What is the evidence that so2bcd.;sz fia9 und travels as a wave?

What is the evidence that soipu 9uc(b9b3c und is a form of energy?

Children sometimes play zcf xyv:47: -l-) mz0f niknbwwith a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound im- n f n:x4z0cy7vl-z:b )kwfwave travels from one cup to the other.

When a sound wave passes from air7 l3,5vwh6o. qz lt9pivvnn,z( l aj4e2dadm . into water, do you expect the frequency or wavelength to ch4ve( mt6qoljd2, 7v.al9v l n,wh5azn .3 pdziange?

What evidence can you give that the speed of souihyv8wp:0(puttzj1 b5mplo6 *t21 ,n2knefi nd in air does not depend significantly on l26 f1beohy (it01,jnzpntp u* 5:8iw 2kvtpmfrequency?

The voice of a person who has inhaled helium sounds very high-pitched. djla5ijtw qb/ jnj1hs3486)xWhy?

How will the air temperature in a room affect the pitch z-6grg5ogvghb 1kd8+ of organ pipes?

Explain how a tube might be used as a filter to reduce the amplira o()a a- 4byv3q/onztude of sounds in variouqboaayon zr)( -/ 3v4as frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar aeta,jt9s*:p wc n9 t/(Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridg /t:j,a9twcae* s9npte?

A noisy truck approaches ,0fkwmjtn86v you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter 6fnmw0 t,jvk8” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be duzah* pvq+ d3qpgqe / +0dpsw; .)zar4ue to “interference in space,” whereas beats can be said to+dgqv s ; .*4r p+dhpqa aq)wezu0z/p3 be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lox;u6sxm5 a)u fyi dodocg:5 y9 ib(7qr;id 5d6wered, would the points D and C (where destructive and constructive interference occurmi)5d a giu7;dr( 6y6os xioucfd y;95:bx 5qd) move farther apart or closer together?

Traditional methods of protecting the /ol; st.f8erp hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ear ;.pt fels8/ros?

Consider the two waves shown in Fig. 12–31. Each wave can be thou 20/44d)t(gwmp+ g g2x jb5bi gyssgpyght of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? b dsj4( gp)gi05gy +p yb/xtm 2gg4s2wExplain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move iv7w *r159xovt zkw 1:.pen+q /dwkvjv n the same direction, with the same velocity? Explain.r vwpevqkj wd:1x+ * wv71n .zo5/tv9k

If a wind is blowing, wilvv8ite5/ njw; l this alter the frequency of the sound heard by a person at rest with resp8ivjevn;t /w 5ect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swijty- bhfl9+3 bng. A monitor is blowing a whistle in front of the child on the ground. At which po3bhyf+ l9 btj-sition, 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 ,*hs)a32ely iid 1g3+ k fjceilake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate thed s+,a yk* 3elhig)fc23i1ije length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the dx2 .;l ugah8becho .28;bau xhldg 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 depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths i9hw9tt twqm7kv45lc ,zn()jlwh1w w*n air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on lxkx y 9:5 9svlwk9c0q*hu2jay08rgw a foggy day. Without warning, an engine backfire occurs on another boat 1.0 xsa j5uw2xkl h ywc9*gly08:9qr0k9v 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 striking ea r5 sphe7(8.bxe/jw the water below is heard 3.5 s later. How high isep5b (j./xa7e erhsw8 the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concretehik94r5gt 5ba pavement. A moment later two sounds are heard from the impabt 5 a9gihk4r5ct: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent49r8hfhk etvv);*vl.2ez, auugg o3 j error made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 erth4j.9uz*2 ulhg vvf8k3,a) oge;v$^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 12tg8a 63e(fhc 6mu 2nht0 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 intensity;a5 ju8ntxnw 4 is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 y7v an 7a)zag/dB when fired simultaneously at /a7 z)yanv7ga a certain 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 wi*+ 3qg m*bg;qwoy :j12: bcoidec81b)qc d iqmth four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint:1*d:biy om+ :3;o qd)w* qj2qc gqigmceb1cb8 Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, where ehm; dmgufs/-/fya enf6*n3b x.6+lzas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgr-bm/n ff6 * /sg;umd+ yzfxe6h.3nael ound noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frog ptia f.z iw4o6k)shl1 ;,.rmm a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphoizpgrw,ia 6m;.tf 4h1s.)k lere 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 e4ve3 jj+nz8lpy62yu. :nd ilan 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, while thyjtm45 nf2i;9dycfvfl*5v.le more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you wtcyj9in;5*.dlv f52lfm 4fyv ould 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 reg/ppd6i ,qjf-za6 u3s1lpal y+istered 130 dB when placed 2.8 m in front of a loudspeaker on the sta f1,dl6 yqus3ai6pp-zl/p j+ age.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of7gx reax g l6s;( +cb1tuqg3f+ 2.0 dB. What is the ratio of the amplitudes ofx qcg3+gb( gx+ur6a s7le1;t f two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled,my v0 4qoe3mdci;: az. (a) by what factor will the intensity increase? Increase by a fac0 oveczm :a4 3mqy.;ditor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplits+1fmt1p kv i5udes, but one has twice the frequency of the mi5v1k+tf ps1other. What is the ratio of their intensities?   

