What is the evidence that sound travels as a wq5b*a0zl 2xzvjzs- +dave?

What is the evidence that sound ia ;snlgnt.a1 z:3,z vds a form of energy?

Children sometimes play with a homemade “telephone”t dur-lv 3do69 by attaching a string to the bottoms of two paper cups. When the string is stretched and a chitov9lu 63 rdd-ld speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the z+ ps5tzd2-ks 8;dt exfrequency or wavelength t tdzps t;k- d+5e28zsxo change?

What evidence can youf,ivkggedn 9eqd7jg e ho uc- :i/bx7,s(d+-( give that the speed of sound in air does not depend significantly on frequen(bg+ fudg oeq-edkx7j9 i n ,7hvs-/:d,ecg(icy?

The voice of a person who has inhaled helium sounds ve8ed06r xx5 yvery high-pitched. Why?

How will the air temperature in a room affect tbr e7(g. 1/., 9ant*xxj jeo ce+icpjihe pitch of organ pipes?

Explain how a tube might be used as a filter to reduraft0c cu ys)k8w :*l)c.lhh,ce the amplitude of sounds in various frequenchc:fhc *).k uy,0c)ra lslwt8y ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30)pn1bra ;ya; /a spaced closer together as you move up the fingerboard/p; ar by;naa1 toward the bridge?

A noisy truck approaches you from behind a building. d*n 94 :th-xs m;shzmlqy41uhInitially you hear it but cannot see it. Whenh;nu4hs t qxyhmm z*l9 s:d1-4 it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” wx- lmi(iwm d4pkwe :86hereas beats can be said to be due to “inti:(-dki 8x ww6m4lem perference in time.” Explain.

In Fig. 12–16, if the gf t w99mgbi;57eb,wii-s vl7frequency of the speakers were lowered, would the points D and C (where destructive and constructive interference occi9btvsi9 7b, 5w-7feigm;wlgur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with hm e7 , 4uyov01-4lwxz e0ohzrvery high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in add04zmuxe, o70hzr lvy4ho e-1 wition 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 caz (ke x9w5n-j1a up2vgn be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are thj1neuvp xkz-2a( wg95e two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer (,ahwhrzx9 9kmf t,/ w(si*eemove in the same direction, with the same velocity? Exp/xh hrt, a9,z *wesw(mf(ki9elain.

If a wind is blowing, will this alter the frequency 9jh ))rg8* sj fc1gxvaof the sound heard by a person at rest with respect to tv8r 9x)gj f1h gj)s*ache source? Is the wavelength or velocity changed?

Figure 12–32 shows various;pmx p f5f;-s;;u ituas()xop positions of a child in motion on a swing. A monitor is blowing a whistle in fron sp x; ouuf5xpa t;);imf;-sp(t 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 bibf 2t9o( bol:y listening for the echo of her shout refot9 ( foib2b:llected by a cliff 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 th /mz 9optwky+(e 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 tow/p+ y(m9kz 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 wavelengthmdew :ck; n9s+s 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 dri-v cj7l;;emsjix 6 now:cay:3fting just above a school of tuna on a foggy day. Without warning, an ee wism;nvcycl j: o: x76;3ja-ngine backfire 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 the top of a cliff. The splash it makes when striki2 xuh;l44hvy kng the water below is heard 3.5 s2 y4ul 4xh;khv later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hu m)0ef+m,e zflge stone strike the concrete pavement. A moment later two sounds are heard from the impaclez,ff0) emm+t: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erro2oqf8n)f 2hwajw-n;me+ k em -r made over one mile of distance by the “5-second rule” for estimati2+8n) eawe-hq nof;wj- mf2 kmng the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB? zqt jv3 f9;3co   W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of;f8rt(r fr:f b a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level oogy):o9tl2tp28bbg2h 9no uhf 95 dB when fired simultaneously at a certain place, what will be the sound level if on2:22o by8u 9g bgp9)hottnhol ly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equdrj1 f3eaa h7z 15av8yally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this perav7afj 1rd1za eh83y5son 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-noise ratio of 58 dB, w-tc4e6vd (a hfi c hn7 ;vu9na*suy);lhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal an;u7 -; h6y ca ctu9nhflad vsv)4n(e*id the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the powe m( k cb301zwd2q3ijnb:qf*jar output of sound from a person speaking in normal conversation. Use Table 12–2. Assume3*0md( :wj2qqknj3af ibzcb 1 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 t5)yy 9edgbrx*m9n l nod8d4)0lq 6dd.gzn-x eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A -lhp.fdtm 32ka:cyg; bi 8 4yois rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in i g438oybm .cap;dh2f-y:ltkturn 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 registe(rmpdcs 6g 4f+red 130 dB when placed 2.8 m in front of a loudspeaker on the stage+gpd(s 6f4mc r.
(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 differencemt+/ncay iab s/:k76o in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by tt csny/:+ /kbaai7m o6his amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what rt7doi,4 5gdw i+:k6c tw)09muin c zifactor will the intensity inc uo5 79i )i:tw +iwgc,i40krt dzc6mdnrease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacs 4pj wj(g 0umyjga*gw3u/hv;s6a n56ement amplitudes, but one has twice the frequency of the other. What is the ratio of theirg us 3;njauh g0 w54* magjpjy6s6(/vw intensities?   

