What is the evidence that sound travels yi3n;880, bvuq xt*xxw kv e0gas a wave?

What is the evidence that sound is cti v2i)ue;o b 2,(jad6vqs: ha form of energy?

Children sometimes play widnwi0r4 jfsns zmd 9x97.-r.lxm 0ugz84oms5th a homemade “telephone” by attaching a string to the bottoms of .x -5mfwiogx49mrzd0s8zn.s7mdl 4j nu r9 0stwo paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passl y(;nr*+i lwaes from air into water, do you expect the frequency or wavelength to chawill*+y(r; a nnge?

What evidence can yo/bqks3,5-gd zj8 syis u give that the speed of sound in air does not depend significantly on frequency? b i53q-s sgks8,dj/yz

The voice of a person who has inhaled 0p2k 6e)r/pf.mqdhy e helium sounds very high-pitched. Why?

How will the air temperaturer821m,0r q btgw;3ibafl-hxn in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce thec0fn0f 3invpg9dg(p/ amplitude of sounds in various frequency ranges. (An example/0 cp9gvnff d0gn(i3p is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as y,uj2unx;ezcul:suq5 ,d l1. gx n15kfou move up the fingerboard toward the bridg5l5kueju l q,;21s .d: znfx1uxgunc,e?

A noisy truck approaches you from behind a buildii0bzrax 3acdwz90 .i2cg1wc0 ng. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of0d awx2cgc ir. 9wb3c0 zazi01 the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can bgz5 kh7)iq8o aha 3r7pyy 4 2b3ox0koje said to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Expa 5obzh) 3o j0ia ogypqkhy 8rx7234k7lain.

In Fig. 12–16, if the frequency of the speay 41pus:oj36wjwg/x8 y 3qie rkers were lowered, would the points D and C (wherw 6qgxjy/ jr4o ywsp:338eui1e destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing ru5yql y(5a3e+ln m;g of people who work in areas with very high noise levels have consisted mainly of effort yu n+y(;5 alq5e3glrms 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?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a supde-e wg 2aobn) d8a)3k hha93derposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), a)aoe8 nkda-heg 33d9da)h2 bwre the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source cy 3qk t0l; kw wgwg2s2;jwr.*and observer move in the same direction, *3yjw;gtq.lg2krwc0 ;wkw s2with the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard htou (xb+9 )hl 6eyg/cby a person at rest with respect to the source? Is the wavelen 9xuyth h/l6c)+goe(b gth or velocity changed?

Figure 12–32 shows variou12 ocf jxn,9 e.uv(j2bjg4l bws 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 frequency for the sound of the whistle? Explain. 1(92jn4o w ,be uj2gljxcbvf your reasoning.