  What would be the sound level (in dB) ofcxkodtn3u7 . ud4. kso(. rw0o a sound wave in air that corresponds to a displacement ano 3dc.( tdru.0o osu7.wk4xkmplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz t: 8ft4o+gc qapdi:) daone that t4:fqadc +8ig: )paodhas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an etj *mc8vo 7 *ti1lgpo0ar can detect when the sound level icjlt180ov tgm*p 7*ois 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the /; fxh+*1y;9e h0 gldidz/g bqv rtm3oe0zjl+ratio of highest tgl hgoe019mvr /htj *qb0x zzfeldi;;3+/d+yo 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 fundament6n)b8x1ot zo ) r aun)rhw*mqfpk:3m ,al frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tens3an) )q*x: mzn8 ur ow khm,6o)1ftbrpion must the string be placed?    N

  An organ pipe is 112 cm longc6e pkdto4o3 +. What are the fundamental and first three audible over+oo6det 4kp 3ctones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency ,u,q-3eo dz xi 4szog3x0,mg hwould you expect from blowing across the top of an empty soda bottle that is 183 ,g-s0zh4eo,oi,uzxx3 g m dq 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 op )kf+7g8u 4ol2aqeaj wen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz),wf uq)k+o8 age74 aj2l 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.cwcy +prhs, - has a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if.cry+- hs w,cp it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and yp5,* r ppsn.b. zfec w:dd7m*is tuned to play E above middle C (330 *dbyn5psfmp7.z,c:r pd.w*e 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 organikj2 i2o r2rl6 pipe that emits middle C (262 Hz) when the temperature is 2o62rik2lrij 2 1 $^{\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 atm s;(v::yix2 (w+x8tc dqjnbz 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpieceb07 c ra;pt1z; frv;khdx t:u9 of the flute in Example 12–10 should the hole be that must be uncovered to play D akzd7f9ttbu ;pcarxv;;01h: rbove middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at a) :v 7lok-vkr:v ms6ivny other frequenc:)vkl ms67 k :-vovrviies in between. (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 resonazjlx.(:ba9yri9ud m )tes at two succesz x) ai(:m9.ylbrd9ujsive 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 nlb9tp,p7 i9 eivfk.*$^{\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 wqp,1hqvcab9x htfs2q0le y.1kwq+9uh x9 :4 u ithin the audible range for a 2.14-m-long organ pipe at 20shwelpq2auq 0 9y h+ u4:xf9cvbq ,19hk1tx.q $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximaterh 01r f,9e1nw4o.f pp/ibcfl ly 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the 4 ofh9i e.1pr r p/0l1cn,bwfffrequencies (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 +t0cp c (y 5slq7 cq,ncidck32to adjust two strings, one of which is sounding 440 Hz. How far off i c0q3(q,pslkcn2i 7t cdy c5+cn frequency is the other string? ±    Hz

