What is the evidence that+6x/sr/t ,cnx myjg,it.r))r uu+nga sound travels as a wave?

What is the evidence that sound is a form of enej r7idtu5 .sak6+hw: qrgy?

Children sometimes play with a homemade “telephone”n,cj u n-kk/uu*0pj d3 by attaching a string to the bottoms of twp -cu0jkku 3nnd/ u,*jo 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 )f dc*re)ff0z+sk ql,, do you expect the frequency or wavedfs)eqz0*+kc f lrf,)length to change?

What evidence can you give that the speed of sound in air does not depend signhhki1on)df oer ;.vo xfu1.57ificantly on fr)n.1i;ud oreh5 1x7fhfv koo. equency?

The voice of a person who has inhaled helium sounds very high-pitched. W6)v5(gfc5yb widhu +*c hfp)aqvb8o /hy?

How will the air temperature in a room aug 7mk112b8/ gobdkbzffect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds x0m2g:o5f9icbu jpo9k3 xga :in vargj9o 0o cgxm2 u9:5bk:ixap3 fious frequency ranges. (An example is a car muffler.)

Why are the frets on a2 s okt+i5rnjh-3tei* guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridge? jtesr *3- 2ionit5hk+

A noisy truck approaches you from behi7fxa.;bl onw1 nd a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Sectio.; nfx7 walb1on 11–15 on diffraction.]

Standing waves can be saq ) abjht;l8x6izs::au9ibt3id to be due to “interference in space,” whereas beats can be said to be due to “interference in time.” Exzjt:h ax6aqui l) sb98ib;t3:plain.

In Fig. 12–16, if the frequency of the speaq .; 2ciae9 c+y(awbavkers were lowered, would the points D .ywa;ave2i +9qbacc( and C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people w3,.i5)ny, vjz0 w)yfirb ng gzho 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.5ribiyz ygv wn0,. g),3j znf) 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 ofzo *9 asksm3uci;nq+c,*27q yjua;ci 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 frequssz2uko cq*3cj y9aq 7c;u ;,*imani+encies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift o4w 4kurcd:k2*+ mznhzony54if the source and observer move in the same direction, with the same velocity? Explac +5*z4kz4 2:h4nwrudo ymnkoin.

If a wind is blowing, will this alter the frequency of the sokaio 29ak ;jk-und heard by a person at rest with respect to the source? Is the wavelength or velo;joak2 kk9a- icity changed?

Figure 12–32 shows various positions of a child in motion on a swing.xk j5gsw2t85: baxuyb i)fz30 A monitor is blowing a whistle in frogw 8u2stf) j5a3 bzybi5:kx0xnt of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo ouu aek7u ef67.f her shout reflected by a cliff at the far end of the lake. She hears the ecf 7uueue7ka.6ho 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jusig,d-4cs b5f vt below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.cg-, vbis45 df    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air aduep3 5s rxb.+/uvk k7t 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 school9j w2 p71l trpj2,uesa of tuna on a foggy day. Without warning, an engine b l7,jas2ep 2jutw9rp 1ackfire 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 the2yireo1 t/.uu top of a cliff. The splash it makes when striking the water below is heard to. u2riu1y/e 3.5 s later. How high is the cliff?    m

  A person, with his ear to the gror pwqop0g/infg1 bu-)5i+: zdund, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and t+uzin 5dwf)-/gpop0: 1iqbgrhey are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error :s3: +f lxeaekmade over one mile of distance by the “5-second rule” for estimating th::x el ae3ksf+e distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of zoukp/7su-m axdn.ro ;4 s(7fa sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensity vtexku ,a3d* /is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneousy u.rqq/.;) )gtrg6vioxiz h -w2fgi)m r q2u;ly at a certain place, what will be the sound level i) rr/w. yiq- ;tgvh. iig;g2fmqz6 )2r)uouqx f only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisyof1t)xmmwj3( uqi -6m jet engines is experiencing a sound level bordering on pain, 120 dB. What sou1tm-j3 )f uimm6x oq(wnd level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-ne;:uf pm68m -w:e 6e .zaqs.av.zn tfnoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background .:wqz-t f8. ume .:a6em;evp6ansnfznoise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from w*cou924j 6 2pjtxqqda person speaking in normal conversation. Use Tdq4q62u jwp*2t cj ox9able 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 ear m-66s5c-7h ae ; edk s34vzff5ppcdicdrum 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 the 8* pkgo+lev,6 r-p bunmore modest amplifier B is rated at 40 W. (a) Estimate tep6 v+*,kop nbg8-ulrhe sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dByu 2vujj- t )id0cb0)o when placed 2.8 m in front of a loub 0-2uo0utdi vj y))cjdspeaker 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 difference in sound leq 6,rutiq::rb vt;r:u vel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Sectt;:rvbuq ,rt 6q u::irion 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factos. a 0z)z/dv nqarjk0m l,*id*r will the intensity increase? Increase by a factor o* /l.kazz0iqn 0 ,)*sda rjvdmf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice theix;3gk3,bdcsf*v d9emsv ; ,c frequency of the ocdc gi; f33ds;v m,vxe,b*9skther. What is the ratio of their intensities?   

