What is the evidence that s9x) lynz.k ,amound travels as a wave?

What is the evidence that mj97 qtg( nv0 (b;nzpdsound is a form of energy?

Children sometimes play with a homemade aafxtd;:8 ub1ytmn8 .vj;8 im “telephone” by attaching a string to the botmvn.8ba1 8ymj;i:t txd 8fu;a toms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect k0 vm+to.dhrm0l8a x1the frequency or wavelenxhok0 lvrat0 md.+1 8mgth to change?

What evidence can yo1hccgfv( wcac6 4;ah aq1m1z1 u give that the speed of sound in air does not depend significantly 1(14gcqz h1h1vwac macf; 6caon frequency?

The voice of a person who hasoguks 1r1ug i9d3a2ndt3de-kt )k 3 6q inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitc(k,aq ojz:.t. ef e1tih of organ pipes?

Explain how a tube might be used as a filter to reduce the amplifvnyh3k1x l.h jm/8/mtude of sounds in various frequency ranges. (An example is a car x /n.m1vj/flhk38h mymuffler.)

Why are the frets on a guitar (Fig. 12–30) spac4xdn,c fzrbn) mp132h ed closer together as you move up the fingerboard toward 2ndcbhrp4 )1 f, mxnz3the bridge?

A noisy truck approaches you from behind ayuca p 7p:,6r(+/hcvabxt j)y building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on dih jap+)yc7vart/c b,p yx:6u (ffraction.]

Standing waves can be said to be due to “interference in space,” whereas beats c7 tcrghq2 8)iv0 u1h4r4tldwuan be said to be due to “interference in time.”rluh t01 t748g2u iqcdrhv)w 4 Explain.

In Fig. 12–16, if the frequency of the speakeq-6i 1m;xtiy-:r xtkx rs were lowered, would the points D and C (where destructive and constructive interference occur) move farther apartx:;y16mi-k ix tt xr-q or closer together?

Traditional methods of protecting the hearing of peo;9 dm+55n *njjpyz(bdmxq, nawx ,ky9 ple 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 ay*mk5jbx+5zp;9 w,xdqj d ,nnm9n ( ynoise, 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 thoughgr 83aswfbyw8zey4-/ 9 kxc6it of as a superposition of two sound waves with slightwr/ie c3wgsy9f86ykz -bx48 aly 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 source a1khator9 9b( ;n;xgurnd observer move in the same direction, with the same velocity? Explatu ;9na( kr9rx1bg;ohin.

If a wind is blowing, will this alter the frequency of the sound heard by a bb8 ml.s 4o)v8an .xbpg7v9drperson at rest with respect to the source? Is the wavelength or veloc bopn 9dx.mbgarv874 sbvl )8.ity changed?

Figure 12–32 shows various positions of a child in motion on a sn)s bef4s/jr1wing. A monitor is blowing a whistle in front of tsjb/es r4 1f)nhe 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 length of a lake by listening for )7xj-qcw* r7lggl/pothe echo of her shout reflected by a cliff at the far end of the lak7xr- qw7gpl)gj *oc/l e. 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 belg b xr).jsq-e t4-qr4row 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 seawate-jsr rbrx-4e q q.)4gtr is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air rj ev.gtiiq q 2i. .ue*w8a1k)at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tunasma8n4 g4 wqw( on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. wn8(4sgmq aw412–33). 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 majy*jj3 b.rns7 kes when striking the water below is hea. jn*rj7sy j3brd 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the cow uvso*z + 4w8, /m8cf/(dxq eloe,yabncrete 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 1qw,(w/4f,c+am zeevy /s8bod*8u lox.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 dia,9; 7xxr e* ox,g9czuz)m hfustance by the “5-second rule” for estimatingxgo9 e hu,x7 c,9* zaxz);frum 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 ofthivo2 +8rjv0:d nq7ks t/l+ z 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 soui*bm*/ i)gya m su4kf6nd whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound leve d;6ne*mfin 14vkt *mkl of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, nfmk;n6 kd1 *emiv4n*t ot dB’s.]    dB