  What is the beat frequency if ml0f vvzj-7ntr(+ +p ftiddle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 k:t; ;fsiit;lfk kxt,;Hz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating f:f kiif k,;;xt;ts;tl requency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350z*ssna) m0 qj8-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasonn8sa )z 0mqsj*ing.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. T*n,(skciu r;hn5 0y:6bmzh yrhe tension in one string is then decuzsi60 y;m,h nc:yn* b(krhr 5reased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be h e21jt:7urnp7 votmmjokv6; .eard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0°;ne76 jm:.up2rmk o t1 tojv7vC and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency.uj/y3s cwyen s7+ pt0 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 wheny/esjcw y7 ntsu03p+. 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 standsry14d1dgqfo5*k- vt)fw8 dv w 3.00 m from one speaker and 3.50 m from d w*fo1fvvdr t1kd- 8)5qwy4gthe 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 supposed to be vibrating at 132 H qj2szn.o )ro m65hv*sz, but a piano tuner hears three beats every 2.0 s when they are playe *2q6nvr oj o)h.s5smzd 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 m wjw73 *oyezy:any beats per e3wyy jw*:o z7second will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequencmvhz h ;gn.01k :vxi jv3-ynr4y of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speehjh:n3gn-zi4vvxk m0.r; y 1v d 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 e*izy2k;i* x )or:3uelwo.y isngine whose siren emits at 1550 Hz moves at a speed of 32 m*w3:2uelr)*zxis i k.yi;o oy/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source brrgpw; ol w.cj-(c9*miy:/f is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? (cw iy:/pcmorl bjw-gf r9;*.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 ea 0;jc::4.b ot;m;w:ngw qmjn q)jugaquipped 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;j c:w 4:nn0g)j:jbaqag. umtqm o;w; 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 ultrahmvy13c lovs z 9b-q)3sonic sound waves at 50.0 kHz and receives them return obvyhqmc l-zv1)93s 3ed from 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 speed of 5 m/s As it flies, the bat emits ani9, w-qnec 3.pxqrsl/q;j9 ae ultr/nrq e9jq9;-piqsalw, 3cxe. asonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving 7 7r 5cgfx)gkhflat 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 station at a speed ofx5f ) ck7ghg7r 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloc8k13 bcohl75a ;e xmpnf-y4tod-flow speeds. Suppose 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 fry7m1ebl cxnaf58h -k; o3p4 tcom the sound source?   Hz

  The Doppler effect using ukdta1;atk x28nd),pkltrasonic 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 Hz. When the wind velocity isuy8t x*d id9 n13uk(y,fq 5nks 12 m/s from the north, what frequency will observers hear who 1y3 *k(k,i9 tyxu n dnfu5dsq8are 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 movk8+7/v6 b hmfog fsh(ue zy;.qing on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels a1z78 ffp-e-4sj-hdg /qzqr; c br6si gt Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the sh-b4 se/ 8gz1-6hrcff7i dqgjz;-p qsrock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet whe9q2q:saus cusjs1p 1/re the speed of sound is only about 35 m/s aj2sq:9s 1usq/1cpu s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wavegd5 o(os ;g*ai angle it pr dggo;i5ao s(*oduces
(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 w 9i(vaq0azc f-+lysks7x* 5x$/theta$ 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 aboio3b xmlh01h 2ve the ground flying faster than the speed of sound. By the time you b ho01 hm3xil2hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a slko2pm.eh3+q1z.c m qonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which lkqh3 .ommqc2p+.1e z 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 thed( 1bfl zoy6faf19+bx jh 3l7z human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pi*u)8 wyahqj7 (9g rtrope symphony. It consists of many plastic pipes of various lengths, which are open on og a)wh8r9u* t7qyj(r 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 c(pfajodoi8 (* s9xom /lose to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mpxmio( jo* 8(fods9/ aosquitoes?    dB