  What would be the sound level (in d 5hqp*kei*izg awu, );B) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0qa) *u i;eh*piwgk 5z,.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as rloo7tk o k0,e4r0z bh9mm9;floud as a 100-Hz tone that has rk4, bte0oo kf zomm;h0l79r9a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies tv;y9 /v*z.k qr+px ztrhat an ear can detect when the sound level is 30 dB? (Se 9/rzzxkv .qtpvr *y;+e Fig. 12–6.)

  Your auditory system can accommooa ocn) hu zdc34ig)4)/ dtz:wwm*8dodate a huge range of sound levels. What is the ramt g)4diu/dnhzwwcc3o)ao84od :z* )tio of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. Th 2wn18 3gicqw hw,m,rqe length of the vibrating portion is 32 cm, and iqhwrw3 m,, 18c2qnigwt has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 z) x 2-gctnr,tcm long. What are the fundamental and first three audible overtones if the pipe -xgnt zc,r2 )tis
(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 yots.)pu 1:x *ppi uc4gxu expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it :4sxu. 1ci tpupx)gp*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 0,be3x ivvzd0pig4(p spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes required? vi ,pgz v030xb p4dei($L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hzgqkle/3/ n ,cc8jf/rz as its third harmonic. What will be its fundamental frequency if it i r/ f3q keg,8n//lczjcs fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and ir 2b fgv;:m5+vwkk v/ys tuned to play E above middle C (330 Hz). fkvvmywb5kg :2v/ +; r
(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 h 4hvbd 54m;sg)g6jpwan open organ pipe that emits middle C (262 Hz) when the temperature is 2wh4bd;pgj mvhs5 4g)61 $^{\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 ao4hp) j* s-xebt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flucd.(r/kz rux+psz w/ s0w5u(m09e e eite in Example 12–10 should the hole be that must be uncovered to play D above middle C s( +m(wr ewu/ 0p.d9ezckesi/0xu 5zrat 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 2 4g 3 zezzmdozek (2baq+,:dmHz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or+e 4(d:z2,z eoqbadzg 3mkz2m 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 su )onp.pc8y b7n5zf6t *,sbapi ccessive harmonics of frequencies 275 Hz andb), c i5ys *nfpb6pp8z.n a7to 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 chz,xu(5 eq *d 8zcf,a$^{\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 r a(z j8u+pc,qeange for a 2.14-m-long organ pipe, (e+zpjqa uc8 at 20 $^{\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 tijt)w9tw , t3nv -wkqr;54kw so the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in kqtw-34j9s) ,;t iwn5k v twwrthe ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adju:h3 ue4i/d r)t4.tytovk5visj.913z d qzwrs st two strings, one of which is sounding 440 Hz. How far off in freq r)9 zr4tdk5vus3to34h i zy:e.vi1.d qswj t/uency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hzm89t21 ye vvmffxv: ss9p pq+2) 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 operx 770 liwlji*i;xy)viates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneouslj;xiliv7 iw)li y*7x0 y, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning for1zp vgn8;x p7rk and 9 beats/s when sounded with a 355px 1r7gpvn z;8-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tux/a,exfmv/o 3z ,-8 fis (g;b+lleav,+aliyrned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the bx zia -l/vys3rb,+ la f;a/m+,fgee o ,xli(8veat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flut+wsosb /ja,w8(cgvh /es each try to play middle C (262 Hz), but one is at 5.0°C and the otherbh( sscgvao+w/ /j,8w at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of*6vybs v/ulr,;w / ssxa5 ni5d 441 Hz; when A and B are sounded togetsvdr,6n*xul;bsyw / vai55s /her, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible 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 oo hd,5d)+atxc ne speaker and 3.50 m fromh, o)t d5cd+xa 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 ek 47wua- zzki 2gfon .,87rmkto be vibrating at 132 Hz, but a piano tuner hears - uaf4 .z kr7g zn,kik2o7mew8three 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 wavelengths 2.64 m and 2.76 m in air. How many be83yisx jnf-qe1pq+ ,4 vyl8gwats per second will be heard? (Assume T = 20qx-3ysfgy+j41qv lwp8,i en 8 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cv(..v2 z.hgxb-r 1 wkml 2atx,r5epaqertain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect bvl, aerrp kg2.qht 5 xam.2.zvw1x-(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 des3mzp 20giru:tect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/sriusz 02g:pm 3
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is mov27u efho7 lu8ting toward you at 15 m/s versus you moving toward it at 15 m/s Ar2tl 7he7 fouu8e 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 equip e4 jjh9/3brlp yvycah6l3a6.c3 w 7rhped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. Wh j3yhj93pc /hh64avrela3 .76blcwyrat is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic soundp :kdc )-vkhc7 waves at 50.0 kHz and receives them returned from an object moving directly away from it at:k cdp v-kc)h7 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it fe a9 1sc ,vrye2n0q5vklies, the bat emits an ultrasonic sound wave with frequenevnsq2av5k e , 90yrc1cy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was pla0*ztya/,zkx6 zr1u /qjx 9ibyyed 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 stationjua6 xyq zr9,yz/k/bi * 0xz1t at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wb)jymf. upji)iki*y *lq-(3xaves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from k)iy3i)b*f.pijm* (l - yqjux the sound source?   Hz

