What is the evidence t qxr m+dn6c7b7tj)(x b7;l ifnhat sound travels as a wave?

What is the evidence that sound is a formk tp1, twhvc78h3e8kb of energy?

Children sometimes play with a homeq7 lwy q1+s+/tlmto-fmade “telephone” by attaching a string to the bottoms of two paper cup l-qw+mtl/ s7yt1o+q fs. 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 n.)vyxf+6/w1 y8 y g i4bevkmsfrom air into water, do you expect the frequency or waveleng4evksy6b8g niyw+xv .f1y/ )mth to change?

What evidence can you give that the speed of sound ibp: 3 io3ohw5rn air does not depend significantly on freque5 hwoo3:pir3 bncy?

The voice of a person who has inhaled helium sounds very high-pitc q2x .tz f39 /xo7vr;wdy7bptqhed. Why?

How will the air temperature in a room affect the pi:8slv5i3 qoinwj7x 4..y bjfmtch of organ pipes?

Explain how a tube might be us+1f697 dk/yrheb( x rry don7;onquf. ed as a filter to reduce the amplitude of sounds in various frequency ranges7e7nr(d. qo6+9;xdrkffybh y/orn 1 u . (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) ip+ *r1nposuz9oy0;dk , mp*x spaced closer together as you move up the fingy k p s1i*x0mzno*p d;r9+,puoerboard toward the bridge?

A noisy truck approaches you from behind a building. Initiau;rxu; (vr(m7 k4nudally you hear it but cannot see it. When it emerges and ndmr( ; r7xuavu;4uk(you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to beaf ifd) a.k;rb4i6 *rd due to “interference in space,” whereas beats can be said to be due to “interfereiafkb 4)i*r .;d6arf dnce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, o6* ib-ig sqp.x; ke1qwould the points D and C (where destruex-q;ois61 pkg.*b qi ctive and constructive interference occur) move farther apart or closer together?

Traditional methods of protec8ldi,r:yov5l ting the hearing of people who work in areas with very high noise levels have consisted mainly of efd ol :8,lyiv5rforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a s-q75/ - mtqnb,n5i msd8toyrhuperposition 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 q/ts,85m-riydmon t7 qh5 -nbapart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direc i:r tk25b zk:qmr(i r/dpy/2)ziay3 n-pnk :ation, wiy3k:n(- k:ytpira:)d/qzbr2i 2 n iazpmr k/ 5th the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound hear l*r* ehvwm7b7k;u9ijd by a person at rest with respe* lm b7ev ;hiku*jr97wct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various k0 : .wj8dttcyla2xkco,n3*k positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Exp0tkd*nloay. w cc8j,x2 k3:tk lain your reasoning.

  A hiker determines the length of a lake byh++0 q0.cabh/ukgu*+m nka be listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echoh + .+euhumb *k /a0gqn+bk0ca 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side o0fy1;oxb(nv,zrp o 8of his ship just 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 deptvox8o( fz1;b, yp0ron h.    $ \times10^{ 3}$m

