What is the evidence that sound traa p-.1iwn0 tkeeo vesnv/g)4 )vels as a wave?

What is the evidence that sound is/bae tw d58)er a form of energy?

Children sometimes play with a homem m4o va ca15i3d9g6clgade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how 5m4cad ic13gl 6agvo9the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency or-2- bcs1 ssnnk wavelength to changes1s -k sn2nc-b?

What evidence can you give that the1xdi;zjf hp::ug huqfc1767 rst2 ;tp speed of sound in air does not depend significantly on f6:7h sqfu1dr7h j;pp:if2 1txcug ; tzrequency?

The voice of a perso *p39iqbia 9eky lu,*f1fqrd 8n who has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the/dz 2mze5zm8 yzk.am. pitch of organ pipes?

Explain how a tube might be used as a filtaafq f)2 -34 pw)4 pnfbhojx2rer to reduce the amplitude of sounds in variousn)q rj2hfab)w4p4 2 x- pffao3 frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer toge zap.(c+mkwj.,g8m hxn.xz)rther as you move up the fingerbo.w.),mnkzc zx+j .rg(mpa8xhard toward the bridge?

A noisy truck approaches you fro:i zgo1k 1aj ,jhq+ mkv,;lrb3m behind 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 S3bq, 1hrkkvjo1,l g ;a+:jz miection 11–15 on diffraction.]

Standing waves can be said to be due to “interference in(na ht3ybi 8ve 7 k50rt;mgas* space,” whereas beats can be*aa50; h8k37tmi (evyn stbgr said to be due to “interference in time.” Explain.

In Fig. 12–16, if the 19t j lquz/ejtzmwl* ( bk5z80frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference 8 ul1*5zzz9mttkeq j /wl(jb0occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in kt(u(wv*ke9 lareas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are wornv*( (kl9wkuet 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?

Consider the two waves shown in Fig. 12–31. Each wave car(ndu1fkc2 zw6t* vs /nm5 z(bn be thought of as a superposition of two sound waves withnd fb(ms*u(2c z n 156k/twvrz slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the e::pa yf0 d984gzkvx lsource and observer move in the same direction, with the same velocity? Explaeg z9fv 8:0:4pdklx yain.

If a wind is blowing, will -hxw p)yr* *: o5vpwbjthis alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or veloci)rb:v hyopw5j p x*-*wty changed?

Figure 12–32 shows various po j o4x4ay ap799hrtrr+sitions 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 higherx+j 94p9yr7rhta a4o st frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length ofo 2b(qe wom6+2bot(gpty/ v 3z a lake by listening for the echo of her shout reflected by a cliff at the far end of the l+t2e( 2ovm/qbozy pgw( tb36oake. 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 just below the waterline. He heac1pf7mjtqi3sq*y z )s ri3rj2 vfgg3 /(wdy*0rs 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 spe2sq*7z01 ypii3fqjyvf )/mrwds3 jgcrt3*(ged 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 dt;86zzj( yd2u6e snmin 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 boamj -vx i+- y9l2eyx,oat is 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 tim+ xeajm,-lyv92-x yo ie elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes whev2dppwcrteo7nh(e7( :1h1nen striking the water below is heard 3.5 s lateecr1 (2hepdovw7hnn1 t 7ep(:r. How high is the cliff?    m

  A person, with his ear to the ground, sees a bgr56:uaj )/ rbaz kp-oyzy) ).vrav)huge stone strike the concrete pavement. A moment later two sounds are hea yo-zz:k)bru6payrg/ av.va)bj) r) 5 rd 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 om bnzh7c3: v1tf distance by the “5-second rule” for estimating the distance from a lightning strike if the hcv z3t:7bm n1temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound acn d 9suc49kwob fuueo, f+75-t the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound who n 0r+y1mkrb:.azgv6kse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousl7 a+v rkre, lm+r7hd(jy at a certain place, what will be the sound level if only one is exploded? [Hintlrdjv( +r+m 7r,e7hka: Add intensities, not dB’s.]    dB

