What is the evidence that sound travels as a waxkcc+-hdirz jci ; 0 ztj,50l*ve?

What is the evidence that sound is a fozv/2h c93 qvux:l yy*irm of energy?

Children sometimes play with a homemade “telephone” bu 5sgpu/7yp3f y attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how theu7u3y ps5 gfp/ sound wave travels from one cup to the other.

When a sound wave passes from air into water, do youp;r(grdbir;tm s 2k9: expect the frequency or wavelength to cpgktb r(:di29ms r;;rhange?

What evidence can you give that the speed of sound in air does notarq;tb 0 l+e:nmp.m;t depend signifip qtr m+:.;tblme;0nacantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. W4 t7ho( t4lavdhy?

How will the air temperature in a room affect the pitch of8db 3zf s:xho5hovz,e ay3: 44xi7 iwu organ pipes?

Explain how a tube might be i1 z9c*e 6w.x flz.)bhscci h+used as a filter to reduce the amplitude of sounds in w6c1.+c h*bczxf)sihzil9e. various frequency ranges. (An example is a car muffler.)

Why are the frets on a guitj )p 6gr;/dbyjwe1/i+cyq yhm18v )lo ar (Fig. 12–30) spaced closer together as you move up the fingerbo1qelyco/1 wr6gy+/; y vpm8 j))bj hidard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it hr)z87 -4;jj dpp hewsbut cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explainhd p); z-whr s8p7jej4. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to bw9nm3a vl b0klrc/q, ag+psf86qhk/ ;e due to “interference in space,” whereas beats can be said to bp/bc ;f mwla38s6kr ,v0+qql9 nh/kage due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsx+m . ; xgtgxbl;n9oi. D and C (where destructive and constructive interference occur) move farther apart or closer togethl9xgg+.;nm;x. b xioter?

Traditional methods of protecting the hearing ofs xeqo p5xv*/1.qv5*+ wksrtz people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which+ qsx v1 ev5r/*twx5qzkos*p. 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. Eaci kgy,u35mae*e)do8a djwj92y ;mx. e1mk z4bh wave can 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 the two component frgbzeej8 5mikom.9eajywy , xd km)2da; 143*uequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer x+dfos18:ihti 9nypauv3 4* o move in the same direction, withod4+aihxv t8u 9 3f1*y:nsiop the same velocity? Explain.

If a wind is blowing, will this alter tk de-nfm 3 9:sad+em7uhe frequency of the sound heard by a person at rest with respect to the:en-me f3s7a9dmkdu + source? Is the wavelength or velocity changed?

Figure 12–32 shows varioum*o:n45t8/u pc youi ls positions of a child in motion on a swing. A monitor is blowing a whistle in front ofu:/t*ymi 5on up4 8lco the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of here+w u/3ide ;gh shout reflected by a cliff at the far end of the lake. She hears the e e+3g;iewhu d/cho 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 waterline. 0ju(rog(s0rize1r7 tHe 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 var 0rjeo1gt7(0( zru isry significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng;ich p--3wvet0*2sv a.s qcobths 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 tnae4- xxp z4b*una on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapsesen-b*xz px a44 before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top o vnxq47hp t(7cf a cliff. The splash it makes when striking the water below is heard 3.5 s la4x q7n c(vpth7ter. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strik,oalif mo5,e u0t9ol21i vuv ;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 are 1.1 s apm;a lo,5vu i9i2t,uvf1o oe0lart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made ove3s vix2mlqt :cx2vk)v-+bdi 8q-lh. lr one mile of distance by the “5-second rule” for estimatin vi+ lt-cx s8:)l 2lkqqbmxv-ivh2.3dg 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? ipwqv); +zpqai v;2t.   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 whos mpg ,p p*e,6 jhu) 0l;o3hyqm/mb-udte intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously atjoq d1 knlmp;,am+8f6 a certain place, what will be the sound level if only one is exploded? [Hint: A;6 ndp l1kjfq+o,m8am dd intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with 32t*ggcp z +z4ayn xlzr, ;:fmfour equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if nzgz;lrt3p fg+,ay: * cx4mz2 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 ofaugoh38cy) 7p m;fp1fgo2to 2 58 dB, whereas for a CD player it is 95 dBh3tfymg u;)o 28opf 7ao c1p2g. What 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 sound from a person speakin:v kqn d*xmm74g in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mmx4nmk: vd*7q outh. $\approx$    $ \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 awtv 8m1ue i 4+liu5mt9n eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whil0v z fn+yah/s4liw gyc:/q0ds, -x0owe the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect a iw sx0n/c,ylh+of z04v0 q- wy/ds:gat a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when plnna zg.d+)od ;aced 2.8 m in front of a loudspeaker nd+dog;a)nz . on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound ltj9 qm( ex+a2t vgi-k ax2i4w)evel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels dataji2 )ke +v9mxq(i gwt -x42iffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripledsnfa8g4m7h d /, (a) by what factor will the intensity increase? Increase by a factorfs8/n g 74mhad of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacem+:fl r scfng 488)azip ct-+yjent amplitudes, but one has twice the frequency of the other. What is the ratio of their inte:48c jifcny f lr+p+g )-saz8tnsities?   