  What would be the sound level (in dB) o+b:c/xrwqu z- f a sound wave in air that corresponds to a displacemcu +q/b :wz-rxent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loudu;zp grbv(- +2rlyr6 r as a 100-Hz tone that has a 50-dB sound level? (Sev pgrbryr;-+2u6l( rz e Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can de; gtat n2wc7wa o,d60inj 9n6ntect when the sound lat wc9nwo,nntan7 g2;i d066jevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound doj rtp(i:d a a5y05rgm1 wu85levels. What is the ratio of highest to lowest intenta5185ri w:d0p mjgradyuo(5 sity 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 l3/qcb5bb 2 ezoength of the vibrating portion is 5 /e32boqbcb z32 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 aud3j7d:7vq et biible overtones ivdi 3:ebtqj77f 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 would you expect from b/(a1ykdqv7u cz+o ud7 lowing across the top of an empty soda bottle that is 18 cm d7a u (o1y qkvdudcz+7/eep, 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-tubetioh8 /v(wy)xdq,z0se dtu -;zp (q1d pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requuyz,81q /()s- wqtx(t0e i hzdd ;podvired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 b2e me(*;vn h/w)g2u oe ptx.lHz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originaou tm wvh2;2b nple).ege(*x/l length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abo:avhqa h.)vv*a gte (w(4j*grm i :+tlve middle C (33t: *v+h*g) vtaeg( a ajl4rh:wm. vqi(0 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 that3 a vk zj,)q7cplge8 js)1lg1oiojz:) emits middle C (262 Hz) when the tempzi 8ecvg7 ) )pogsj j aj),:q1ozkll13erature 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 83oydolh d27nppc7+ lat 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 them22en i *;hjie hole be that must be uncovered to play D above m 2e ijen;2*himiddle 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, -oj eya(i3z 52da)fypand 616 Hz, but not at any other frequencies ina5-)2 p(jfoeaiyydz 3 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 resonates at two s,8melt +o*e rd:bah* vuccessive harmonics of frequencies 275 Hz and 330 Hz. What is 8 e*d*roe ,+atv:hmbl
(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 kx k a)f/-nmn3$^{\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 yl96gbvjt9 9a7ncv es+2k; kxpresent within the audible range for a 2.14-m-long organ pipe at 2bc g+v299ykn;jk6 xa7 stevl90 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to pe*ea3:tm8qs q+s :q vthe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Figma*sq+ qeq pt v3s:e8:. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears ofsu6;bl0rn;a, 0w s)5a- xx:kv wg:utkw 5ifpne beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far iux ;wt05lkf: u5s a,ksvg :xfw- pn)0awbr;6off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) es* ktji rui4;dhiw /io+2m62w v (c,iand $C^＃$ (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, whileu60tft t9; syy.0km dr another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when 0 .ut 0 s;try9myt6dkfplayed 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 so k unx;x7tnf9c/ z28keunded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Wc7n 2/en9ktxkxz fu8;hat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tune m*xy fxlmmd7 4dj9y7o )(w5bnd to the same frequency, 294 Hz. The tension in one string is then decreased bj l 7m)7xwdxy 4yn9fd bo(m5m*y 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 heard if two identical flutes each try to play middle,fb 5m:dw evczj6*dd +.q gq,k4h8sp q C (262 Hz), but one i+v4d*k pzs5,6fqecqjd, gb m8.d hw: qs at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequek(2:;b2c.ds 8bkv8 ynnge wvrncy 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 vbyk8 n2ecn.:b;w8 2 sgkdrv(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 stands 3.00 m from one spead6 +u0rtes/ j2)fyziyik0rzh s9 nf-2 ker and 3.50 m frzfdr+/ kyy t0rfn0h z6)uss-ej 29i2i om 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 supposed to be vibrating at 132 Hi myk-iv6u+: .dw;y pgz, 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 must be the frequency of tvy+- pyud.i:w g;k6imhe 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 wavelen y ,c oi2dkr,,bdflss)wv17 )xgths 2.64 m and 2.76 m in air. How many beats per second will be hear crf,wdv7s 1dy2i),b),kslo xd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequwro*2ppr ga mz67 gps)6x6t6 yn tnr6zd-l3e+ency of a certain fire engine’s siren is 1550 Hz when at rest+r x r6 n-wmzldt* y6ngzr)67p66tapg2o3pse. What frequency do 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. Wha(aiy cizt) 0-:quny4p t frequency do you detect if a fire engine whose siren eaizcq4un )yy0(pi -:t mits 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 moh4b )40czza ttving toward you at 15 m/s versus you movingzb4ac0h)z4 t t 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 one is aav ./ig6c z4xnz-+oqd-z /c ygt rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of .aodg/c6z czi-gv q+x- /ynz4 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.mdq6f.9au6 kl8 ck8i /hykwc/j2w 01vgd,boa0 kHz and receives them returned from an object moving directly away from it at 25 m/s Whatl1 u8mddg9if,8a/wc qhw 2 bk6jko 6/0c vk.ay is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a ncg:2m fqf7g0a0l g1 cspeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequ01mf2g07gca q f gl:ncency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler e)d7v+izpbmlm0t7p m gv/6jhc .*axc :xperiments, a tuba was played on a moving flat trainizj+mdclt6 gm .*0 bamp/vpc7:hv 7x) car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wa0zz95 jl8ydl rves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the s l9jyz d805rzlpeed 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 from the sound source?   Hz

