What is the evidence that zfd xmwwjif;ur )4u3c4a 2+*j sound travels as a wave?

What is the evidence that soun8m cne -,agzjuf9t7lng7 o l,0d is a form of energy?

Children sometimes play with a e9q b u9-rz;xthomemade “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). Expuzrx; e9qtb-9 lain 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 frequz:ys-bf4 a p,lency or wavelength to ch:,a f4 ylbps-zange?

What evidence can you give that d ut 3dd) y.ikxww4*na (fehci3:zc8 4the speed of sound in air does not depend significantly on frwda yd* u4: nki tw)z(c3he4xf8ci.d3equency?

The voice of a person who has inhaled helnmgm-3zp0/x t ium sounds very high-pitched. Why?

How will the air temperature in wzkmzl):b m ()p1qq.ca room affect the pitch of organ pipes?

Explain how a tube might be us50y -p oijv8vt txva/32r8qk 7rvf8voed as a filter to reduce the amplitude of sounds in various frequency ranges. (An2 7 jy/-rtxk8ivpftv vroq5v0 8ov3a8 example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethw:1.tjgwyjxex1 (.vfp*m4 d fu wa*/xer as you move up the fingerboar:pgaftww xd*4*jw e/xv . m f11(yxuj.d toward the bridge?

A noisy truck approaches you from behind a building. Initiallyo /i 8zk-qpx1c 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 11–15 oq i8o-1p/z xkcn diffraction.]

Standing waves can be said to be due to “interference in space v+v7ktfpime, xb v9e-a8cpg;5u-l 5 g,” whereas beats can be said tc e+7bv g-u f vlem,akgtv5i8xp9; p5-o be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency+v unkv/b5h1y kfa7/ p of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closevp+nya bvu7k//hf5k 1r together?

Traditional methods of protecting t(ta3 d0. e2g+j(1 srgowjmbmjhe 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 electronic2e 1aomgj 3db+wtrsj.m0(( jgally, 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 wav7qubf- ol l) h ne8x8 ut2m9f2+ol)jjke 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,xbl -lt qujfo 9u)h2ln8+e28 )m jfo7k (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shi,nklc s / ju)9lch88 aov1xpfn2a+1ovft if the source and observer move in the same direction, with the same+ x,1 8)a19vk l2cosjvp nufn/ho8cal velocity? Explain.

If a wind is blowing, will tvcnycp7x,76/, yga .nq zt( sy;l *eqqhis alter the frequency of the sound heard by a person at rest withaq c*ge6,nqc y ,l(nqzst. v;7xy7py / respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A mow*t. z8ih svxt90ix7wnitor is blowi0hxv. xwz9* tws 7i8itng a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the l 7 uwv;txm7tr9ength of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears t rw t7;x79uvmthe echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship justz*/+ol2 8rqfxxe1wc i below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 15/ fzlc2 oxi8q1w*x+er60 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air qf, h7lds o,7;j st8vrn)m y-pat 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 school of tunax,i:ruw l):ke 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 back)u:ilk: ,r xwefire 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 when strik o47)qmq pr-t3vc fkw (5dc5xd9/pep ling the water below is heartc /(w-l d9x7dv5fo qqmp3pp5c4 r )ked 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grounj: j:j74 mfrr4kl2 7jndea or.d, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in tnjarrj j m f4:.jore2k 74d7l:he 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 the “5-set p6)sw(+lf mxcond rule” for estimating the distance from a lightlw)f+ (mx6tps ning 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 lea7 bl-fh va dvkl2z n3:a6.k7avel 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 whose in 0p/sfbiq+a 3ylzwm6jaa2l 22 tensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound blk)m9c1l1qwlevel of 95 dB when fired simultaneously at a ce lqm1klcb 9)1wrtain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane ws / j)haj/k-eoith four equally noisy jet ej )eak-//sohj ngines 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 intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of .) ;4ucyu1xglm6ejid58 dB, whereas for 4 6m duxjiu1le.cgy); a CD player it 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)il 8n6yw6qm kfm1 ,ha person speaking in normal conversation. Use Table 12–2. Assume tf nk6wh68, qmlm)ayi1 he 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 eardcw0yod,:d zc akyl ok4 x+*+g5rum 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 rated8uv() zi ut*lu at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the i v8uutuz* l)(sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registyafjulwsex. os0 .(03gu3 g:gered 130 dB when placed 2.8 m in front of a loudspeakesxe .u lofajggg.:w0y 30(s u3r 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 c1lq -1vg*c0w0u7o7oqnktwy difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sout0 g con yv qc1wq*7-ko07l1wunds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what f.;i zuq0hv;jlactor will the intensity increase? 0;lvqih;z.ju 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 thet4e k5peek+dthbkso7 8( a,6e frequency of the other. What is 8ekedsath5eo7,t+k k (b64pethe ratio of their intensities?   