  A person standing a certain d05puw3yk s u*boj/zq .istance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 1ob yw/3zkp.suu5qj0 *20 dB. What 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 to have a signal-to-nois :xdsv e+1imjw*o3 ht,e ratio of 58 dB, whereas for a CD player 3* hisdj v+1mt:,xeowit is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conve s(+,fn-ndwc krsaticndws k+n(, -fon. Use Table 12–2. Assume 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 striksct3 w(kxm p1tdld9)ze;z6-k es an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, wholb/bb4-.gwk j ouw+t7v g j45ile the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a lou4/gu5j b+gw4 lw7jtobo k v.b-dspeaker 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 r c8p0o 045j8yo+martrmaa. yeegistered 130 dB when placed 2.8 m in front of a loudspeaker on the st+omty84p5r 0ejmr.0 yo 8aac aage.
(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 typica1i kvx/41pv.ooung7 g lly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels diffepv. g4 okvg171niox/ur by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wcd0or6i0ci zd+ xi0um8l b 0-rhat factor will the intensity increa ddriuci0x8m0 -zlo6c 00 r+bise? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice *)uoy rlp ;hyh:o89 uwmucj9. the frequency of the other. What is the ro:jyh.wmp o u9 hl8ru*9);cuy atio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air e o3fm7h+wj v5opa80rthat corresponds to a displacement avrh jawp+8m7e5 0of3o mplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lk2g di esbtzd/ +-1/ +wajf4wkoud as a 100-Hz tone that has agf/dk bae+ 24 d1tswiwkzj+/ - 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detclrxf32 dq; 8cect when the sound level is 30 dB? (See Fi ;xf32qcrld 8cg. 12–6.)

  Your auditory system can accommodate a hug2j ep ka *jksls8-7t7ne range of sound levels. What is the ratio of hit2 sa7n8jke7 k*p-sljghest 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 freq*rgk1v+o4p llu zp)1fuency of 440 Hz. The length of the vibrating portio*k1 +r gz14puplvf)l on 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 firs,eb0*a5wz b;w; ishwdt three audible overtones if the p,0*b wa ;w;ezbws ih5dipe 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 across the)8 vjce3uvv5b (fwhb7 top of an empty soda bottle that is 18 cm deep, if you a 758b3v(vuh j)fwevc bssumed 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 opey3i ysx0shr iyw(4w0/n-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipess /yrxwy0h0sy i4(w3i required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequeax4u4hq*mqk qa8 q m6+ncy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of m +xqha6k4q* 8qa4u qmits original length?   Hz

  An unfingered guitar strquuh6(2 i10iq gtpd/ eing is 0.73 m long and is tuned to play E above middle C (330 Hz)2hqi iq6 du/(e p0tu1g.
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz) wz9:72vck qfk ihen 9vci:k q27 kfzthe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at cb u,g-fna+r, 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flutew ajg5ea vk*m:f + v)*rxoe6,e in Example 12–10 should the hole be that must be uncovered to play*5:x oa+ra*6v meewef jvk)g , 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, 440 Hz, and 616 Hz, but not a0,( khey ami1at any other frequencies in between. (a) Show why this i1a0(k hyeam, 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 resont,+ s p)dhsc;sj2 qxz2p;hg,dgu+ (g fates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is2gzdxp;hh;pcgdgs+s tjs q(u ,+f), 2
(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 gwlzepc:r/0vw4t 8)e nhdqu6w+i), x$^{\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 t ;qix7z,ftl u8x3x:mjhe audible range for a 2.14-m-long organ pipe jfm,7zx8qt3l;i : x uxat 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 anm.piqc *6xjro c9 k 4eya0(z 0vrsx,/kx8 qn6td is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves r 84x90nqit,6k0r 6vc.(opjz xxa*qyc/ s ek min 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 ji5tyf6-i w8r every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is t6y8iw5 irtf-jhe other string? ±    Hz

