What is the evidence that sound travels as a wa)-dwy h8+aq a4.louy ; sct9sqve?

What is the evidence that sound is a form of energy5xd;vj5 -z1 ask ffh8v?

Children sometimes play with a homii+e qf g:6-ffs;z .ojemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearls; iq 6+.zjg-feffoi: y how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequ srh2itr-zo8db ;o7+ wency or wavelen8b;2otwh odisz rr+-7gth to change?

What evidence can you give that the s9jhfo(; 4dc5 j iqltg+peed of sound in air does not depend significaqdtg94j5+c; i(lh ojf ntly on frequency?

The voice of a person who has inhaled helium sounds pul .p a+l78aoxm 6/udvery high-pitched. Why?

How will the air temperature in a room affect the pitch olx 8j2w 4 oyxuvjuu819f organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude 7ptooxpt 7 rftc7.:*2l jpf v2of sounds in various frequency ranges. (An example is a caftl*77 :p r7f.pp ox2co2 vjttr muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closapj1lyhmpl47 h9b v/4 er together as you move up the fingerboard to4/m4hp79 l jhva1pbyl ward the bridge?

A noisy truck approaches you from behind a buildinbdg7mmo+r58 b g. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is sudde8 o+mmgr5 bbd7nly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be saiv4) -t;w +t h7mu(dxosy*do dxd to be due to “interference in space,” whereas beats can be said to be due to “interference in time.uo *;dwtdxms +dtv7o( h4) yx-” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,qo;2kymm z1a,ihja 8nbqluj*4 c 8j,7 would the points D and C (whey*nb kqjzcmliuoq8 2m;a 7a8jjh,41 ,re destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of pron///ccyxz0hdy- 5s6g jo, vu otecting the 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, headphones are worn that do not block the ambient noi xv/ /oyco/j-s6 y ,ducnhz0g5se. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as 1bc7 8uzdadxj 4do*c h/)+sqra superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are dh41bq xcs*d7rzo8 a+/duc j )the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source aumjcek p2k d,i8. a2s4nd observer move in the same direction, with the same m a4 .dic22pj s,ku8ekvelocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heanv vx1y.v 9q)ard by a person at rest with respect to the sov y 1q.vxa)n9vurce? Is the wavelength or velocity changed?

Figure 12–32 shows varivq 21jiq 5mavyep.4 6vous positions of a child in motion on a swing. A monitor is blowingpqmy ev4j6.5qaivv2 1 a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by liste5b, stk t0xz+hning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.thz5,bt0 +kxs 0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship juxlpc z;wgz 0o7ntegee7w, 1ibq ,+5- nst below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume t0oe wgw7,e1nqx-l ctn7g+5z , ibpe ;zhe 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 ajos7:d)a 23qlpkxy jm6 7d z,ot 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 ij:p6*)xq8) xofa1db s -ndfl ws drifting just above a school of tuna on a foggy day. Without warning, an engine backfire occuxo6fqa*:nbx8lddj - w s)1)pfrs 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 whenjm) ws z7u*3jzz*o/x- z1gmlo striking the water below is ml)jx3 /wszmz** g1-jzzuo7o heard 3.5 s later. How high is the cliff?    m