  A person standing a certain disto;(4a:b sx f.;i yvrcwance from an airplane with four equally noisy jet engines is expersv:iox. cw;ra f;(y 4biencing 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 hk68lldc2pprkg2)2ky gc o ow)e 9+1grave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dle yc2+ p)r1oog2 r dkl8kggkp96c)2wB. 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 ; vxo/ es:cuh((uen j.g*f9;xl 6qope output of sound from a person speaking in normal conversation. Ul :c(hqvex*xuopf g;6soune.9(; / e jse 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 strikes an eardrum whv0uq51stpybh w +.6t kose 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, whi81 u9pyn/vin go)l6s fle 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 a9svfinu8)n l 1ogyp /6 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 mwy ij.8y*z-i dB when placed 2.8 m in front of a loy i8jy*zimw .-udspeaker 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 differencsbcf5a9wi +g ly+8ow)e in sound level of 2.0 dB. What is the ratio of the amplitudes of two so+ic)98wg 5ywfs+b ol aunds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripledn:rl q.z:6hrz, (a) by what factor will the intensih6rl nq:.zz :rty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have ee *(lnzab ;v)pqual displacement amplitudes, but one has twice the frequency of the other. Whalv; *b na(pz)et is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wavefn ;qah 9o3yd-/ctt9hq :.xp )pgl0ju in air that corresponds to a displacement amplitude of vibr xnhtqc9:of) 9p-ug.q0y/jtdp;h3al ating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what souym6gq b-xqk;. nd level to seem as loud as a 100-Hz tone that has a 50-dB sound level? bm; yqxg-.k6q(See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the s:d0xp -gj2mtp,u::vm6 lyhtr ound level is 30 dB?6h::mr vudx t :gty2pp0m,l- j (See Fig. 12–6.)

  Your auditory system can accommodate at+-2 uk+yy:vld8,g5e2rvlmuoc6 tlr huge range of sound levels. What is the ratio of highest to lowest intc+vt+:lvdtr mre2g k 56,ul2oyuly -8ensity 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 frequenca-z8o0da ig5j y of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?o0 5gzi8aj a-d    N

  An organ pipe is 112 cm long. What are the fundamental and first theby-8ynsn8j1) ,gfi s ree audible overtones if the pipey8j-8,yg)esnsfi nb1 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+v1t 2jik7/86o t8fpq mtqz du you expect from blowing across the top of an empty soda bottle that is 6mfzqo8 8vjd7/ttu ktpi12q+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 p5ykb 99try6c ripe organ with open-tube pipes spanning the range of human hr9c5rk9 ty6byearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency op/ 3 ,fs6e3jk/vth-xmzz d,j2:ljw kvf 540 Hz as its third harmonic. What will be its fundamental ,2j hmd,3sxjwpl-ze v vj/t z/63k:fkfrequency 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 midd8 j d su,;xxi--iirr1cle C (330 rruxxj ii;s i,c8-d-1Hz).
(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 ui*+e-/ +hoq obw* qnnthat emits middle C (262 Hz) when the temperature is q ho/n+ we+io*b-uqn*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 4gq /sa7hxjy-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 Examplh zi s)ub)77 *e bsuj+fx*)uwje 12–10 should the hole be that must be uncover es )7fh7*b*)uzij su j)x+uwbed to play 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, 8zz. yev kfy;34ds0ltn,8sfabut not at any other frequencies in between. (a) S,403 nfz;8fksel.ydt yazvs8 how 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. h+y(xoi 7jp8pIt resonates at two succeshjp+o8xiy7 p(sive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 65ll8a s1wg9ahrd ot4$^{\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 for a 2.14-m-long orl;sc a d7p fqdm;yw4)6 0r2nkvgan pipe at 2v)q;l ckwap ;2n7ddsf0r6 4 ym0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxrwl 0m3:ov qonws;mnn0.xl25co 4j 5k imately 2.5 cm long. 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 snl50w 4 nro3 .qmow :0o mx;k52nvjlcinformation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat eveog ju: wj:h7rvuh:.i 2ry 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? h j:7iuw:ujo2hrv .g: ±    Hz