  What is the beat frequency ifp(xhqx0 *dqq6 middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates p jjsosj2mw2mg6 j1) 6at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequemwj16 jsp2o)jjs6 m 2gncy of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and d2f drf1*8kil 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequ8r *f2d kdli1fency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in oj9h 5 w1 qms1qqb40 b)7,edstzn2luxnne string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Rehb) ,4dn01s5snw qzjl2 bm9x ute1qq7call Eq. 11–13.]    Hz

  How many beats will be heardjvtw2 xr )t9/01mm1 jqgadxg; if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and the othx1m1/vwj ;grmxaj )q92tdg t0 er at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork ,zd;y2f e pfk,) bz:fsB 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 frequencies are possible when A and C are s:b f2)z f ;efsk,,ypdzounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m vxai2fhc ), r;lik. k)apart. A person stands 3.00 m from one speaker and 3.50 m from the other.x ;a.rhkfi,)2ci k l)v
(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 mlhst) c)v .+tHz, but a piano tuner hears three beats every 2.0 s when they are played together. (al )v)c+msht .t) 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 air. How many beatsx3. ntyrg37cy8*l3 hh ,jo nv,l:vwac per second wigo3 aljlvcn8rw ,tc y7*hyxnh 3,.v:3ll 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 155;cmzw7 2utam7)+pkqy i (ju2 x0 Hz when at rest. What frequency do you detect if you move withuxjuq cmz(2ya2mtip k7w) 7; + a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What freqeu v)2jxff g8,uency do you detect if a fire engine whose siren emits at 1550 Hz movefvef )8,gx 2jus at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in f(0bb/y v*wntn a;flt,k b/0l7 muhl 05xrf4 glrequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same?4(* nbruykft/mgwbbl,;hvf/tln 7l 0 a00xl 5 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 hornp7huts2(rpzz 3jc r6o -i ygvki 38*l5. 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 the frequency the horns emipr i32zsh85 yi *(co r3lu-ptzj67gkv t? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sotgp a*sgji/y:xh 9q a 2unu112und waves at 50.0 kHz and receives them returned from an object mov*11gautg9u nhy sj2/x 2a:ipqing 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, th.vlzypo, 6 o*ee bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does theoo v,.ze lp*6y bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was play8j+ocm0cr2esn8f/ 88 hdizg v ed on a moving flat tra+hv/zn8c m 8 8jcs2 e0r8doifgin 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 the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow w o6 1sn (g4q 1 2qgqgmbo01zugjksy+-speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue 1qbg jyus14+m nkosqgg6wg-(oz 0 21qis 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 us)8hzqr*2b ei0 ptgizu; 1*vyging 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 f +qy0jne()yukuj 0v+jqw sio0y q;*1Hz. When the wind velocity is 12 m/s from the north, what; 0 k+v( qsujyj0yo1 euqy*in+f)j w0q frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an objecm4nxwg 8b)5 iis+5;m vuqyamd 9frx:-t moving 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 the speed of sound is 310 m/s (aw: eered7v2ihrb/wb, q r 780h) What is the angle the shock w/bev 7her, 8 bwh 0qwder72ri:ave 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 atmm,jb/ 9wh/ yhdosphere of a planet where the speed of sound is only /9/ dbjyw m,hhabout 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 85001rj pw(6 **xlmjbml7 g m/s strikes the ocean. Determine the shock wave angle itmx rj jg 7bp61lm*(*wl produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle f+4 u fs)s z8sg,cetjkos(s-+$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhe)fjft6j,krh d+2mr8kad and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determt rdjkf8 6mjk) ,f+r2hine
(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 dccb-4ezc9 bq a.8wf-w ownward from the bottom of the boat, and then detect8zw9 4cw qea-.-cbfb cs 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)?    s