  What would be the sound level (in dB) of a sound wave in air that c5x 8u fsdz854jwbq;nv g rmw59orresponds to a displacement amplitude of vibrating air molecu85n48b;5wmvfgzw9xd j q5r sules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as du g56 b*is8:odfd2soloud as a 100-Hz tone that has a 50-dB so*dsbd: so doig2586fuund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect 4et53zvk*1yse5ylxvc 8a i w3when the sound level is 30 dB? (See Fig. 12–6.z4y i3aw vv 8le35*xeystc5k1)

  Your auditory system can accommodate ao .d48 -vncyj6de6tn z huge range of sound levels. What is the ratio of high.6 ontd 6zdnvj e8y4c-est 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. The lengtk1yjfe3*o 0 /zo atp4.7njetth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be plapk01*fz.tj34te7 n jo /a oyetced?    N

  An organ pipe is 112 cm long. , uq/lfvv0ih:What are the fundamental and first three audible overtones if the pipeh,0fq/vlu v:i 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 blgv1mm9 o c-w3heq yp8(owing across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed typ(3qm1cg9 o8m-ewhvube?    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-t3xw8ob:; a(o km:anopube pipes spanning the range of human hearing (20 Hz to 2komwb:3np(ox: a;a o80 kHz), what would be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hs :uo v8pbhi(g 8mxe74z as its third harmonic. What will be its fundamental frequency if it is fingered at a length ebsm4x(u 7ig8o 8p v:hof only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E 7mqpw y9d*h:n4o n-o*ad t+gn above middle C (3o+4npa:gh o - 9tw7ndq* ynm*d30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length .k4 yn97w 1robw53d..4ycockcwty zq of an open organ pipe that emits middle C (262 Hz) when the temperatury3 c 1tc4ydk.5.yr 9wk wzb.4 7oqcowne 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 at 20 9hd tetzlym 0tr -da )4l418we$^{\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 shouldm5y4g53ibug u the hole be that must be uncovered to play D above middle umgu3y54 big5 C at 294 Hz?    m

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

  A particular organ pigdly 841j;cbfpe can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betweec l8ygbj1 ;df4n. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It e+z1xcpv(5 ylj 0.rth resonates at two successive harmonics of frequenciese+cxlz5(1yt hv rj0. p 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 9q4nv bhbc c 2,ft28rk$^{\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-long orga qe)ci/:, jxen0ryz97n9 ewyxn pipe at cwjy0re,ey:eq )97xx zn/n9 i20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm lo g xjgf:2ks,:a d:ldo,ng. 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 tof: jo dsg 2dl:kxa,:,g 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 wrnmm 5d3pbxrya7 9 sw::u4ix8hen trying to adjust two strings, one of which is sounding 4r4n bsarmx8 umi 397x pd:w:5y40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 jar95abmv-n ( 03r8vpc)gt+ l( u tidhHz) 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;,sgn(7txi mzph77 hj nht ie9d: qf5, operates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separatdhpz9i7 tx(g:,niqnt h7, mfej7 ;h5s ely, 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 sounded wit8d2hadu ovt35h a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuni dvh8at 32d5uong fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one sap j drw. /igq:q(cu/6 9f4ubytring is then decreased by 2.0%. What will be t pc6b9u fa/gyqqr4uij:.d /(whe 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 fluteehpfvx **a+q3s each try to play middle C (262 Hz),fh*e*pax+ vq3 but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, 1ar(k sx8 wxtq jg+j:8and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C xxrj: q8tkw1+ a(gjs8are 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 m0m g+fyh1yci:b a:g :z vo:8vb apart. A person stands 3.00 m from one speaker and 3.500y agfb::1zc vm8+gv : :obiyh m from 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 ay r8t(a. 6svd9lj7c cpx) e+jit 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played toge7cc) pe jty6(. a9sirdxl8 +vjther. (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 beats g / 8xsn+ps7 ss7*kptqper second will be hqk st7psns/7*8s + xgpeard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequ25j4mplpe2v aency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detecplj52a24vmp e t 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 detect if a fire ex/ eabbcr;:: engine whose siren emits at 1550 Hz moves at a speed of b:/e axec;:rb 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frk,ocr mn *18q )2xwaemequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward o,am2x1 8c m*qer )wnkit 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 equippedf7fp() ic* u/t soj-hkd9clz1 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. What is the frequency tu*o d hc)kpzslf1(c-fj t9 7/ihe horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonip a;3)9s hnufp 0u afl)r nlnl(+tgi)*c sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/sa* uhg3l( tn)ru 0a9p+snp)li) n;lff What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As i 8 g ng1pi+5rvo4ke3ldt flies, the bat emits an ultrasonic sound wave with frequency g3d1oe4plvn5g k+i8r 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 p952o 9.uapm hut*yutxn,x t u0layed on a moving flat train carptxut,h9mu0tao *nyux 2 9u.5 at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasso/9:3ov gci7nfzk- bfri . ,zound waves to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taof7: ,c3invrf/s kbzgo9. -i zken 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 ultrasonic waves of frequen/9)oznmuu a2.eh 2ky dloob0w2:6l(jrch/r h cy $2.25 \times10^{ 6}$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 12 5f- d(fdlley 6ug) 5ddm/s from the north, what frequency will observers hear who are loclg5d5d fedu)6d (fly-ated, 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 spes 3 1uo-fvo,kved 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 Mo.vl - kcqde.-ach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of thlev-c .-o dk.qe airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet whe (7vl(gbvx; bcre the speed of sound is only about 35 m/s vc l((;xv7b bg
(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 an 9nm*1bkfs:azyig1coitl ( zc 7opkc,/t -- /ogle it proap g-7nk, lkyi9t(c*-:s c1z /oobti f/1ocmzduces
(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 st t *nhij0)d 5oz)ea8$/theta$ 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 exactc42 -i d1ybzxwb /;bsvly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the son4/bs bzb d1-ci2xw;v yic 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-Hz sound pulses downward fro yf:f+fjzdcg1u(5. e i(orf,am the bottom of the boat, and then detects echoes. If the mu5 fj1yger f ffa:.(i ,dz+(ocaximum 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 the human audible raniy;( qxdl0g.u (ks/bsge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consqtk3 i/e w*y8pe69p9-v oekdwisbj :.ists of many plastic pipes of variousi.pwj*ko3ty- 6epb dk9we9 8:/ eqsiv lengths, 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 makes a sound close to the thresho dta. 7.a/nnlz8ip tpf4li1p9/ p l+dyld of human hearing (0 dB). What will be the sound level of 1000 such mosqua.p9pz a/ptn8nfdi ld 7.1l+yi4/tl p itoes?    dB

