What is the evidence that sound travels as a v0yek)o7prtox ;e (x-wave?

What is the evidence that sound is a form of ener(8av-d/*1ijn+rgpqy tev4z q gy?

Children sometimes play with a homemade “telephone” by atthcb2yvepy-t u 1c1i0; aching a string to the bottoms of two paper cups. When the stringt1 ey1yupvch 02i -b;c is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, dox ,/5qrttj zz +wfm89i you expect the frequency or wavelm qx i5 rt,9tzf+zj8w/ength to change?

What evidence can you give that the speed of sound in air does notg5bkoc)5j/ mt0b/ dwes v j)2g depend significantly on freqjc)/g/mg 5)0tdk 5 e2objwvsbuency?

The voice of a person who has inhalvkd4c/eneyhnr: ddis 0 4w9 2rps/+k-ed helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pito cvxxk ey()9l807ynnch of organ pipes?

Explain how a tube might be 1,,sd,o rkhi+etl 0 9-uommlg used as a filter to reduce the amplitude of sounds in various freq1e0tl ms +m,gd9ir,hu-lo ,k ouency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3ga,l1a/l wr*. :f5-k d +rkdmhsxig b)0) spaced closer together as you move up the fingerboard t/ kg,sw- ldlf)b:dxig1 +m*rrahak. 5oward the bridge?

A noisy truck approaches you from behind a building. Initially you heyqm-12vz sd(. vv oaqs wl:o47ar it but cannot see it. When it.:vvqdqolo7v 4 aszm 1 2(w-sy 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 b ..tr i(4omkfbe said to be due to “interference in space,” whereas beats can be said to be due to “interference in trk4(.bo.i m ftime.” Explain.

In Fig. 12–16, if the frequency of the ;)*r nsow x/ehspeakers were lowered, would the points D and C (where destructive and constructive inten ;)e*wxs/rohrference occur) move farther apart or closer together?

Traditional methods of protecting th;a5,6ia;0sgcu qi tk/djpre 2e hearing of 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, k6rpje0u ,ig5/c; tida2;aq s 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 wavhb)j w/-l7m51enwhb/ 0cnntulel / e +es shown in Fig. 12–31. Each wave can be thought of as a super1 bu/w)le bwlm/hc0 hn+7tn l -5enje/position 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 apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the sour -) g)s c7tyjr(fxmc.skeuq(; ce and observer move in the same direction, with the samer) smje ;sxf . g7qtc-yuk(c)( velocity? Explain.

If a wind is blowing, will this alter the frequencryg vtv-*; iy 6z2khua1d;d3 ly of the sound heard by a person at rest with respect to the source? Is the wavelength or veloczl162ytgdauk ;i*3dvh y;-r v ity changed?

Figure 12–32 shows various positions of a cq5,i0 u 9f+6bhhpwgdjd. ,amehild 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 d hd,eq6abpi fh5g9, m.uw+ 0jfor the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake b:l)ni6 3 lshmsy listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s):63lsshn ml i after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterliv0jl2qc)i d( wm6pf /xne. He hears the echo of the sound rj2m0xfl)/w(v d6pic qeflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20 x7js;hl-b /t lh)/v gb4 rghn2$^{\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 d1la 0/cgelx;i:ux0s( 9k 1c70 wnk- fswkwanpay. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by thea0lfc(u s / 0p ki1nxkc79s x01lwak-;egwnw: fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when striki p:v dxrt2icvzo/+,m8)/4 wbyyll:hcng the water below l tyrxw+ozbvdyi2:) c/hvp, m/ 4:l8 cis heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stoq 0a10* :lk1gq hhjomjne strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1 hjq1:ahk0qj m0g*1l o.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over ttc;z d/z )ni:one mile of distance by the “5-second rule” for estimating the distance from a lightningn dictz) /:tz; 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 oq7rd r(f(vmyo ew )q/6f 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 ofet2dlg1j w.x sm;bx(,mq* wu r:7os8v a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneo 4)tygb/v+t);,a2rbbx t yblf8y a ux0usly at a certain place, what will be the sound level if only one is exploded? [Hib t;40+vbatfxglar)t, bby/ y)u x28ynt: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with fvd ,s ,k0v83l/fuaelmour equally noisy jet engines is experiencing a sound l 08la/ 3um,f,ekvvlsdevel bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a sig qr u: uhjddtp5) emp+2e+4xp4nal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What ip )j54dep4p:e+xq tu+2umr dh s 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 spou h)w-+1jis 9-uelj ,esq)ns eaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly )j9l+h o1sj-se uw -)e q,inusover 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 vj (,dh 4/pmwyfkuhh .xg1) zlh)0qg4m g(b;zarea 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 more o8b,q pyk-. ywmodest amplifier B is rated at 40 W. (a) Estimate the,8 yy.-kpwob q sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130ppp9t 7q1q +at(, lawggypj*. dB when placed 2.8 m in front of a loudspeaker on t1yw7p j,9 pqt+aqgpal( t .gp*he 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 dif6,qgqs5aks :,d hbwu0 ference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amoun:6,0b s aqg,ukdshq 5wt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave im08vk3h wap,f q hh6m 9muv7p6s tripled, (a) by what factor will the intensity increase? Increase by a factor ofm9f 0k vm ah6q3,h8vpm6upwh7    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equvgsyr2 /o,k2g4j4itqofgp29 9 fpwz(al displacement amplitudes, but one has twice the frequency of the other. What is the raqv2p jw,9g2k2i/4(49togo gfsp yz frtio of their intensities?   

