What is the evidence t n .xb2i/ nzh6)wfm uk9bti7,phat sound travels as a wave?

What is the evidence that sound iswg q/0hdx8f,wmuj rp,j 5.rl6k8/;yv-i jjw s a form of energy?

Children sometimes play with a homemade “telei nyppi413uf +hihr94phone” 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 i9yh1fippu4h +3 ri4 nheard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passeszhe ft6 eq)l9,i1qbx 9:6f dco from air into water, do you expect the frequency or wavelength to chang9q: l6tfhoebi ,9)zq fc16dx ee?

What evidence can you give that the speed of sound in ax 18m 8 yivf.vw6ptu:mir does not depend significantly on mp8m86v i: yvuxw1f.t frequency?

The voice of a person who has inhaled helium sounds very hi b t8+,gsvm rt)uhgq856n5ctagh-pitched. Why?

How will the air temperature in a room affect the pitch ou hm2;sn oq8rt. 3vt2qf organ pipes?

Explain how a tube might be used as a filter to reduce the amdz8qc9 n 0s2m7zpa+l pplitude of sounds in various frequency ranges. (Anlm pqpa +zn72z980 sdc example is a car muffler.)

Why are the frets on a guitar (F h bo* +k50un83cmeaf 4niqop:ig. 12–30) spaced closer together as you move up the fingerboard toward the brq+hibf3e *nm0 :aonku 548opcidge?

A noisy truck approaches you from behind a building. Initially you h0(:2vw;h dspr wc(atp xl*wmg /d36xa ear 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 no;w:26c/ w xd v (rmgsw(x dp*pht3laa0ise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bemwim;y mm-l6 d88 oz+mivgk ,;ats cak+dg8m;i -vz8oiwl;y,m mmm6n be said to be due to “interference in time.” Explain.

In Fig. 12–16, if th-0r)ohev z:0ago nb;4jl amo1e frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or :gro4ah0mvb)-ao jo01 zn le;closer together?

Traditional methods of protecting the hearing of people who word +i6bxf93c lr rswce9q*0gs4k 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 h3qcrbl9rx06 +* 4dcfgsi ew 9seadphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a sdz2j kw)el5x -v,kp7superposition of two sound waves with slightly different frequencies, 7)ks ewjxp-vdl5 2zk, 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 and 8 gx1)+s d8bmzjdtwv. j(d 7of7dqy.aobserver move in the same direction, fxo ba7w(.djvd s 8 qd.+)z17 j8tdygmwith the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by an/f*pc tn0ag+ person at rest with respect to the source? Is the wavelength or veloci/ncp nf +0at*gty changed?

Figure 12–32 shows various positn y53 9v voepb+1 4 7tnhcf)w1)gmipiuions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on t5w yp7v4mh1g+tfu) iv n3o) 1nipb9eche 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 of her shout bh5,+/ti ozyq reflected by a clbt,z q5i+/ hyoiff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterlinob0uw, - p ko +wtcn9usp(;rn pf87e,me. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. 0 p e o7ckfs w-mwp98(rbo,nupu;, n+tHow 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 wavelj /00w4o.khbuahw,c(t 8pjz fengths in 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.c ijcj l2o(tb .)oa):jkqmv2ox +mo7 on a foggy day. Without warning, an engine backfire occurs on another boat 1 jokcovxm jt:7olq()bc + 2.oj)i2 a.m.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliffp2 k e s9dcuxxc8d;+ma czpbi6-z:6.r. The splash it makes when striking the water below is heard 3.5 s later. How high is the;um .x66kd+c c9eiaxb28pzc :d-zrp s cliff?    m