  (a) Calculate the wavelez2psm:/z4ea t ngths 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 on a foggy dxsn3n/5fw .po ay. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much timxw5/ no .3pfnse 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 3;q,y )oy)st :yvxkqh. The splash it makes when striking the water below is heard 3.5 s later. Howyh)sy qx ;:yv 3)qk,to high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concren-g)s;6 bi ntute pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Tabngs-6 b);tiu nle 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percen2) dcrx-4ve)skcfv* gc+f4 vat error made over one mile of distance by the “5-second rule” for fe cc2xavk4vf* g)4d+rc) -svestimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soj.oz5z wa(5evp( j3 ,g isygb1und 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 wu;wfnk qz3i6ei8b81q hose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firedmw ii:w2sa/ot+8. meb *ztkygo;2 l r* simultaneously at a cerz22we/w imo*ak. g8+t ib;y:*ls rt omtain 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 with four equalllm(1gh*fgf.w y noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? *ml gg.f1whf([Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise rati(gppc3;ttb6 +/k hho zo of 58 dB, whereas for a CD player it is 95 dB. Wha/ 6g k(po+bhzth c3;ptt is the ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sounwhm 52dq06fmhi;uslpahou5z) b/v;0d from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly un/ )6wl;5b5 ip sd au hzf2vh0m0;uhqmoiformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose aybn*.*tgt*2uupb0xw x ubo.;rea 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 m k(xexoi- . )5rqft zy kgpkqkz96-98wore modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn tkq kwg ixp - ot99)5- krek(z.zyx8f6qo each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB whe1qvpizah 9 (oisa;+tns);* gnu;t si 0n placed 2.8 m in front of a loudspeaker on the stage*voa 9i 0ans );sp g h(+qu1ntii;;stz.
(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 le4 *ukm 2sol:wctu1ej/p*, ;sktke1vv vel of 2.0 dB. What is the rati;w 1spotmc2v*u 1kt/ j:k*lev4s keu ,o of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intenf2o*/ h53ky.wnbtebe 0; wept sity increase? Increase by a w* pbw03;.y5behntokfe2e /tfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal 4y jde2/+xa ojdisplacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intens+xyea2j 4/oj dities?   

  What would be the sound level (in dB) of a shc+z )6 1f w7guma 7kgsirt8;gound wave in air that corresponds to a displacement atarkg)s7+ z;f gu c1wg6h 7i8mmplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sgk9;u r pdc p*88os*ceound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.) gpsk*8;9* 8uedr ccop   dB

What are the lowest and highest frequencies thae 1(f:pk) ohtnxdzge-1*r 0e at an ear can detect when the sound level is 30 dB? (See Fig. 12–10)oxn*hr-p1etg z kf : aeed(6.)

  Your auditory system can accomdn0*k7 ilg 3dqmodate a huge range of sound levels. What is the ratio of highest to lowest i ndkgiq*30 7ldntensity 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 len dwwx.q.-z b2xgth of the vibrating portion is 32 xx-.qdb wz2 .wcm, 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 threeka;s u2vnit6ppl s 0; xq71p0o audible overtones if s;2kipslpt6;uqx0p0 a7von1the 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 t;lrqm)m rmvcw00 /a: whe top of an empty soda bottle that is 18 cm deep, if you assumed it was )mrva/wl0rq c0mm:w;a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the6 c*1zzrv9nz:)xqp r d range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of r*pzxc nr z q9:v6)1zdpipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fr0)dlu3v ,v ejno k :4kqvp))laequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length pqvl) l0kkvj a)dv4u ):,oen3of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and i6 8pa5ffwmw lwu-pq 8*s tuned to play E above middle C (330 Hz). mupwp ff8-*58lwqw a6
(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 d7d; cb*w;s shof an open organ pipe that emits middle C (262 Hz) when the temperature is 21 ;hcd*w 7s;d sb$^{\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 n s5uh8l994pl2w;ofs.bf uhwat 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 the hole be t/bvo lsl om0h-5bwf v(oz*32k hat must be uncovered to play D above middle C at bll*b2ofw-5skhvoo v 0z (/m3 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 zk 4lu7q+av.h gtdv14 at 264 Hz, 440 Hz, and 616 Hz, but not at an z vl.ua1 4k7hgv4t+qdy other frequencies 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)ip4m b e*j 2po *95hrm arc*cbl5l1nm ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What is ljlh2oice)5 *b*p rmam9bn 5*4mp1c r
(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 x0z3hv b jdr g5s*88i hyrp/)g$^{\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 pr aqan:t,nq0.3eaj d+d esent within the audible range for a 2.14-m-long organ pipeajtq3da: ,+ena d0 .nq at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm opxjhrao5 )per83c6kxe 8d,3 long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in th3rpk536j8 r , 8de)hocxpoex ae graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust tf10y1 -ocfsb fwo strings, one of which is sounding 440 Hz. How far off in frequency is the ot11yff o0cf s-bher string? ±    Hz