  What is the resultant sound level when an 82-dB sous ,8-zdr.zxi ./ovtp dnd and an 87-dB sound are heard simultaneously?- zitrxd,svz /. dp8.o    dB

  The sound level 12.0 m from a loudspeakeraw +c0 d)1p fkfe5vx-u, :vatx, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming5 f, )dvkp:few xcvu0-ta x+a1 it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1fp*xc:v7pt3t0l bsl 0000 Hz. The power output drops by 10 dB at 15 kHz. What is thesppc 70tt:v3f *blx0l power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear p2cu a w za0p4-0 xejhrmt5g/t6rotective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane ajr 6x/a0hm tge2cz04wpt5u - engine?    W

  In audio and communicationsxtuj9.kne (tk3lmn *+ 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 frequency /q nks5+d.n1+v rsmyu1$\frac{1}{2}$ 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 bw ud oh)67+ebe4xu40bjr o,ka etween fixed points with a fundamental frequency of 440 Hz and a mass per ue0 64b,)j o4 7xruub a+edohkwnit 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 jre 5.h3ko7mo 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 fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is thekm3.ohjr7 5 oe frequency of the tuning fork?   Hz

  A 75-cm-long guitar strins*6 8 g,eod0g t(d:srlgl8vrsg of mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the stringe gs0,d l*8t8vsgg 6(srr l:do if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was (kykpt ;mw/9yobserved 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 in them3f hyspp:p0d 7u7j4d 93izpmr0c1w l 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 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 frequencyp7pcr 7uyhf4 pw0d im: dzp30sj93ml1 of the sound?   Hz

  Two trains emit 424-Hz whistles. One train isj.l 2aa pt*q3m stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the othea.jp q32m lat*r train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam -fn7s4c q rq6 vc66-kxsf yuu0train whistle as it approaches you is 538 Hz. After it pa66yck qu7 vxs-qr4nfu 0csf6-sses you, its frequency is measured 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 livo51 6auyx9q ;*eud listening to the difference in pitch of the engine noise between approacl51;ueixy6a dqo v *u9hing 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, sounding together, produce a beat frequency of yf 2d1ye5 fsx u/ e;ea1t2ef5n11 Hz. The shorter one is 2.40 m long. How long is thee teexfy sa; f5y1e2251n /fdu other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a ;l gr7raama+f))kx1) p ajhrpa+ pi)4stationary 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,gj)r)1h4ak ; r)axp l+m7f ir)aaapp+ at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blo8at9x0nl:fjr:/ oa9ad polc .od flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were diro 0nxp.al9o/aat c:d8r9 f:jlected along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth lme - z lnh.0l sf)h2yih51 5nr*lw1npis flying toward the 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 th1.5mh* nz1y 2lrsi-le )nw lph05lnfh e bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencyr+owjsi s n3 rht.58.b sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 8.r. rnsj5bosw3i+ thms 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 fror786i gd ipqj(57 klnomwn5 9zm 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 the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (S8m( 5orln9wdi56qzkj77gpi nee Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromis;*.to-kuwze gq:s/vo ed by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nzeq/.:vg s-uto* ;kowodes. 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, called “singing rods,” involves a long, slendzxx1 d(si:um3qo ktar o44:/ 5t:abs ker aluminum rod held in dk kao(sx:t3 :zo5bix1ra msu/4t4:qthe 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. 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 threshx1oc/ l5-v1i st8hge4ju f: tsold of hearing for the human ear at a frequency of about 1000 Hu v:xgo- 8i5csj41t /tsf1elh z 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 aod,ag 5dpbz ;jio f92(t Mach 2.0. An observer on the ground hears the sonic boom 1.5 min after the pdgp(zd,ooa i5j2f9; blane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 ,5bxvv -:bs k u 4xvo7v;2qbly$^{\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