  What would be the sound lehtj ;s)z9. 1rlu 9slgnvel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz? ;j1tz9n.9h lg usr)ls    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone thar8jadu8b c 1(yt has a 50-dB soucyur 1b88ja (dnd level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the bg. q,z, u0k)cl5ogfcsound level is 30 dB? (See Fig.k,uz oc,. 5 blg0cgqf) 12–6.)

  Your auditory system can accommodate a huge range of soundec;waabc.8 p ;1f;zhf levels. What is the ra8f p1w;cafhab;cze; . 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 fu 1.bbsg,hwdpkr (pxn2t: 0ie)ndamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under whatkpx (d2 s wb.ir)1bteghp:0 n, tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three audiblpwl,ln 7he 4v7e overtones if thnplw7l eh,7 v4e 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 yoadg 0xp,7km 9cu expect from blowing across the top of an empty soda xa, 9m7 kdpc0gbottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe orgt.rj 37 ggyvb8an with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHb7y 83jr.gg tvz), 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 Hz as its thir gmluwgv/46jx;: 6 cdgd harmonic. What will be its fundamental frequency if it is fing4;cjwl vxg6 g:dum/g6ered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to plw4e1xc(ig3e a ay E above middle C 1g(xiwe e c4a3(330 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 iia2o g*r9v0s of an open organ pipe that emits middle C (262 Hz) when t i*isv r92gao0he temperature 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 ab:.wi s-)p olht 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 Exaokzbr51 2id7xleoz +t 8-ye 3ample 12–10 should the hole be that must be uncovered to play D above mi+beeo8-zdta 1i xr 3o2kyzl7 5ddle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, /bq(rpl .zz: zand 616 Hz, but not at any other frequencies in between. (a) Slzq /zb:rz(p .how 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 tub0uynrl; scn uml : en)z;5it/*e 1.80 m long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz.e yl s r;un/cz; 0:t*iml)unn5 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 k)n3irb1j2;yo(e1+vlk4ow6 szd m xz$^{\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 p2ah 4h)msx(h5b vjh 9:hlr/khresent within the audible range for a 2.14-m-long organ pipelhr 9b:h 4)mv5/hk(s hhx 2ahj 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 to the outside t*3/ pd w-;:whocqwr4 lgja(iand is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the gr;34hd ci/awt wp- gjwr:(lqo* aph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s wc,uovnw va8g2h 8p8j1os7z .8aqx-zi hen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otheruo g-87.vcapa 2si jnxw8hz q,81o8zv string? ±    Hz

  What is the beat frequencbje (.yb 1/nhy0 /cmuby if 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 whistlexo9ag0g2a 2dx t xmiu9-lxq0 5 operates 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 simultaneously,m00 5al29u9ag o-xxxixg dt2q estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuni6bdg2h3wme oh8va8a6so0c ; qng fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain yohvqw2 6g8o08;cbo s6de ahma3ur reasoning.    Hz

  Two violin strings are tuned to the same frequenc u4q;jg tpc/0uy, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 1 cgup qu;t0j4/1–13.]    Hz

  How many beats will be heard if two identical flutes each try to play midk h. bab04vl+xdle C (262 Hz), but one is at 5.0°C and t4k0bhv.x lab+ he other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B e tfw0t r *vu*(g8zddk4+,vs fhas a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, t,fgr4wzftd(0 vvk8+**se utd he 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 one speaker+xn, b4m0kl9( ooljv1* hvlbr and 3.50 m from the otheb1+nh(x ljo,rvml4 *o0lk 9bv r.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano ty1+geqw3 vt7uc6ksa;py f 6e0uner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency fveq;7tek316sg yycp0wu+ 6a 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 wavelength9tdd q30colv5r 0j vp3y vny*8s 2.64 m and 2.76 m in air. How many beats per second will be hearcvq58lpy93d r30v jt0*dynvo d? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 15 ij,d,myaf 0on*ztj4.50 Hz when at rest. What frequency d*om dji ytjn0,f,az4.o you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing stim zwvg pyr+2x itz7(./ll. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 y(g7+z/mvtrwip2z. x m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shiftb1qx +ato7o .n in frequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactl1onq tob+a.x7y 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 cyf+(mho3o b /qw,sl5 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 resq3ofyb ( w/+5lc o,hmst hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them y6(py7xlj;k52zjq 7 ktwl :zgreturned from an object moving w g y7kj q6l2lj (x;zzyt57p:kdirectly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a5lz20d z1zrz 3u0ax *,z ckhcs speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflectes ,zzxh0ka*z cz 2rud 50cz1l3d wave?    $ \times10^{4}$ Hz