  What would be the sound level (in dB) of a sonfcw hv-z7b 5)bo. m u-w8ada4b9zla1und wave in air that corresponds to a displacement amplitude o4a5w9 fm)w1an .o8 lad bvc7-b-zhu bzf vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as9 n lld+eeskr94:s,stt-sdi6 a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6 96s +l-,etss:isn 4kdrtde9l.)    dB

What are the lowest and highest frequencb g0smd23* efdies that an ear can detect when the sound level if23 be dgmd*s0s 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What 43ncse ,nt (/mh gh)xmis the rm /3),n heshgxmc (tn4atio of highest 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 fre klrmkg/( ;6i jr0 lq(5nux)zcquency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass )x(l r6(ij/mgkqlrc k ;5u0 nzof 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and f:pf4ykw m4*.knwg t+nirst three audible overtones if the pipe is.4y nnpk:f *w+km4wg t
(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 wouldcz)t *cv p:e4pfl0a 8e you expect from blowing across the top of an empty soda bottle that is 18 cp:t )lf ce *e8z04cpavm 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 c ( xorm .tt ::++ 4cbr6bzof0f)vnvwuhuman hearing (20 Hz to 20 kH mv()bv. ftfn4zcwo+ 6::b+ ocxr0rt uz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. Wh ljm.wti3u( b/1im5vaat will be its fundamental fre/5t1uba v(wl m3ji.miquency 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 tuned to play E above middlg4 e0xkz tqm01e C (3304 k0qzmtxg1e0 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 organrm8pw ;cdrcpa0shnb4o-d) r- ew/5 :qutn z5; pipe that emits middle C (262 Hz) when the tempwzo;8ph-d pcq)wsmnr c r5u: a4-d r;/te05 bnerature 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 aubg/:m+qq tra/*k7u-q:p x6 k.(qbm vzs m i4bt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flu x2 -rm z iyme(dv9zc1 p0qb00g(vt5adte in Example 12–10 should the hole be that must be uncovered to play D above middle C 9ma2 g(rd1x pzdyivc0t(q-m00ezv5bat 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 Hzgij 7:9pj9vx k, 440 Hz, and 616 Hz, but not at any other frequencies in between.kji7v 9j:9gp x (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 resonates at two su i:sj.u6hma )dccessive harmonics o h:i)smajud6 .f 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 *oel 8idq jf1qr2*b -z$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range ogpsj (bf 0oxqm84o2.for a 2.14-m-long organ pipe at p2g o.boosq 4xf0j(m 820 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm l e4xgr.s/- aj473bsooe:sqmaong. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in g7 4msqs3eo:.rax /ae -4bsoj the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one foel 14 ua; 18stv0snbbeat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off e1bsn4lt sv 8a;fu 01oin frequency is the other string? ±    Hz

  What is the beat frequency if middle C (268s4nxi2p9rk4kr:k * yshn 7k xmz7jg1 2 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 whistle3 hiz- )oy:xhv operates at 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 tz)yv-:h3ix ohhe operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-mp)6s.t6skf n. ws9rotq5ub/ Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is t )fm.wo nktq /s5ssbp 96.ur6the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tu1n l - nqtj f0n4ysv)ssb-1/icned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Efbn t qsy-)/snin-vs41lc j 01q. 11–13.]    Hz

  How many beats will be heard if two identical fll 2oi+e(p 7nhsutes each try to play middle C (262 Hz), but one i p(lh+oen72s is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, ) 7)pbq*b3 ihokg8xg eand C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C argg3)x)7ko*bqhi pe b8e sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are c fj-*29 sx7*jskmh gav5tl h91.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the lm5jh sj-v9 xs t7*9g2fh*kcaother.
(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 viq3x, pu yawy0buij g6:atu +(nte-a-+brating at 132 Hz, but a piano tuner hearsub, -+tq wa(jy+ 0 uutian:axp6 ey3-g three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats pe0d/kl5 90e7euh7 9mhnvhaoji r second will be heard? (Asn he 5j09 k9 od/muelh0hia7v7sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s v;r+xs,01 gft rjath+ n x52a q6wwqi3siren is 1550 Hz when at rest. What frequency do you detect if you r;t,xw16hfrqgix q0 5nt s +3 ajwav2+move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose siua kaq z,b+lpmn.5,+m qepd. ,ren emits at 1550 Hz moves at a speed of 32 zmke +ab+,l ,uq,dn5mq. .pa pm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 20p-n dk+f+e9cjy -0k libg3 3ue00-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly thpu-feyk3+93 -jlcedk0 g +nbi e 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 equippeo 8s+7biq be)f..dtced with the same single frequency horn. 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 emieec7b.o8s +)dt.bqfi t? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them ret/ad0gd8a3oei(lu y x/ ;b8 tmiurned ile8d(0u8o t3gym/b i/a dx;afrom an object moving 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 spmwu )- y 5m:4dkxj,bnteed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency mybx4 wu)5m:dk,-tjn does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was plaj3+uh *2terea yed 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+hej3ut *era 2 approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suc9yf*jau* z ky8m,lw2 ppose the device emits sound at 3.5 MHz, and the speed of sound uca9wm, yk8*f2 zjyl*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 ul3 ek9hd5os5h 6bzi1wdtrasonic 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-kd2 l- eroo1xt1c6df Hz. When the wind velocity is 12 m/s from the 2 edc1k6 -fl1 d-oxtornorth, what 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 object moving 9omdx6 dz*;(cfqg w5 lon 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 Mach2re5he nf);ln4pua7 zj*kx ws nt7 (l. 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s motiowensf *l pz l rh.u7x;n7jea5tn 2k4)(n?    $^{\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 offe1r j;6rpzi0 a planet where the speed of sound is on1 rpzjefi0r ;6ly 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*hk-1q p7*-cxcnsgod /s strikes the ocean. Determine the shock wave angleqdx1 *h opks--ng7c c* it 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 6 ug:bq39csy3i( fjw u$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and c5qow1ci) w:h 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 distancchqiw)o:5 wc 1e 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 pulsehi9qv 3 9r7qims downward 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 mqqv3h979i r i(in fresh water)?    s