  What is the resultant sound lxi4jlgyh:/*k 3xo; owevel when an 82-dB sound and an 87-dB sound are heard simultaneouslyl3/:wyg ;xjohxo*ki4 ?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, isf gvb t+vglj+ hc09hv1a yo:h/,i18fp 105 dB. What is the acoustic power output (W) of the speakertvf v8hgvh+ yj,9 1 ogahf:0i+/lbc1p, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outskj8t1m9r 4 jjput drops by 10 dB at 191mst 84jjkjr5 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft ty yplzm62ihn 3k4l8: mhpically 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 interce8k3hm p4n z2:mhll6 yipted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain,ey*.9/ xvj mfh $\beta$ 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 t fc87ac r :s.tdcp,x*uo 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 a /i k p0z p/mt7d.rheyw,hg6 3dfundamental frd,wg06 mi z3h/ p ykdhp.r/et7equency 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 x+:a1 -lbkqxm* yw q9rt4w:h xvibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and:mlhxt w-qya:9*+1x wkb rq4 x 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 tubeu/r8vwa2 yxll5m9 9yw that is open at one end and also 75 cm long. Hy9y5/ar lw xw 8u2vm9low much tension should be 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 rexdis wb+3e)c-sonate 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 from two sources. Themj a:,v 8e gcyqg76:km sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves abovka6mqgc, m:8jg7 : yeut 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 qlyq.k0 w+ mh.stationary. The conductor on the stationary train hears a +w k.myq0lqh. 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 aa 2,y ;ib5u;jxnz:uqvs it approaches you is 538 Hz. After it passes you, its frequency is measured as b, qv 2n;ia:x;zjy u5u486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening )xxo;10.a fepwbugs p *udfe8 )gg e:2to the difference in pitch of the engine noise between approaching and receding co g)8) uf*we.psfd1ga; xx0b2uege:pars. 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, ppjpj *at(a z.gy4i.6n+h) kttroduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. it6( z) yptjj.g*kat+ a.pn h4How long is the other?    m

Two loudspeakers are at oppow;k)b*gez dvtj s-j:7egp7s, site 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 freq,-v zwj *djkb; :t)ge7ssg7epuencies 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 normally about nj-s cvz /.kh67b4xthxvo( w) 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves werwj7k x6-(hcv.s/obthz )vn 4xe 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 moth is flying t1-p8tq / qwdbcwm91hcoward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflectsq-h9cdwwpcm b8 tq /11 off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approact p1e(,uwy1hwa(qs*k9t0)7g w bg dme hes 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 det g(edt*sk bq,wua7tewg( 1)9hpy wm10ected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1 u6hz.(r exc-* v 9cz50ehv*otolsqg *2–38) 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 musi*5v.qershlz 0c (e69 -uo gh *xcot*zvcal 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 open tube.

  Room acoustics for stereo listening can be co; si rm)gxiw b4:+vdc7mpromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing w mdx iw: )ir+7v;cbs4gaves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing h6td yt)q)xp0rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringinxytt q60)hdp) g 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 frequs uu c,+dl/6xroo)3aew(/ d lkency of about 1000ekd+(l w6 r su)ou,/xlo3/a dc 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 observeih,:c gk73jye a(tm6 ir on the ground hears the sonic boom 1.5 min after the pla i7hja,yg:t (ke m6ci3ne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat i3m-epzu q9.v ls 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