  A person, with his ear to the ground, sees a huge stone strik6rm-1 / jr nta*p6yrb/gjtfh+e the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they jm/ay/r+bhf rpj1t*6 6rntg- are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made oveq ) (xj+7hc7ud+lf6z0 uxnhbk r one mile of distance by the “5-second rule lqf (7c0x ukzj xhn)+h6du7b+” for estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity ofj; )xs9kqbebq .gk0w nin 1d;2 a 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 whosez-*mk sx*wwt1 r ape*gx: l:-j intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslygm ob:t xss gvmih1 okb/+85)/cgo h2( at a certain place, what willb2h/cgm)t b1om go:h8 +x 5(/vgkoi ss 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 with four equally noisy jl;bzoil2g5 a +t-j(. / sasqtset en-il25tatz/ja+sgb q (;s.o slgines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to h*p ,m,q v nx*a-m .qkigln/7gsave a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the backgr*igq/nm *g vqnaxs.-,,l7 mpkound noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spcb)dtp 7(2nlseaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centsplc 2d(n7 b)tered 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 whb z7) pqip(do3ltc( 6vose 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 i7lbd bk0nx /7zs rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in dec0 nx77/zkblbd ibels 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 regist/*t9(b5x vvn dyro0overed 130 dB when placed 2.8 m in front of a loudspeaker on t tno(9d5v v/b*yxro0 vhe 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 dif8*xfdhqp.xcoxa91 okp kx.6( 33usu pference in sound level of 2.0 dB. What is the ratio of the hd.(8xpk*u3 1a x.pqopfc9u xko 3s6xamplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what fa.mwnl/-ae z(t dnf16cctor will the intensity increase? Increase by a facto m(fcn. -1nazlet6wd/r of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tw98nzhp6 a v0nixb v8.nice the frequency of the other. What is the ratio a0i8pxhn 8nvzn9 b6v.of their intensities?   

  What would be the sound level (in dB) ofxd)+h6ptr0e ys m1d+td jip(4o9 xqz. a sound wave in air that corresponds to a dis()tdm i0 x+t469zej. x+pqydd p1or hsplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound di26wsol .lo3level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) oow2ls3 l6. di   dB

What are the lowest and highest frequencies sk 43yzi8ma -pi,3 o( hn:qalzthat an ear can detect when the sound level is 30 dB?a34miszq(ni p, lk8y 3:oaz-h (See Fig. 12–6.)

  Your auditory system can accommodate a huge rangiuce2 + c:l9xnm +o6oue of sound levels. What is the ratio of highest to lowest intexlu2oci+emo +6n:cu9nsity 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 fwd k8te )uls*y1h* me:requency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under u8ee*hwmt1yl:s*k) d what tension must the string be placed?    N

  An organ pipe is 112 cm long. What arx: kvn tns6)9dv4z ;mie the fundamental and first three audible o)64xn:nks mdv 9;ztivvertones 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 would you expect from blowing across , zos*1fbuv;)spy b) a*pfi1rthe top of an empty soda bottle that is 18 cm deep, if you assumed it szfbo*a )1 r1pb v upsiyf,*;)was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanni(2z,8 8nba 5zwxh ihpkng the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pip h8 (a8zkb52hz,win pxes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string ,)7.el- pwk6g hfa(cm wstp:nhas a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its originalg)wk mnh-, c sf:p7.t (pl6eaw length?   Hz

  An unfingered guitar string is 0.73 m long and eor 3(u fd- sv 8szl+tfmc-s7/is tuned to play E above middle C (330 Huf7lc8rs so +-dzmt-(s v3/e fz).
(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 zno 3zrkesel,y7v7 e *n223a7 j1ejjqan open organ pipe that emits middle C (262 Hz) when the terey e7*7ls2 a21e3jze v,ojnn q3z7jkmperature 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 a *0nejn: x-zvq:*wgqy t 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 Examples-kbx9 xlh 5)u 12–10 should the hole be that must be uncovered to play D above middle ubs- 5l9k) hxxC 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,hk f3k4 yrl1(f vcng1, but not at any other freqf4n1kgvr(hlfk1yc 3,uencies 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.4 0qltxj *qh4 umhxk5er r:y- qp2:g/l It resonates at two successive harmonics of frequencies 275 Hz ayhh rl gpq j:54q/042kx q:teuxrl-*mnd 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 6:pd.aasdn j. 5ql-q qwdv +4z$^{\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-longre9(2 npf stw :k48bux7/okst organ pipe at 2 o2bfk7w nkr:x/( 48tp9utess0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lon.eymhs2ts anc* 1fn 37g. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Figh1f7e3m s *tsnan.yc2. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two sth . /(syuqs7mmrings, one of which is sounding 440 Hz. How far off in frequency is the ot7q mh(/suyms. her string? ±    Hz