  The Doppler effect using ultras,vyeoqf , d+ 2ddxcw1(onic 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.8z e tmut3id.i3k kw6;83avoo When the wind velocity is 12 m/s from the north, whaako 3ti6vwe;izkmd8t83.3uo t frequency 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 ycz-8l;u30c r,xh oq6bvbv9h lo;ee 5speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed o(i 3v5ay 2ifgvf sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the(ag iv 2ivf5y3 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 planl dwh24lv7.s xq 44hqhet where the speed of sound is only about 35 m/s q d4sx h. q42hv4l7lwh
(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 sf3r6woj ;o v)ntrikes the ocean. Determine the shock wave angle it producer)of v ;jwn63os
(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 3abim9:k;y+r lrig 0e$/theta$ 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 groundksz/2ad ayp5 ,me,m a7m 0efq: flying faster than the speed of sound. By the ti7m0,y/asq :zmedkfpme52,a ame 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 device that sends 20,000/:boch lgif 66 phw0b5-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 minimum tifio6/hcwb:b0 5ph6 gl me between pulses (in fresh water)?    s

  Approximately how many octaves are there in th-) 05c-wqarvkvup-f h e human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pv,v+ *wnkl 6majvtl( (ipe symphony. It consists of many plastic pipes of various lengths, which are open on botltlwkv(v* (n +am6 v,jh 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 makesrq (;l9kk2xc 37qw jqw a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 suq;7w( xqk 9qwc23lj krch mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87- i;n6b 9rjf;hww x53 ytbtp80 da*k2wldB sound are heard wy 6;b 9ni f8hdk bwrplwxt30j2*;5atsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i+-o*o kmkq np-:hol9 m+ c9mnes 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in a9oml *- cko o -h+k+mqenp:n9mll directions?    W

  A stereo amplifier is rated at 150 Wuc tnxll)8a 85cf(o h* output at 1000 Hz. The power output drops by 1th8alf nc85o*u x(l)c0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ecdv p f5z-6d75zz 0vfzars. 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 p- vzp56dd0 vf5fz zcz7ower intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,*r, u; n4bo*laubkee3nef e1) 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 frequenc )sfp4l kn tr2(pe.zo8y 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 oi72 en r/0hz 3b9ixj4wa-fckaq 1qg0fixed points with a fundamental frequqbz oh2 7a1gfw4xjc/0r q i0ek3na9-iency 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 as 5ez gcd6,r)wbove 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 isz,g6) 5wred cs 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 i; )xhpay+vg7 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the stp;)vih+ ax7gy ring 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 resona;vy 4ie il0h/zd i(o.ote 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 the 500–1000-Hz range coming fr )8s gi bnfpo-oj7i7f;om two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the soo igsi7jpf)f ; 7nob8-und 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 nnod s + 8q0azyhvs0dok3m694conductor on the stationary train hears a 3.0-Hz beat frequency wk0dhno9o3 +dmnvsz q6 48sa0yhen 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 538 H mlur:p.:0esa;j ur l0z. After it paam:sp0: l ur ulr0ej;.sses you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can esti-g7an16xpp+u4e kj j j4ejs* imate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Supposei*jj4se4ae-px+ u6 pk17 gjnj the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequencetx6vrbni8 x4 pf5s1,y of 11 Hz. The shorterifpb1st5xxer,n 6v8 4 one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad cu2 fj wd05s1apar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical s5a1j u w02sdpfound 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 aorta is normalk-et 6pe 5m fuao t(eu0h0fn2v03lt9 xly about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasoue 0(630ueta9o2ttmlhk en0ufxv 5p f-nd 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 while the mothv,xggbr ) x;p),e8fof 1ycs1y is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave ybxo s1 gx)1g;,ve r yf,cp)8fdetected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses u* 8:cxkng he9as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. cn8hu:e9* kgxHow far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from v klqkt(:b68mg( 4gy none 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 pm(g l( qygk k:t486vbnopular 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 listening can be compromised by the presence of standi wu.on123 ztlpng waves, which can cause acoustic “dead spots” at the locations of the pressurlzp3uwn. 2o t1e 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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender alumijhilzfvt4 r+2d+w)0 inum +hir zl 4+2twjfdi0 v)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 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 frequency jtlm p8k,)0i;t7d 5i alutr;vof about 107t);kj 0ri;8 tp vtl 5uldi,am00 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer qtp6rba:n(9h on the ground hears the sonic boom 1.5 min after t 6bp9(nh tqa:rhe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ise( bh 5-f8xxnh/tmho) 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