  What is the beat frequency if middle C (262 Hz) and 7b8f 4u qus:aha+ rne-$C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while an.pj s 6:ot8t rlo;ig*iother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans :.*tpr6i jtlogiso ;8 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 irawb )*rrid6m i1;xxz q6z6 2with a 350-Hz tuning fork and 9 beats/s when soun*61i)xaxiwzb6 rmd r;z irq62 ded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to thepb bj1fx6h, 5 0muqn/c 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 togxf uqbn1,c0pb65/m jhether? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical jecsk;1 bt2t5flutes each try to play middle C (262 Hz), but one is at 5.0°C and the ote2bts;1 jtc 5kher at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, akftcu :ix q1t)r5f/;as 7kpf. nd C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a bektc :7t/sq 1.rpf ixu ;k)f5faat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person+evac8x7xw 9 em6hdt7 stands 3.00 m from one speaker and 3.50 m from the 6 xmtee+v7wd9 hxc78aother.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, bidcd .y2. rj;gut a piano tuner hears three beats every 2.0 s when they ariyr 2ddg; c.j.e 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 )s fz.dj;yc 7v2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = fv d)z;j7csy.20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s 0nab -zv8(atm siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/smazv8b0( ta n-
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fre d4.vkpy yojy *ay/h15quency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 kyv.yp / yyo5ad*14jhm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towardsp ;9s4;es8vfv/w boe you at 15 m/s versuseb; 9 v4p8 soewvfss;/ you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When ops vwnc7v 0 e1x 74axw/l:eafg+x5s7ene is ate/e7vw x+f4ngwev xcs 7a:7s0 al 51xp 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 emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends outz b31 8lilw*l (bcf,g6,l:xaj*pl gu uj ))gck ultrasonic sound waves at 50.0 kHz and receives them returned from an object movin g g:llpj luczk w3ib6llacx( g*b)fu),81 *j,g directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a 9u.;tv mpwv.q b6qqww 9xl2 ,iwall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the batvxuvt. b6;9q 2m,iqwpq9wwl. hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopp,c 1b 0nez.dl 853thaxoq/ h,lfw6axuler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car x0,.6dqhlaz x5nlaufh/co 1b 3 e t,8wapproached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suvk)1-pe lk8 cmppose 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 beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away fr1cmp- k lvk)8eom the sound source?   Hz

  The Doppler effect using ultrasonic wavw um4w1/zqxcw8ti78i es 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 Hz. When the wind velocitpl (bzde)2 )-5pib qjey is 12 m/s from the north, what frequency will oqe(bj ) lz2)p5b i-edpbservers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land v6ou8,7r pwv*9huqdj 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 ai 9m9lpju tw/oh 3x(6 cav)r;at Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the dwr;/(u ahxt i9o6pc ) v9m3ljairection of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planeky/wpi jzwbik92-2z4* eggc*90 v; ampd*v upt where the speed of sound is onlyiw/yiug vj042 9d2k* z p;p mzw*ab9-ekpgcv * about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes t sm 87mic,e-qbhe ocean. Determine the shock wave angle it produces-eq8i ,mc7 smb
(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 c-cf5 fep e8rmw1: 96j8fe jli$/theta$ 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 5+tl p:7c:g/spteh wmkm 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 7p p:sl/wthcmg+t:e 5. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses do otu5o) g*af6owqcf+4gd f32,t*l jnqwnward from the bottom of the boat, and then detects echoes5 q )fug d6ot wn,*q2fojc3gao4t*f+l. 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 kpdck v5w .g9,range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consicyc623,g w5zcuht1q osts of many plas6ch zgcqtc5w o3y ,1u2tic pipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the thresqo-(o +fsj/qkaj -.4ygqy g hkwt6 ed*r6s4k3hold of human hearing (0 dB). What will be the sound level of 100j oqe/3sktrhg4o q.d+qg6ws- *(kj4ya yf-6k 0 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dBs-v l /f-f)qg )dv(rrg sound are heard sigv g(rr--dslq )v )/ffmultaneously?    dB