  A hiker determines the lengiics b6t39zfu+la0i / th of a lake by listening for the echo of her shout reflected by a cliff at the f/flu+i6zs90ti cb3 a iar end of the lake. 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 belo1qknwgt5l6r(( h4:j3 zoi agvw 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 1560 m/s (Table 12–1) and does not vary significantly with d:jv zgrqn6 13tglaho4w5i((k epth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at myx--qtlq.dpo7 z 77ky+we ;tp c8:mn 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 tuna on a foggy dyr -l/vcz/8 cj )t8d(gn-2 aeqjehid4ay. Without warning, an engine backfira -dnehj24q/ce- tz v cy(88/rdigjl)e occurs on another boat 1.0 km away (Fig. 12–33). How much time 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 when st*w5pk3z4qe;mfbn u8b riking the water below is heard4wmb*5 b 3nqpfkz8ue ; 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees aeoj1,n04mo-jjcu 2o ek. 6o j k(ljh6l 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 the concrete, and they are 1.1 s apart. How far away doho.ce60j - me6oljonjl2 1j ,jk4 (ukid the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the gq6nit1p5: va “5-second rule” for estp6a5g iqn:v1 timating the distance 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 d3h* ty+12zguwug:znq2d5 b- )ak vcymB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound levee byd/w8y:a 81h9j+a/t-ow+ ski syi fl of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaowlsf 27 4zm d3:7mjjzneously at a certain pl w:3mdj7l7fz2mj 4sz oace, 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 wh8 cm fn;50lmwith 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?ml m;h wf0n85c [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, 5x 8;tyvqfos /r(x8lf: 0fzqt+z w9phwhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgrfo ; :9yxv8/ 8rtzsfh(l +z5qfx0qwptound noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound x 4mn3k/g k vw5fbwb,8from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a v,kbfnw/m 4 b3gwx8 k5sphere 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 anps inq-5a4p+w 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, whilov4x/q xgiwt.:d6g x c,je/c 2e the more modest amplifier B is rated at 40 W. (a) Estimate the sound lc/ vg ex ioxw cg/,jtdq.26:4xevel in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in front o,(usxdu aff 6i3h mk,:f a loudspeaker on the s,(uhfd6m3 :i,f uskxa tage.
(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 a2mlhct1 qw69v 7+x d.d7iwjgm difference in sound level of 2.0 dB. What is the ratio of the ampvw1h9mxw jglc+7 .t qm2i6d d7litudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intenszu4edt8h9o ;5n/gca+b iy0he f0q/9: sq zla yity increase? Increase by a factoba c:eh /i99t8n 0 qqdyz;ufsg+l05e zy/h4aor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitud l j1k7 tg.06fdi,mpq+uk- *zovv0 lrdes, but one has twice the frequency of the other. What is .07i ,dj* q1fk- o0 grzm6+vltvul kpdthe ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that c+ay9 rl ,+l :wmz5mvglorresponds to a displacement ampl9l:m +w5l,gm rv+ayl zitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve /8khw z8ewih:l to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6 w/ khi:e88zwh.)    dB