  A person, with his ear toalfpo8ia3e* (p wch.1 the ground, sees a huge stone 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 pi(1f.ha clpo8ea3 *w far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile off v72zofo2a/ay: tq7t distance by the “5-second rule” for estimating the distance from a light727/:qfa oofyv t zat2ning 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 1hjpnidfqh5.i7(h .d v1p:e)g 20 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sjwux3-s dv/dm * cg:gr(ol;t7ound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whe wxzyc.d8iz (5n fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensit 5d(8.xczizyw ies, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally 3lqlozo, zf59noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities,3 olzlqo59 zf, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ue igm+wg xz. 07nds:stta;27ratio of 58 dB, whereas for a CD p+ zn:usig7 0mtxgtase7 ;w.d2 layer it is 95 dB. 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 ao ojmju/x4 f gl)u)x8( person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the l)u ux(jg4o/)o xmjf8 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 antfeaz9v l-4wj p c wx;7.1/snl 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, while the more modest amplijd9 4 g:nqzho1f m*l(efier 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 coz*g o49(jnqhfdl1 em:nnected 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 placed 2.8 m in fru7q sv-g5jv8kssk e4 ;ont of a loudspeaker on the stage. jsqgvk k- v87e5;sus4
(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 diq05h) 6rf z-vz r3ilnetect a difference in sound level of 2.0 dB. What is the ratio of the ampli fnr)i-i0lrvzh z6q 35tudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tri b.d5s6d;/jf q sch h5wvh(ej4pled, (a) by what factor will the intensity jh;d. fbv4h6 jwc( d e5hs/sq5increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but o- f/ jt1(asjm d5qi7wdne has twice the frequency of the j7q df wi(d1 m5ats-/jother. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corcrt + 0im xk74j t8m0zrk,+1z-afsa3: kse rzvresponds to a displacement amplitude of vibrating air molecules of 0.13 m +r+a 8jzx7st ar is3 mt k4ekv,fzz1mr-k00:cm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-mw hy1c qh,da9xlzx - /htu.e1 cfo419Hz tone that has a 50-dB sound level? (See Fig. 1,1q / za md9l .oxc9y hefhw-htcux1142–6.)    dB

What are the lowest and highest frequencie6tn5i nr fz5p9s that an ear can detect when the sound level is 30 dB? (See Fig. 12–5t pzn6ri95fn6.)