  In one of the original Doppler 1v2b ).il1eamgo. j tpexperiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played tm21v e .at.gljp io)b1he 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 ultrah m64jr0ai)omu zm; o 6al cn3hpcr184sound waves 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 an rh46lcio;o )c0rm a841m3 mzh6jp ufrequency 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 frequwl/ ;hyow0 .-ggzn u 7.dct:7np, hnfoency $2.25 \times10^{ 6}$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 5sen92g7 kmn6w70 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers heagwk ns2 mne769r 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 (hli n (7,ug .frqdxdzrwf7) (speed 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 har,(2awft6 15zs qzq of sound is 310 m/s (a) What is the angle the shock wave makes with t(at2 fq,6zw51ahzrq s he direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters:c.6g nzuz*o v the thin atmosphere of a planet where the speed of sound is only abou6v:*og czuz. nt 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s st-hgh3,xtzz* aj)9gtm+z5 xb82 shbyzrikes the ocean. Determine the shock wave angle i35,z8 a x*g)hgzb2b9hx +mj yzhzt-s tt produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle e xl 88;7rvmtwu(r0.dpnjc q6$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a pla kb3ncay 7sfz(:6mal*ne exactly 1.5 km above the ground flying faster than the speed of s7*3:k6 mzns b(ylfcaaound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device th 8qtc6msp3mf1at sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what3tsmmc16 8pfq is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaraow 6h( pdr:lgx9tc3/ce6 (ec:j*acves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of i4 3gkjlih at )dd:7.n7i l,lcmany plastic pipij 3ilhl:7atc k)d g,4i7n.dles of various 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 soundhjru4t:n 5ci nv:4 nk ji 5wq2,wd/3cg close to the threshold of hudwi t c5njn3:4gwij qc/4k, hvun5:r2man hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB srj. 3fn+ yz;e1mv9rexound and an 87-dB sound are hearyzf1v; rj + .xer3men9d simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed t7j f-8(hrvorlx8ne (in the open, is 105 dB. What is the acoustic power output (W) of the speaker, ass -lthrv(f7(nj8rxoe8 uming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 10ywu* 7v5ufdk0j)l 4kh 00 Hz. The power output drops by 10 dB at 15 kHz. What is the power out0ufwkk*y75hu v jd)4lput in watts at 15 kHz?    dB

  Workers around jet aircraft f6 oqm8cqrd+ )typically 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 ear am od6)q+rq f8ct a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, d5kb lo/ 6ktwouwht s:h789l4$\beta$ 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 towx +8xvi2d4bls8p lj8fnvx3+ 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:jopb2n w9f4e a fundamental freb4jnp f9woe 2:quency 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 v zl r+ 744m/1/hdcbtt;yz kterertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at er zztt ;cmy+/4 t1 74/kbrdhl0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of rs1sh -q01i*whb6z63taa zfi1f /nvqmass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be ff/1 h t1q0aar16z-iqzs s* vi3bnwh 6in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full led:4k u)bvag8 oop ($\frac{1}{2}\lambda$) 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 cominfj2l9g9c lh8bi9 fwj/v9 p x7lg 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 the sound level p 9l9wbx8fcl/ lh9 2g9fjj7ivis 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 stat)+j4hy v (usk4g kp;ngff gl;9w*b9cpionary. The conductor on the stationary train hears a 3.(kky*) jfup;4hggvp l+g 4c;f9s nw9b0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches youi:2u f2q+7kf qcjycn 0 is 538 Hz. After it passes you, its frequency is measured k2f0 ncqu+jfqy: 2c7ias 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the spee, pu rf3tz;f u *o5b;n76hjaikd of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a t*hf7jrnbz65k auf;p i;, ou 3full 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 beatjqw8eh.3 61 w(r) oy1peip fhu frequency of 11 Hz. The shorter one is 2.40 m long. How long i(3 . 1qfhyu)r1ee6 ppw8 iojwhs the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past a sta ku5o7ma nd fz4 (4ln1sdg44 tfiiu(w6tionary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is be4 diwuin(7 g su6fnfotz (44d1a5 lkm4tween 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 iafdji5zck l9 a6etv/ g,-x9.es normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were dirj ct avf.5e-g d6e 9zkil,/a9xected 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 tow*kdwn4r q0dpc )do +0dard the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is t+dqdd 04 c0k)rdo n*pwhe frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequenci )s0jlw3j-ph,;jao c y 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 bl -30c)jiwhap; sjjo ,e 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 2q, -a3t )av3zyskrd:m vg7fato send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns we ka-yfv)3rdmq t3,zg 27:sv aare 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 open tube.

  Room acoustics for stereo listening can be xd e76. w0ccolcompromised by the presence of standing waves, which can 6x.o cecl07wd cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long,.u2aozd2q .y ttd j/,y slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand..d t ujzyqoy,d2.2a/t 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 frequd wb.sm.*awk,*;o d kfency of about 100waf.,owd ;b*d ks.* mk0 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 on the ground h* b:*(e+ae vt*naywloears the sonic boom 1.5 min after the planet(n+ eaw a:*v*y* bloe passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15bn5 g: bd11,jo5mmyrm $^{\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