  Approximately how many octaves are there in the human audible w zm:iyg9, -x kg8r.tcp(,kck range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It con5glbeflnr 5 cfl964uhjh2 9v,sists of many plastic pipes of various lengths, which are open on both ee9fhvllrgc55,4juf 2ln 96bh nds.
(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 ehdmsv5vn ; .y.pl,z6 a person makes a sound close to the threshold of human hearing (0 dB). What will be the son6 mv.5. ds y;vp,ehlzund level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB soundk:tq8l:by:/d- ascz8vf4v0fd z;f st and an 87-dB sound are heard simu: c4fk-f0dzqvtt/dz8:8slf; y av sb:ltaneously?    dB

  The sound level 12.0 m from aqb(8,ijfiva ) 5 r+cjvpeogl1s.j .r9 loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of thosi9aj+frer cib.j) pv, lj5. v8(q1g e speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output1 gd//- 7 ilvtmaxxh(z drops by 10 dB at 15 kHz. What is the power output in watts at 157i/ (/lh -1dg zxxtmva kHz?    dB

  Workers around jet aircraft typically wear protective devices overj do*hjj)m4q .; i.yow their ears. Assume that the sound level of a jet airplane engine, at a4.j ji omh*wy;dqj.)o distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gmu85x+k ;6jx5o mxbl ;9lp;fe2qx k8bpwr ;sa ain, $\beta$ 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 isp exwvb45f z-( tuned 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 between fix /1o iyi1v1.zh x.arj ke6of:xed points with a fundamental frequency ofo .h yre va6jx /i1kzx:11iof. 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 i bs; 5n1cn;sxlgw+0vnnto 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 waxnwbsg n n; +ls1cv50;ter level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of m7xeo/ c 1- v0py(absj ji*cko+ass 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 harmonic in keix1s-bocyv0j(op c*a/+ j7 the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to res4j8aszi12 1 s n4 biwnkdbm-i6onate 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 500–1qt 48tf+;adfx ys ieull236 q:000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the soundq4+6la28ef:3i fqut ; ylxsdt 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 cond mhua1e;vd.n v9pc82f uctor on the smf v 9 udc8vnp;e12.hatationary train 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 steam trai4kydse:f *tb 9uwx);x n whistle as it approaches you is 538 Hz. After it passes you, its frequesy :tu*ek;4f b9dx x)wncy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you ca)4i8+eo *y afgr nn+vin estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequni4)g vi8+fr *a+ eoynency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, t) 3rsmfkx h)ka4zu : 2:sd(dpproduce a beat frequency of 11 Hz. The shorte pa 3f)2:x)mdz dks:4htksur( r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroa)*m1+ mkpsngh ymt r9.bg cx*)d 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 poss1kxy)mn9 cgp.ghmtr+ b)*m*ition 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 bloo vfn0ed )k60na ,piz.g-r9rvp d flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if nv., 9-k nipdpvr0e0)fz 6rga5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while 1t p7-.vhqtxhw( r+j w9o xux 7nqet46the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kxn xj14ot7wuxpq .tt(e r76hwv -9+qhHz. 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 sorr-r+x dwz(8igm 68+r qdn: t6nxz8sdund pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 msd indw-r6x s 8x6t:++(r8rnzr8mzgd q 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. 1 aock,ik5h m73fjal/;x l9 gp22–38) was once used to send signals from one Alpine village to another. Since lokl xm;ic7pok al3a2 hjg5/, 9fwer frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromiswa:ftrr-j 3 y)ed by the presence of standing waves, which can cause acoustic “dead spots” at the 3)rwajyt r- :flocations 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, caller*ec fc5pb 0.od “singing rods,” involves a long, slender aluminum rod held in the hand opb0 ccf.e5*rnear the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human e2g z,0izjj;y far at a frequency of about 1000 Hg; i0 ,j2jfzyzz 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 observf)b-j os h-ab)er on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Wh-jb)ab) -sofhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is68sl sw zz.--(qi sapv 15 $^{\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