  Your auditory system 1scfr;5 8cdn0r b3 2,j blsqzrcan accommodate a huge range of sound levels. What is the ratio of highest to,c5lc1q;8r0bdrj sbr z3sf2 n 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 ofkt ja f.:j*+ /y9whvfq 440 Hz. The length of the vibrating portion is*a/:vhk 9j ft+fjqwy. 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wh8g xye0rv01wirc r09jat are the fundamental and first three audible overtones if x0 9g 8rcwr0er0i y1jvthe pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowing acrosv ceei27-rpr e+ 0vsz2s the top of an empty soda bottle that is 18 cm deep, if you assumed it was a zis 0cv-vrere e +7p22closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe ocd/ li8n qcxc4qjeli9v 2i3 )hm(-8bargan with open-tube pipes spanning the range of human hearing (20 Hz to 20 k4v2l h id l mab(n-/ xciec8cj9qq)38iHz), 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 5rhf8 6c;5l a)6hw azbf40 Hz as its third harmonic. What will be its fundamental frequency if it isl 8 5a6hfwcbh ;6a)frz fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middl0ru 1 85lvr3,rd3 xbbykpp ix6e C3x3r58 p,iv0r uryp bdb61xlk (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 of an open organ pipe that emits middle C (rv8(+vb o-n)hbp/:fd uyi; tx g8 uz/z262 Hz) when the temperature is 2uh8+)r vpv iby (tozb8:x dn/fuzg-/;1 $^{\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 ang/opn 8wn oh3yc * bb-:try3:mjuac dt8):b+t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute**/- 5s 2ruoeugarsil in Example 12–10 should the hole be that must*is 5o2res -*ula/r gu be uncovered to play D above middle 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 pipenxp h8v rk3d1az w0:.j can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betw w0hdnp:3x.kavj 8r1zeen. (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 end4mv2t 6p;y mjxh 6yck2tp,xlp+- s6ts s. It resonates at two successive harmonics of frequenciescplm xy6ss+tp;y6mt h 6-k 22 tjpv,x4 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 r2gd 4hrqn4g,om-r:i$^{\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-a5g :n4fh reo3long organ pipgf 5eohan :3r4e 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 kioq286* ft/q6 yru5ybet*yw the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the t86 tyy qb/ io56re q*fy2u*kwgraph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat c/ a9yi9 jiga4bu9pz;every 2.0 s when trying to adjust two strings, one o/j49gi p;9azibycu a9f which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if midu7*qffuqd9 , qo .aci63ql)ia dle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, whi7)y2u f)l(9 ivt*pkyy(.ehwzpdsw7m le 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 simultanewm7)zl 2y.wh(y*yvusd ekti9p 7 ) f(pously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sound-)a: xxt)(i cj p2u/bgpk.e1k lamr)med with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hzab)-/lmj.2c):txxkm(pak) r1u e ip g tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 H0*/l hj;xocn) vta6a az. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two ntahja 6ovl/0;) *ac xstrings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identimgr 8g2s*on *75m lf.cgn,dbpcal flutes each try to play middle C (262 Hz), but one is at 5.0°C and the *c,no2 g87pmrf* mblg n.gd5sother at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hasr8-rrq zamf *6 v9*sct 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, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and Cq8 r*m6zr-tf as r*vc9 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 sc,eo9m7d1k8a6 cfc yapart. A person stands 3.00 m from one speaker and 3.50 m from the fe8acc,sm d1k 7y 6o9cother.
(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 supposedlgy gm i(h87l76vuk 1t to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be6t u781gvm(7lyg i lkh 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 wavelq/ubv o i(oq.4engths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Asv ob./iq(qo u4sume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz wh j:op wd8;lo1nw)c zhxx;( m:cen at rest. What frequency do you detect if you move with a speed of 30p(zmxh;x)lo w:ojc1 n wc 8:d; m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you db*1z5 vqoke+ip( nfi2ae 1*csc9.k bretect if a fire engine whose siren emits at 1550 H r 2ipqkci+bv 5eos91nc *k(z1befa*. z moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency it ,t0 6w0dk*et)hx1oarl0 ojuf a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it att,j100 *o oerwlh)xkt0au6d t 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single fre )n om nxp/4xm4t8*ekfquency 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 isnpomtm f/ ne)4k 4x8*x the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out g/ p)t os4y-v p,dzr*qultrasonic sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What i*pqt/r )p-sy,dgz4 vo s the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/(o i, f; 9(4cxx5fx)7thjb jez-w-irapnvfb2 s As it flies, the bat emits an ultrasonic sound wave with(5x aze)j27bfpj wi-oi9, r4 bv;f(chxfntx- frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expec9f 9wv n6dzk0riments, a tuba was played on a moving flat train car at a frequency ofk0n6d wv f9z9c 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 ultrasrp9x(q*b 5zgdound 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 frequency dg*5 p(q9zbrxif 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 freie m2d93)u ztc-yhw +hquency $2.25 \times10^{ 6}$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)vl( ra+kcx2u m/s +cl xvra2)u (kfrom the north, what 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 speed at ),dl6fvv+t5xddkmm/ 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound 5hya 8wk ytjrex9c bg/nj70,3is 310 m/s (a) What is the angle the shock wave makes with cj5 kxwt89b /eyj0nh7r agy3,the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin4q,r h)wm j:vr atmosphere of a planet where the speed of sound is only about 35 m/s whm,rqv 4):rj
(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 n,5) txik0ea:g vtn+nthe shock wave anglegti nn)kxnv0,:a5e +t it 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 oos: 3vtwl0v: w4: 4c :msevss$/theta$ 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 exactle.(deh tnj *2fp0rrd:y 1.5 km above the ground flying faster than the speed e 0:d r tnreph.df*2(jof sound. 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 devi.u73 w/euhkic ce that 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 2hu uew7/ cik.300 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audiblcl rm8.(o;)ky zh ylv.e range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a gv52 :n rup6nkr8; hscdisplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which av6 rr unsg25pn ;c8hk:re 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 tzsm77)8gso1 mxp2qr nr02q c close to the threshold of human hearing (0 dB). What will be the sound lz g287) x2rsnpmmc0q1tqs7r o evel of 1000 such mosquitoes?    dB