  What is the beat frequency if middle Cek k13*s2zjc t (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 kHz, while another (brand X) operates at ur+ jf.nl5u 0 fbj.a;ylwx /6lan unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency .lj b/xruf+;l06nay lu.wf j55000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when souni,ih5lgg4k 8pvg+ .fd ded with a 350-Hz tuning fork and 9 b +i 8 kid4vgfh,pg.lg5eats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same pm lt7t2 w 0uus4(tk:dt rpn44w,kcpe72m j+ lfrequency, 294 Hz. The tension in one strlpj7d(t4rwp7em 0t nlk tckt+u4s2m4 upw,2: ing is then decreased 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 heard if two identical flutelb7 htoe6ua :nd6 ,8wus each try to play middle C (262 Hz) ht6nud:7w eo,ab6ul8, but one is 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 frequency of 441 Hj9daot zm-5*2 qigid- ya68 svz; when A and B are sounded together, a beat frequency of 3 Hz is heard. Wdv2 qoydamai- 6j9*58stz-g ihen 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 s+i wdb(v ea4u1hqp1qs.z 67sftands 3.00 m from one speaker and 3.50 m wusq.q 4s1zbhdevip (f1 +a 67from 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 Hz, but a piano tuner h: -a9yz0( xz7mf xlygsears three beats every 2.0 s when they are played together. (a) If one is vibratixg-0xmafl 7szy(: z y9ng 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 i:fl9m (dx;ft drhv7k0n air. How many beats per second will be hea(hf:krf ;lvxt7d m90drd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when atiyxr8g k ;cx*q72yo 0d rest. What frequency dg k72ic* y r;oxq0xd8yo 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. What frequency do you det9 v2jdwu .g(pqect if a fire engine whose siren emits at 1550 Hz gw j(9u. pdv2qmoves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving v d- 0zcj6lhej.5 (v7e;hvjcwtoward you at 15 m/s versus you moving towardjvc 0 jw vc-h;e67 (h.l5jvezd 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 hor pk1xga8* dev8n. When one is at rest and the other is movingx8 g*ve1a pdk8 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 out p.c 98e+./w6iiovpdpop rv .) xssj4v ultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequencv)rp8 .pdo+ vix ov.pwsjc4p /9s.i e6y?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 -fvu8 9pjl6ex*2eqf p m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30e6*q - pejv8l2p9ffxu.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, o*vj)smh ra)vi 1os*uw -m jc313go7 pa 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 approached the station at a speed of 10 m/s oa sm1* mwprjvg -7js vu )*c31hooi3)?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloo aq(-w) ax+7( w5xs/pdznbvocd-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 frequewndxvwz(5c /a (7asbx-)+pqoncy if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect usingyli 9mp/ bhf6p z8p6.j 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 frequency 570 Hz. When 4 nv1: n+f6 iufkaheg,:wd/ggthe wind velocity is 12 m/s from the north, what frequency will observers hear who ar gni f f4nagge::k1vh,du 6/w+e 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 if its speed a d8ayofml -3mcbw4,ns 8mxn27t 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) Whatzi361kj2 n uo;f0irzv is th3 zk;i zn0i12ovf6ru je angle the shock 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 atmosphhv5t88 ); k jd7xgpzqzklg1. r3 u.zajere of a planet where the speed of sound is only about 35 m/;g8 ktvzj.3rja kz u.zx 78 p)dq1l5ghs
(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 wave (7eo5gf 3 a;zmjn0uu m;sbts2angle m5f ge7us2( o am0zt sbuj;3;nit produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle bv .x+0 eaxi v812u5cwmod( cy$/theta$ 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 grt4cee kunt3+ z -vm*;mound flying faster than the speed of sound. By the time you hear the sonic boom, the te u+;mcv3ntzmk-*4e 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 device that sends 20,000-Hz soup /ypbqob *e4y8.db t3nd pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for w8edp. yb* bp4q/o 3tbyhich it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves ar3at 5-y+ca djee there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of many 3kc .u/bw)klj plastic pipes of various lengths, whlwbkk / u3).cjich 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 thrc2,mfsi354 bunf gb btb jb-8qhzn- ,6eshold of human hearing (0 dB). What wi 8tz um4g j2h nb-f53,qb6n,bs-bficb ll be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an .k75 uy9lnm1r otn .mn82-dB sound and an 87-dB sound are heard simultaneouslrn n5m.1u79 n kolmy.ty?    dB