  What is the beat frequency if 7ubmhqbayvpn-ko1u5 6/70e q middle 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 kHz, while ap4 h89;akn/bh5f vk2 jkn3as pk6wi7k nother (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played sepwka5pnk/k 397pvinh s68k;4 fbjka2 h arately, 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 sbw7 9)l ziu as6rl7xc.ounded with a 350-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 reasoning. uxb7a 7w.sicl96 )zrl   Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The*4wn2iw:2ruw (xis l d tension in one string is then decreased by 2.0%. What 2nxdu(4*isrwi:l2 w w will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heawmrke05vfr9 :c07j p2f) x4nqp : wtjfrd if two identical flutes each try to play middle C (262 Hz), but onk54wf) cfwj:9xptr:jq m7nrf vp00 2 ee 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 Hz; s tp /upk27o,ewhen A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togo/sk , pt7upe2ether, 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 d-drh3,c a2eir 1n/)hbq.we l 1.80 m apart. A person stands 3.00 m from one speaker and 3.50 m fb1dahw el,r)ir-hce q/.d3n 2rom 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 vivb*z*,5(resasq x xj;brating at 132 Hz, but a piano tuner hears threbrq 5a;, *z*ex(sjxsve beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengt lvkvid5t b tr)h29wids a+44)p +qqo,hs 2.64 m and 2.76 m in air. How many beats per second will be heard? ( ,rpaisvqkbld49 vh)d5ti24+qot )w +Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fuy-:0cc9k ht(uw3 :sm4phcp l ire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/sc swk4hccu:m9lp-h 3:0 uy(tp
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine se n-9) ;r srm 9h:t)w2memttnwhose siren emits at 1550hrwsm) 9:;2nnrm9e )mtetts- Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towardzuir. +idhcry 5 vl8.cq8 i*u: you at 15 m/s versus you moving toward it at 15 m lr+yi.8*di5c 8qurh:.iuzvc/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 lpfv +t-ihb)1 frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? t1)fbvh+pi -l Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounxo5 +9oieah3vedntc4oa8nmi0n a2 mu(/;ok *d waves at 50.0 kHz and receives them returned from an object moving directly a x /5aakm+2ie3neinv oac uth 4o8on;90*om(d way 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 2.:v 0poq .tikqw9byi it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wayk.v0qwi:p.9 qboi 2tve?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was playedbt4 tz8 4tp j/kl(9v3el v1tfq 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 wl19tlt(4t8 ztfvb4k/j3vp eqas heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure bloodnzjvy()p7ai,gs j,yi ;p:r) i-flow speeds. Suppose the device emits sound at 3.5 MHz, an) p gay:;siij),,z vrj(pi n7yd 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 from the sound source?   Hz

  The Doppler effect using ultrasoni5 ps2-i( pzkekow is vsh:p(x3bd6t/ 3c 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 is 12r9rg3;wwk8f4c wfxau hpai +, /duf, 5 m/s from the north, what frequenrh;gkf/ rc4+9 i ,awp,wa uw8fxf5u d3cy will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at 26c 8l(lrug*pw j0ai1q 0 $^{\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 s2bab4b: ( h kny ng1n12e;eqfypeed of sound is 310 m/s (a) What is the angle the shock wave makes with the 4nk :ebqf;ygbn1 h21ba(e ny2direction 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 c,*p2.6sw (ddy0 mgqpy z7yomthin atmosphere of a planet where the speed of sound is only * pcmqw7yys 2z(d ,6goym0p.d 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 83 lif4/t: -filmou7pw:ahci7 500 m/s strikes the ocean. Determine the shock wave angle it produces3h4m/i7uc- pi:if a 7 :olfwlt
(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 s*)ni *v9 qcmb0z( pck$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and hau*w8h, i lqc;cfg34see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane hi,g qlc8 34*hwu;hafcas 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 sound pulses downward fh novh r7h gzsftwp3*/oj1pl+s9/ +s4rom the bottom of the boa1h /fo7z sl+jwpvph/39t soshn 4 *+rgt, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in therk j0 s 2-sbkkvuqe6/p8.y;kp human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It 5,:txpn6cs7i1igldo4 q 0z smconsists of many plastic pipes of various lenqsxli6dt,4oi5gz0s n1 : p7cmgths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes2utei+0 ,vhyufq0o ;v a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 suciu,2u;y 0h+ft evvoq 0h mosquitoes?    dB

