd4a0sll0$/theta$ 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 exactly 1.5 km above the ground59yiee4k f :h-u0 xkkd flying fa e0k5f-y9iku:hdex4 kster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. 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 2uuj(w95h2i kz 0,000-Hz sound pulses downward from the bottom of the boat, and then detects 5ji2zuu(9 wk hechoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octave2bvx6rhrp -/v s are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe s .4x 2ks 77rsdr:ocphiymphony. It consists of many plastic pipes of various lengths i2h 4x.ror:77cksdp s, 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 soe:zqwqx7 92xk und close to the threshold of human hearing (0 dB). What will be the sound w:xe zxq7kq29 level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an s3, znu m3gpy.t)pi f,i :0slx87-dB sound are heard simultane3 tszm pi.3xynpifgl 0,s:,) uously?    dB

  The sound level 12.0 m from a loudspeaker, placed 3 qgqi2csl9 n.czl, -xin the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directions? xzn.gl2-3q ic,l cqs9    W

  A stereo amplifier is rated at 150 W out(o p-aw9w eao+. - vycbb)upl t2+:kjwput at 1000 Hz. The power output drops byp2-)+tab:+cw(v p j-y .k beluw9owao 10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wepzt ge5y1 ci0 qfwl5w-2k9c8d 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 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 airplany9 2k5 5dfg wzci8l1-qet0wpce engine?    W

  In audio and communicattgqq2 7bg9f 8kions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned,pxro; yr1vx, :sp7 xamo4-zr 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 b*qavhh:6ac (d 76rwtmetween fixed points with a fundamental frequenc*atmcqr :66(h7 hvwady of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical openao/18:hdquuiewx/m of v 4+h 9;ji4le 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 hea/u qj4dfi /vhoxwae4 hu 18; lo9m+:ierd 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 mbrh .qypze4zijr wzo2ioi2 4f :d;7 50ass 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 third hf2pzq iih dw5y:b;zoj.4r r 047i oez2armonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loop 0,avf;mae/eu clw v 0+d .i/py($\frac{1}{2}\lambda$) 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 cf d8bot*8qd d)oming from two sources. The sound is loudest at points equidistant from the two sources* 8dbf)qddot 8. 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 on t6; zskozvv+9 lhe stationary train hear;l6+z s9zvkovs 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 steam train whistle as it approaches you is .h0t vriqf*.8t kwf ;jjcs*z* 538 Hz. After it passes you, its frequency is measured as 486 Hz. Hk;zsrh v8if** .w f.jtct*j 0qow fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listeaejga5l+pj ,; ning 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 h, jj ap;g5ea+lalved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequenybicv.y- f -g8jp3 x7ucy of 11 Hz. The shor g.f cj -y3b-7ixpv8yuter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rai in6mc-s qy/6ulroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 1/y nc q6u6ism-2–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally amiwulvog+8ii;k zwvar9a, b2(v q,2;bout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from tgz+m9,ivl( wa b;r2;ikwvouq v 2i 8a,he 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 md- p3 7eia+.zjj jfq5n/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound ajjnj.e fi-z53dq p+7wave 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 as it approaches a moth. Thep;s2-kijl;,o0 p a iqc pulses are approximately 70.0 ms apart, and each is about kp0s2,ai jp;;ol cq-i3.0 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)evg;3oim t3gt 5gq;i, 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 to create deep sounds. When played as a musical instrument, the alpenh3;g5t o vqi,gi;ge3m torn 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 by the presence of sjuniq;m(j5 ie8dt/p- q8pvm. tanding waves, which can cause 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 frequenjpeti;q/5 v8q n(p8 uid mm.-jcies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, calleaks0x8bs8n z, d “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 rod can be made to “sing,” or emit a8 kx80ssaz,b n clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the ho bqgqq6v(bm3h)uf7*3gb( 0 el/)xrama3 jco uman ear at a frequency of abo)7f) ( jrgxvmqel qu m 0o3q3/3ha(c6oa*bbgb ut 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 gr9:rcjr 4o/hf )ysy9a* oyfw4oound hears the sonic boom 1.5 min after the plane passes directly overhead. What is th9 *y rfor:ywy9/fs4o4joh)ca e plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is hq+ *oehua0 2f15 $^{\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