What are the lowest and highest frequencies that an ear can doggm( g(8y1yp9grg s4x.b(* n j+ nlq,w hxn8metect when the sound level isxrm*gmyx +yq(.h1 n9g, 8lpb4j 8(ngogn( wsg 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound 89- ) qsq; qna7- obvhytadx9qlevels. What is the ratio of highest to lowest 9qt--q7)b8v hx9oq ay ;nsqa dintensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of thnx 2ji0z+nytkq+7gf .8mm9ar e vibrating portion is 3 n9z.qmjfm+8x+ta0 yg2i7rkn2 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 aud:yetk2)h;.g 5 nu zid +3itpqaible overtones if the pid3etuz n gq. kpii;)52ya:+t hpe 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 bwby3 bm*7x(pv lowing across the top of an empty soda bott p3b*v 7mbyx(wle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the r m+// 2cd1ogh e(8monjumf7 jbange of human hearing (20 Hz to 20 kHbo+( f2umhmj1oe nm/87gc/jdz), 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 thiref.+tn . 5/*x hekqc9lfs,pek d harmonic. What will be h l .eq*,9kfxset5p / c+fek.nits fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string i1x9 82dbwpqnxs 0.73 m long and is tuned to play E above middle C (331xqd9pb2n w8 x0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe thatknsmj2j69 + te emits middle C (262 Hz) when the temperatk2jjn+m6 se t9ure 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 at9p *nyy 5)uubg 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should r6zs(u ,oldi7 8lje2jthe hole be that must be uncovered to pla7 2ji6(lo8,lzd sejury 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 g+7*rofuck- :a9rd4z y8v yzeresonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why thi*v:zye7 akg4du98cy-z of +rrs 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 reslcp::af 3x9fu y aca68onates at two successive harmonics of frequencies a3yx6ua :f9 8:fal pcc275 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 6vktqkh(sr(2 is +hy 1$^{\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 a5 (j6t5*eimt)aqo vwqre present within the audible range for a 2.14-m-long organ pipe at 20 5ej5qq 6m(tvoaw* i)t$^{\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 tsfrud5wkz. .85nw6f ao the outside and is closed at the other end by the eardrum.6n.s5dw5r fwa 8kzu. f Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to ad/t wk eqyb9b14just two strings, one of which is sounding tyweb149b q/k440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if dfh)4j s p .cvv+ig8x7qn- .g2e6il cfmiddle 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 2vhmyime ep5no), 2j 4ro w:,)m3.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by orm o:)e,m2)mwh yvjn,eip5 4humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350n*v +x3(r4wgrm ggq8p-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fowgqg* rv rpn8m(43xg +rk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tw) 5c,4b cnzxvension in one string is then decreased by 2.0%. What will be the beat frequency heard when thc, n5) 4czwvbxe two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middkfrfu(v x5w :3d*v;bj x*lg(fle C (262 Hz), but one is at 5.0°C and txrf5ubvfwg(k x ;j3 *l(f *v:dhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B,q. 1gbqdz8k6c and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat fc8q1. q6dz kbgrequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are,v h.8zfqhntv,n.4 qf sh9;ph 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m froq nsh9. p ,8nqv4fvftz. h;hh,m the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed2x/tw( robo3n 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 musbo3 xtnrw(o 2/t 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 2.64ag 4( s,asx6 kksszm2 -bd/+vc m and 2.76 m in air. How many beats per second will be heard? (-kagb+a6(msdvk2 /s x,z scs4 Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when 0 (6+t8 4pbjotscmdowg q 1k4vat rest. What frequency +obt 14 jcg8( dvqpmk6s0 wt4odo you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. W/kq8eyab zy4/ hat frequency do you detect if a fire engine whose siren emitsya84bq/ky/z e at 1550 Hz moves at a speed of 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 you at 1fex uej rx3b(068p.kl5 m/s versus you moving toward it at 15 m/s . jkr3ebxxuf 8p(l60 eAre 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 t-:wo+lv; ghsfrequency horn. When one is at rest and the other is moving toward the first at 15 m: tl ;h+wovg-s/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic u: 1kl9b l1k;p umn:6w)eteqe sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the receivednku6t):w9p: lke;eqb m1ule 1 sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emi-)w8emk v tsdt+jz :1nts an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear i8-zt +j1wtedkm:nv )sn the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playe ewzope.6nm ,6d 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 the statio6ewpezo6., n mn at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppos4eqmnc c-btfun8l(0 jz )e : gmd 4j1u2p;ek8ge the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected g (t-lk1nz gqu b :j8mfu 2c8c4enped)e04m;jbeat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasoni qq4vxl/v4xu w hw ru1z +.2e*i 3xi;rj4fw5nhc 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 sou86. )1tppgopor zb8 w,nmn7u pnd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest, . 1nmrwpg78z) o tbopp6 p,nu8
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its :jjy 4tbca d:-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 of9f qo8*bly,g m sound is 310 m/s (a) What is the angle the shock wave makel, f *oqmy9bg8s 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 atmosutb(pd am :,4vphere of a planet where the speed of sound is ontpbdmv:a , 4u(ly 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 stoi.c1 /kx7r gpo) zs6trikes the ocean. Determine the shock wave angle it producecir.ps)6 7z/x ko gto1s
(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 yj.9u a7igx z-x6zxd cn.f9z6 $/theta$ 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 gn*s vls3(e;*i oxz8 ruround 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. Ses*ozv* r8;3enl sui(x e 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,i;h-b:rvp; q w000-Hz sound pulses downward from the bottom of the boat, and then detects e wihbp;;:q -vrchoes. 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 rang9 q o 9p cls/w/iflld5:h/a,mse? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dik06u dlhfs*r:d m 46susplay called a sewer pipe symphony. It consists of many plastic pipes of various *krsm66:4 d0sudlf uhlengths, 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 perx:hc1c+t 9og oson makes a sound close to the threshold of hum+t1coxgo:ch 9 an hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant soosym nyfo :))f0)q6qtund level when an 82-dB sound and an 87-dB sound are heard simultaneousqt: qf om0)sf))6yyon ly?    dB