  What is the resultant sound level when dh2d3t1z;,gv-hus9hki 4r r 78 qvos gan 82-dB sound and an 87-dB sound are heard s -ot;gd 439rhkr 2q 1g,s s7uvhz8ihdvimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 1e9+kg:u g8d o2zdrct4bm0 5rf05 dB. What is the acoustic power output (W) of the speaker, assuming r e kurdzg5 f0t4b8d cmo2:g+9it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at yj1n9*qj)d ph1000 Hz. The power output drops by 10 dB at 15 kHz. Wyd9j)h*jqn p1hat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically we fs*53 v9a /xog96kcy qztz-.fm jjh/iar 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 axtm3 * vj/a k99ghi yfqo6zfj -z./5scn unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatiunon+(8ue1n m(p;w 3+/ wgfiuo9xy eb*wju9 gons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violinvc tm(j o8a x(a2d9;vb is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed point py.bvz*22 0 tgdf,zg .fbfo0g/mjk9 ts with a fundamental frequency of 440 Hz and a mass per untg2y0fptbkg 9v/z 2 gmd0j*o.bfz .,fit 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 vertical open tube filled with /sg*ddnx:+ bnwater (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:*n/ sdb g+nxd tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string l 4 **,o em3vlfgeor;kof mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamev*f, r3eo *mo;l4lgkental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed(/ev 7ev lv;uk ) myoz-/t)rdk to resonate 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 fro8ih wz+5gvt2 am two sources. The sound is loudest at points equidistant fra+5v8z gitw2 hom the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistl;gmvm 6aq,un3iwp h-:qv6z4zz/i v u*es. One train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. Wqgh u6zivmzqz-*n v6wm;,upv3a4 i/:hat is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approachesjr n 4u,s)ywl64i4 pcy you is 538 Hz. After it passes you, its frequency is measured as 48 wiu,4 pc4r)lnysj4 y66 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 to ty.,iv;zvt +z ahe difference in pitch of the engine noise between approaching and receding cars. Suppose the s i .vvt+z;z,yaound 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 frequency of::gyu0z/ fwc q 11 Hz. The shorter one is 2.40 m long. How long fuc:: zq/w0gy is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it fbvz0 -0 o+h2 yh4ynbmmoves past a stationary observer at 10 m/s as sh-h v2yn 0 o0bhz+fb4ymown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normall:zhdtx0l o( 8*rl6juk;rls 4oy about 0.32 m/s what beat freru:* s68(l4 jtlxdlzrhk o;0oquency would you expect if 5.50-MHz ultrasound 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 mokrb1)7glifx o-and )*k7 pb.lv -sx-p7n;i e lth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected ixri-) n *dlsbkke )lp71 bv-f ; .ponl-ag7x7by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth.p 5d2mcq2ia)m s-ms +cv3bv8k The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from onsm2+ck3)vd2-cam8mv qs i5 p be chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 1-p4fgu qlc v/0uq 5/bj2–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is clo/ bj 4qvq-5cp /u0fulgse to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presl bie169eazdrdujqt0,1zou/ h l,l** ence of standing waves, which can cause acoustz 9 ul**,eqr,zi6jbtl uoel 0d1hd1/ aic “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, cay:b:ege( yu5pat 826dvcv *hx lled “singing rods,” 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 roaucy(6 h85:xy g* 2vevbd:etpd 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 fe(f+np o wgd 4:)jxm*bor the human ear at a frequency of about 1fod e *wbjgx4(:n+m)p 000 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 groun7;-epdap d6kq d hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitukda q-7d6pp e;de?    $ \times10^{4 }$ m

  The wake of a speedboat is y;dz-yo7 si7aetx3 j6fz: v unu,.pv315 $^{\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