  The sound level 12.0 m from a lojvnvn. 1pr *1fmpo:0rudspeaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiat0*v n rrmp:n 11opfjv.es equally in all directions?    W

  A stereo amplifier is rated atq/ja ywo61 ; hhrs8z dir12fi; 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the pow; r/sh 6yzdhi1jir 81o2 a;qfwer output in watts at 15 kHz?    dB

  Workers around jet aircraft tyq/zh jznjfwn-3mwy; ol *) ..fpically 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 tjowjmf*-h3f/ q y .znnzwl.;)he power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatiouv;y u96zjf gs p4ax.n w(eo:))xtsw-ns 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 tv,efp: tk:h f2ni ,n9s5d8 yatuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with al0n)k vf,pv4m fundamental frequency of 440 Hz and a mass per unit length olmnv 0 4kfpv),f $6.1 \times10^{-4 }$ 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 fils*. kpvlqrp8 ao:-3ft 1dv7sd led 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 0.395v:1pk- a*l 7rs38f.dpdtqsv o m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g f:v+rd)xnbw5is near a tube that is open at one end and also 75 cm long. How much tension should v xw+:b5dr)nfbe in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fulldhp(g06z 7kr m 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)oy/2*w/ci t 7x ep/0opys:y:x6fcf )xfnfjt sources. The sound is loudest at points equidistant from the two sources. To detp x:2:/) /jyffo o6t7*cs xex/cff 0nwypity)ermine 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 statiog7b4(f0votyj 3z ipbw-w3 t9z nary. The conductor on the stationary train hears aiztw7bt3 jo(v4p 0f -z3 9ybgw 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 psx /(vx wnh2/is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movinw /sxh nv(p/x2g (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just x5:hzbr7s:9e13 zm u6r8 tre4hrsle uc1nl)h by listening to the differenc:blh r1hr)l r 1usze7tzehnu3e xm9r:s84 56ce 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 goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, proahx 5wv91*40by ybz kwduce a beat frequency of 11 Hz. The shorter one is 2.*54xwbw ah 9vybkz0y140 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad s5f+qwyj7 - z 0avc.jwcar as it moves past a statis 0fvaj -w.yz7qw+c j5onary 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 passed him, at C?

  If the velocity of blood flow in the anmc c;r n2mjsy2it8-/orta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? 8tc 2mcr2/ynm jis-n; 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 md)1h pt3cjbn* /s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency oth3bdj )cnp* 1f 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 it approaches a moth9z(59lrp jkkyaid 5 s5. The pulses are approximately 70.0 ms apart, and each isdki5(jrsk9ayz5 pl 9 5 about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. c:ke*uq3z:./ uiskp b12–38) 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 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, anepu u:3kkb i:/q z*.scd which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the prestwajfpy 5;2)0nshm2b ence 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 the standing waves in this ramfsy)j h 2wtnp;0b2 5oom.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendevw3e0hod 1 r8p)xxzg8r aluminum rod held in the harv 318oexhgz)8p0xd wnd 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 thres0qbpd .c - qk8r+mzr,dhold of hearing for the human ear at a frequency of about 1000 Hz is crdzrm8q p.db0,+kq-$I_0$ = $1 \times10^{12 } W / m^2$ 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 heae **pk h+3ofjars the sonic boom 1.5 min after the plane passes dkf+*hap oje3 *irectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa/5sg uls9 o7tgs,i:n7c7c4iod j jw*st is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h