  What is the resultant sound level when an 8m ujkji5 .q 4qv rl+p1h64t(wo2-dB sound and an 87-dB sound are heard si(q.ouqtkr6+5 hl1mj jvp w 44imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placckfc.d: mib m)qmd:c6-g6t 3ked in the open, is 105 dB. What is the acoustii.dm gtqc 6d:fccmk- 36:m)kb c power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outputh56js yfv--uq drops by 10 dB atu-5j6-hs fqy v 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typ-1,l h5iyoyvtchsl3je x+ 46kically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected x4k5 v- 3hi1je y +c6y,tollshear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications f c)/wch2ea4km,p 6s n1y *bugsystems, 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 ffsa 6x/bm5odlu :ne4 8requency 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 cbo45h9r 9ru/ us9j vhym long between fixed points with a fundamental freq rs/j9 h5b9hoyu4 vr9uuency of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a 0oloqvs/pu-) jo pn m: x8d:2qvertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, t8od :o v0lqs2op:-uxjq n) /pmhe 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 of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one qowz/w: ;lnd1end and also 75 cm long. How much tension should be in the stringqw;:l 1d o/wnz 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 resonauiw fi9l2;bat:t6 g q-te 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 thu2dep3v)y h jgx(a u+0e 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 thg 3ph+ auvdy2x u)(0jee 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 conductorlze-k k)ms*ju4z 9pb5owwyd:3jph :1 on the stationary train hears a 3.0-Hz beat frequency when the other train oj3ze)zp:91* p4k:ul m hdbws wj-5k yapproaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle n0px( ,j t:pocas it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How:npoc j(0,tpx fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars ju6jvodt kzg9a7 - oah59st by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops bya h-d z7jgv59k o6t9oa 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 alja1 nbk pshcxma7 -*.;7 1wtw beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othewjx wpl a7k.thb*;cn7 a1- 1smr?    m

Two loudspeakers are 0dygvba -xd-.m1ir th90dy)t at opposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is thet-10gmadhvry x-b 0iyt.) 9dd 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 aorta is nufyrz(4v+ d)25a9)/wpzjek p8t ysbqormally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultr)z5uqse) 2 j4zbt f+rd y wpkyp89va(/asound waves were directed 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 whh:g+iyuu 5 4zvile the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What ig45vy u hu:z+is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series3lzp7u.(/ga hg4s fja of high frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from uh sz7l gaf.(p/34j agone chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals f5cffo*fp--ajo(+dez c 8bx a pt1 05tmrom 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? (See Table 12–3.) Model as an o ot05p -(8j a fz-+cbmcfxdtep o1af5*pen tube.

  Room acoustics for stereo listening can be compromised by the prp3+n1ocb a x:nesence 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 thioax n:bc p+n31s room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slendebj/ m1:bykp4qj o9. ibfdh/n//f hp8tr aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a litt/8mjj/nh t ih kb19o b pd.f/qf/yb4p:le 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 threshold of hearing for the human ear at a freq2oxg zrwza1d,s. 4n :nuency of about xs:wz,. g dra 21zn4on1000 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 obsex27sc xher4v+v/un6 wh cg6 7rrver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s alu7r h6 cgxs4c vv7hr n2/+x6ewtitude?    $ \times10^{4 }$ m

  The wake of a speedboat u6d*l+2( aex b:/ylux7g cxeyis 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