  The sound level 12.0 m from a louu.k4blu)+1ow 08ng /q+sk u ;ricbkkqdspeaker, placed in the open, is 105 dB. What is the acoustic power outpuuoun b 1k8l ci.wk +r+)/;q ksgk04ubqt (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 1ktf0pmk9. / ua50 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?. fpu m9kkta/0    dB

  Workers around jet aircraft typicallh(ov 4 ur ox,.1z,bnfv,dwf:8t:p empy wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of .ed1(vhn:rf,ot wm,,xf8pb:uop 4 z v30 m from a jet airplane engine?    W

  In audio and communicbp(6m oj y0c+pations 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 frequ-jquh:/v36/b mrk g blency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fun)f1gf b j7*e 8vfdb/agdamental frequency of db)g8 1gfj /ff*7va eb440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled with wa .xbpabv :6c+gter (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 fork when the distance from the tube opening to the w6c+bpvaxb:g. ater 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 strindua+3py zi bhp85h l( n43acj9g of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension ph8h3a5i3apc j zb( lu4n+y9dshould 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 ob+eycqjqgn11;tm 0 etc, at+3jserved to resonate 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 intl0iz) j)d)ye the 500–1000-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 persoije)y0t )l)dz n 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 stationarhn j6q0j:3h lry. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approacheh lj r6q:hnj30s. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachmr3i,zict .(aes you is 538 Hz. After it passes you, its frequency is measured as 4zr(c3i,m ta.i86 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you c7 fpa9bymne43an estimate the speed of cars just by listening to the difference in pitch of the engine noise between appro34ba 7nf 9empyaching and receding cars. Suppose the sound 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, soundingf8y qjrxf hrk9ztq4rq w018 /da9j5/j together, produce a beat frequency of 11 Hz. The shorter one is 2.40qkf 9/r5qjtq 981yr/a0 8fj rhz dxwj4 m long. How long is the other?    m

Two loudspeakers are at opposite ends ;u pbdh-.h p/kof a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have pa h-p/hu .kpbd;ssed him, at C?

  If the velocity of blood flow in the aorta is norem twja(p4/v0mally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow a/pj 4vewm 0(atnd 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 the mothf0 l:lw6xbolze z(2wk68xz cf3l a86t is flying toward the bat at speed 5 m/s The bat emits a sound wwl3b2zzl6eckfo6f a8 lx:8tx lz w06(ave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as i ivmeza5/ 3j(wc/ir( :l wpj1gt approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3w( w gr:lcz3a(pj5vj/ m1e/ii.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 3h,jxdl/aye 3 4vqe:s6vgo )zto send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the 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 calleve eo63qlh :/ y)sd va4g,3xjzd 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 c*a-+lo7ub3r j tw;aeoompromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencir bajolw;3+e - o7tua*es for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” inv 6 m-vatp)k4moal2)vf olves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod caapa)o4-v2v k)mm6 ltfn 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 thq0s :zqfz3)mgxs(srdh) o)6 (b, ce ihreshold of hearing for the human ear at a frequency of about 1 b6 :)z0 c(i)zshr hqme3 ox,fqsgds()000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic bohf8 5y(a-)m ssz3o bmoom 1.5 min aftermz( 8 f )5omhoyss-a3b the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat y2vz8 rw 3n gzfk;qpq.2p5l1sis 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