  The sound level 12.0 m fromvype byf bcahdwn33 / 428p2c0 a loudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directioa3b v02efyn8bchy4 /2c3pp wdns?    W

  A stereo amplifier is rated at 150 Wks7-8l nrlv5u* ) fldo output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts al *5-r8donvsf l7lk )ut 15 kHz?    dB

  Workers around jet aircraft typically wear protectibtdumvo:d80hrx u 1(+ve 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 i8rh( dd+x 0muu 1vb:otntercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain /k/7s (drm,llkwg ir)p0w 0on, $\beta$ 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 violi:jpy, s724 w5fazks pmn is 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 betwee j hx0h2r 7482kgh+zdv8ucbbcn fixed points with a fundamental frequency of 440 Hz and a mass per unit length rd2vhh0gx48b bc7u8h 2 +ck zjof $6.1 \times10^{-4 }$ 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 vibrat)m9r yo8ob8tm4(i nne+ 0(rsyzpoxf;ion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning for8 nbrzyfmi+o)9;pxno ys4e( r to m08(k when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near-;h; d 4jwo6zk8m0kiyk ispb lwa6v -* 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 mvwhjd;p k6 80-wz6;b - k4iloskm*aiyode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loo +-fkl6krwyq1 p ($\frac{1}{2}\lambda$) 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 500–10g l hu:)f*9rww00-Hz range coming from two sources. The sound is lou*gwr9 f w:)uhldest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The condugll0koay 00+ tzed0 p *,oin;uctor on the stationary train hears a 3.0-Hz beat frequency o+;dguzl k*0itpy0 nl0a0eo,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 538r+daueyje o 1078mf v+ Hz. After it passes you, its frequency is meas j 7e0+vdo8r1ya+muf eured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listen5njsq bpi)6z:ut4jya , pdcfzu- s, /(ing to the difference in pitch of the engine noise between approaching and receding cars. Suppose the so qit-syc dapfp(,4zz6b5ju:j/nsu , ) und of a certain 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 togeq 9a7cyn6.q, d c)tddvther, produce a beat frequency of 11 Hz. The shorter one is ct)vdq.9n6c7 adyd q ,2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moviz9 sh(;r ow qqc0(w,fbuk6-ges 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 fr 9h cbri;zkq6sw-q, u0gfo((w equency 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 bl fsw ih np1,2*o1g+t(m3qxytx ood flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the redfgo*nw,hyts im 1q2 tp 3xx1+( blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying toward th j+ wixk7wzxqzd a;66.e bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave refleax qx6d +w6; zi.jwz7kcts off the moth?    kHz

  A bat emits a series of oe u(ml*e4*;acyjle6dwo89 shigh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and el;4sd ea8(6o o9emw u**eyljcach is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to sdm6 2l8rqx(yf .iacm3xya1 *iend 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 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 aamd*8 .3rqc6 (m ixi1yylfx2the 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 (fggj kqw;yhr)w))q- standing waves, which can cause acoustic “dead spots” at therqk-h)qywg)gjw ;)( f locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, e 7 vna)u l n:nz3vxbou;0:f1svgii0d2z3*zrcalled “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 :roa 3nev2zxuul7i3f) g zv:0sd inv* z1;0nbpractice, 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 ear at a fre(sj y;p-n lvq;dpmi ;mqt9 :/oquency of abo n:/;qds; ;vl-im9jp( qy pmotut 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 obse .ic.a3l(/ jk4nqqttk nw7 (bkrver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. Whan47b( w(q..3k aq jkkc/ nltitt is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15u.) iea9;q/ xa syqa4tqksx2* $^{\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