  Approximately how many octaves are there in thei6k p0u:jkdq jf1 45gt human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe sym x. zemqoqcrv)r8 q2u g:;hv0cr80t1 rphony. It consists of many plastic pipes of various lengths, which are ope.urh; : q1evvc c2zr0qtr)ogmr8 0qx8n 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 nig7 eo65of:;e8r t h1naer3ea person makes a sound close to the threshold of human hearing (0 dB). What will be the she 86g nei7re3eantrf5 o; 1:oound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound art to8n v+;m/g7l(m 3q41pt vpyfdrby(ir.,e v e heard simtpblnvg e+m r(m.,4ttdyyvv7r/;ofp1 i (3 q 8ultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placedi3lgn8sg8( li1 bq+ hw in the open, is 105 dB. What is the8 (8w liblg+13ghi nsq acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rakg,4wl +t84yd zs thxqyp vvi(8*:+ewdez6 o3ted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts atlgz4vdet4 kw* 8dy 8+ w(,heovsp i6qzyx+:3t 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over thujwhx2*afm0 3 2qmtbl 49+zgdeir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and thtm4bzgh29j3xm fluaq* + 2dw 0at 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 communicach. kp2+r1 u vas uzz7hh*4rm/tions 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 to a frequenc khd:fy t3yw08y 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 fixed8g32 :. c-*bjqylrr r mt-pnn jc8qq-b*jtpn4 points with a fundamental frequen-8-b nb:4j2n.q3ct nj-r*g*rypt m q cpl8jrqcy 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 vibi k(l8xpxf i8hq1w5u(ration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, lxwihqp 5 uk( x881(ifthe air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2cj/h6zgqxe* p-/r:ilq n k3:q2gm8zj b(q/z h.10 g is near a tube that is open at one end and also 75 cm long. How much tension/j 3g( mjngziqq:r lq//pxq*kbhz-e :8hc6z2 should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fullajv 6e/*q8bhw vw89ab loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sourcef,d95tzd9 hf(uj-eg ps. 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 sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency o-d95fjg d tzf(h,p9 uef the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. vyw;f1gqau * 53ub*shThe conductor on the stationary train heawu5**v 3gsb;au1h qyf rs 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 apx8).bs wls de9proaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train )ebsl 9.8 dswxmoving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of carcfrg m q 1jrjjc378(k/s just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a cer 1j 7f c/cgj3kmq(jr8rtain 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, produce a beaeveboq-laa0-+vh6* m b0ug;ms c* s3jt frequency of 11 Hz. The shorter one -*sh- ;0l6u je0 v+vmagb3samq *ocbe is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it move4.7;vm *vo4:q3(mkcgi w( *(dnhnch fbma vfrs past a stationary observer at 10 m/s m( vb3 ackvf (iw4 *:o4nvrq(fdc.n * m;hmh7gas shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is non6pc/7ucdtmk*/.ir;4 / 6j rupdlbb9 0zr lo yrmally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflekj m//d.bot96y/67crl l 4un;u*cpbizrdr0p cted 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 4-liw2 y8cga0 c ajdd:moth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of theayci-dl 8j:wc4dag 20 wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequesd 7u i pq;ue8gxt0(xbf q(6hj m/8b*gncy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3qhix0 psfq7u/eu(tm* ;xg(8 6 bj g8db.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals f b-7.1smyb4 kyhucx(j rom one Alpine village to another. Since lower frequency sounds are less susceptible to m by (yjk.sxc17b uh4-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 compromised by the pt z5bd s,vck byg3ekdgr/c3(e2/s6; aresence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Cg3ygdaebc5v ;b3/k rkz d62c s(t,e/s onsider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumiqs 8hudvh/weai26z 7yj )3jd ds1s,e.num rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. Fw8j27e6 u3hqdz )/sdjivya .,1h sde sor 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 threshl.z8x3cbv/hdp z 99c/n h0.vv tmh r7iold of hearing for the human ear at a frequency of about 1000 Hz 73hcvlvr .c9ni 8v/9zm/d0pzh bxth.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 Mbl f;0 :awir2uach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s ala0filr bu: w2;titude?    $ \times10^{4 }$ m

  The wake of a speedboatmg n0i7wgl q:. xgnc;6 is 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