  The Doppler effect usi1rhw i/uke( - j90pzc/c1soseng ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequencz krwx8ia5wey0k4mv1-0 5f jey 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are loca10x-rj8w wme4 ea kf0zkiv5 y5ted, 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 if its speed at 2a++e o gr z6m-iwh81ii0 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/ :uel ,*noche8s (a) What is the angle the shock wave makes with the direc*heecnl o,8 u:tion 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 where the spee )7e p5;zzqgald of sound is z;qple zag7) 5only 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 og la(h:7-kn:c irl:zf 1gax8the ocean. Determine the shock wave angle it produchg: oilk8:c n(:a17gr alz-xf es
(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 z 8 xy6t x;nce0o-)w1(x puhsv$/theta$ 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 ground cu1 mc on(v 6i5o*.cptflying faster than the speed of sound. By t mv p*. 1o(u5cico6ncthe time you hear 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 sonar devicesa 7+tbg6lda. that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimu7+d as6g.ltb am time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human aud4x uco5is+1/n 9 jihqeible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a dispevu gnof)k3 :h :,g4jalay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whicu f3: v 4,noae:)jkgghh 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 npt2zbh- *1sl a person makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such*t ph1l2b- zns mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 8wqx7ezb*f 6 )sfdo66 z7-dB sound are heaqf*e76f od zz)66sxw brd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. What ipk l(u+hnhit9t ) p /ehf2xu,/s the acoustic power output (W) of the speaker, assu ipthe2//h (fx)t+khu u,ln9p ming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W ou f vj0zb*dxrc4(/pdj v*;d8js1 zs tq;tput at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 k0z8d( st;dsv */ dj r4fx*qvcj1 bpjz;Hz?    dB

  Workers around jet aircraft typically wear protecti(x04 7.o a2jih 3qmbtisz2k r;qx8e eive 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 effec ii08r .;qaiko(3jb eqsz2e m472txxhtive radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatio(iw9kwb tu 1u8ns 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 frebmcgf9oq m 7. .6gov,b7j4mw pquency 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 iv,e. 4e;rm-8 /bbk6xu9w6x lttsynpas 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length of tbaty wsxxu6v6lpm r .-/8ebe9n4 k,;$6.1 \times10^{-4 }$ 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 vibrati .(8 jvdlhbed8on 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 fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency jbl8.(edvh8d of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near atdy3z ,v a-a6 v3j:.adwwo)wx 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 re , y-t6z3vajaowv d.3xwd:a)wsonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fwmza/*1ue ,;v/hdbu7)s itzlull loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sou)cd; r opnw6u4rces. The sound is loudest ao6;ur 4n) pwcdt 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 conductor on .)(zkm-ymgzs the stationary traigz kyzm(m-s .)n hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 53uia/ tp;xrcs (2 i)(tl8 Hz. After it passes you, its frequp;cti/ux( 2)s (iartlency 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 blkk6vtpb pj qkh)devs.(3 :o0 oz*0v,y listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it go: tj6h*p (dzkbpk) 0e 3vlvkv0oq,os.es by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding s 1gyqpm k6wkn4ze1x6+ ep;i5together, produce a beat frequency of 11 Hz. The shok 6 i;+empzp41ng1s6 y qwxk5erter one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pm q3ph,tja bo(z+/n z,ast 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 thtqj + /hzpmab,,on z3(e position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally1d bjwb7*npb; 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 red blood celljb w1db7p*;bn s? 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 irtf 1-0)u ,l deka,d2*xqulshs flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz.rxdqsatfkl) 2u-l0,u ,* h1de 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 itd9 23jyphwh(b*pw6e rlqud zy 3g1+iuo e+ a,, approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 p*2 dup(yji1u z +w6r wley,geho9q,d+3 3ahb 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 tz28n )h9nikw. 12–38) was once used to 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 nkh28wni )z9t be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo x.uot4w4f 64++ e wb 7eeohcxxlistening can be compromised 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 frequencies for 6et e44u fbx+4h x7oc xww+.oethe standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a lonm2 ewo oa21kw-g, 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 can be made to “sing,” or emit a clear, loud, ringing mw-o2 o2kae1wsound. 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 frequency of(/n2zmistv,-aj wgz a 2o9c0 m about 1ot mc2naz 2mv-s ajg,0w9 (z/i000 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 observ2xkzkt .:u+wper on the ground hears the sonic boom 1.5 min after the pwzukx: pk +t.2lane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 *0 srzr4-mrxg$^{\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