What is the evidence that sound travelsi*4*z d 2sxrn ve4plm4 as a wave?

What is the evidence that souz;mm-w*g8 88t:tqcixvr wrz.* ydwa .nd is a form of energy?

Children sometimes play with a homemade “t/ m l q0ctibkou3t.*7oelephone” by attaching a string to thel7qo0ktim.b * otc3/ u 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 the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequety6gd*971 z,yx,q (nc5 gzdg q0tv hfency or wavelez(zdqqv d yxfe19n7 t,gc*y50g6 ,hgtngth to change?

What evidence can you give that the speed of sound in air does not depend h)gx z4x u1htsq.-nd-significantly on frequency?hhdtzx .-)q4 u sg-nx1

The voice of a person who has inhaled helium sounds ve4f)yln(nr i 5tv.yz+nr)b+jh ry high-pitched. Why?

How will the air temperature in a room aff ,uj6 x63v(uel7kwhgnect the pitch of organ pipes?

Explain how a tube might be used as a filter to r7d)8w, y zvuct f5l ehm7bjrz8748t nceduce the amplitude of sounds in various frequency ranges. (An example is a car mufflee cr,t74lydz 8m7fc n )88uv5z t7wbjhr.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as youpzvdx osoh+xy(3/us (gy(;e8 l;(w ny move up the fingerboard towarl( ( szhp(;+yns3oyg; eu8dwvoxyx/( d the bridge?

A noisy truck approaches you from ( *f b+ihspgc4behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-freqcsfb * 4gp+i(huency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can b v1ioz lf:jh(p250*gbfvb idec s;b2( e said to be due to “interference in space,” whereas beats cai *fhg: pj2dfob(5bvzev02bi l (c1s; n be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulduv36zvgqd *d px/sndml9f7* go//s3 a the points D and C (where destructive gf3q/ vsga/d*3l/sv6*d u mxo d9pz7nand constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of b v/qen6ny*l7people 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 detects the noise, inverts it electronically, then feeds it to vln7*nqb6ey /the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shxf5n2 qg1d hjyu sd:149-qc7*k(il est 3puuiown in Fig. 12–31. Each 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 frequencq1(n9d- y4 iu5: p3dcl1fj7e uskxigh2 *tsuqies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obser8/a4 m0knykcsj c 9fc-ver move in the same direction, with the same velocity? -y cfna8c0ks ck4m9j/Explain.

If a wind is blowing, will this alter the frequency of the sounde0 jb2 au2dp7sv tpkl0nr:7(x heard by a person at rest wite20b 770vxa :slnkrudpt (j2ph respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. Agpa. 0w6b apbnav4 (ctg9y wv6v m8+u1 monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound oav b(t.91uvppa0mna 6ybwg g46wv8+cf the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shoutnijev- e 37c) -v5jf2l7im)xoi/m1nhqf z.aq reflected by a cliff at the far end of the lake. She hears the echo 2.0 s ai2f nl7--1.m3z/5jeim7f v cxq ena )qi) jvhofter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the wa)kjm j8gk vwza7xe tz (,+7;ecterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 15zgej;8kvm x tc +ae7 j7kw()z,60 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 3s u ;uenk/s8rmmo j uuq85)y220 $^{\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 of4, hmzgx-s0e y tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses b ,z xm-0ge4hsyefore 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 6k zo6i05a ih)qrv 2yqmakes when striking the water below is heard 3.5 s later. How high is the cliff6akz hy5ri v6) iqo02q?    m

  A person, with his ear to the gro;;pl 5za esn.7 jifhpsc7 n errx:lve4 9f(m31und, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: is;e37n1rp;x sr5zv leemlc7fp. f4h nj9(a: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5s3:gym;odw n d6g0 ev/-second rule” for estimating the distandnwy/gv:g s do6m03;e ce from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of akq;eg5b9zo zl2*+kf h,)x zbu sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whostf slk170l4 7m*vrc4ex xw* qye intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultan nf wtc7yc4h0ls:k:s8 eously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, no:l sycnct8s0f7h:k w4t dB’s.]    dB

  A person standing a certain distance fncn3k 4w:) fr6uozc*7 zrld )brom an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person excz:w) )64z*nnrlo rd7u3fbk cperience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is scqx9 nb;a91q 6n(et +wowqfn6 aid to have a signal-to-noise ratio of 58 dB, whereas for a CD playe9 qn6t16;efqna co 9b(nxq +wwr 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 frdk0d pgqoc+iaxi+ 6 n0gtry2p/f l.78om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly of+ 7karii0p0. od8tp/y6cqnx g +gdl2ver 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 striko4 lvjrt 9o0aw ) q( zem.ii,h*+-iyxges an 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;4crnisr;ii9dui l 11 modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expecilr d1sr9nu1ic i;; i4t 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 ezb 3c grvn-+f,m195+y e w2dnip7py h130 dB when placed 2.8 m in front of a loudspeaker on g71w+ yhy3i nzep,f em9 +-2r5cnpbvdthe 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 bjpwe5x e h8/il:gl.k s/b 3;6r zdrf0sound level of 2.0 dB. What is the ratio of the amplitudes of two0xw /er6rlbjgds z/5 l;8k3:ei pbfh. sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a8w;jpkys+:)p i kz u9a) by what factor will the intensity increase? Inj pak;9p:8yz k wi)su+crease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice tiioblp1a( /4w0w i xp 3p4mox4he frequency of the obppo xwm w1a l4p(4xo4i /3i0ither. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air trsnxv8 r.f:rs u4)/bf hat corresponds to a displacement amplitude of vibrating air molecules of .sv rr4sr:/)ffn8 x ub0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sod a,+zf)ttvet: r7t;jund level to seem as loud as a 100-Hz tone that has a 50-dB sot f +:tr)aj t,7zdv;teund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can uxb:12roav d- xu8h07 zxckgzr+4rz3detect when the sound lev z0z7g1 x:oh3r +2akx4drcv8u rx b-uzel is 30 dB? (See Fig. 12–6.)

  Your auditory system q.xbptf y r ur9*/9oxhil803p can accommodate a huge range of sound levels. What is the ratio of highest to lowest inteu0tx8* .xpp3/r rb9yoh9iqlfnsity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin ha*ag.cg bn15ugxzd)) xs a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass ofga. xn)cg gz1ud*b5)x 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the funw5qt h xcew8v4tdvd30 76zu;q damental and first three audible overtones if the pi4tvu7v;0xqqtd3ehw 8 zw5c6d pe 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 freqgs/.omz ) k 1f 5.p0d2o*zphpxvxenw-uency would you expect from blowing across the top of an empty soda bot-g .*0zov/x)mo1 5xphzek2p psf wdn.tle 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 build6uykt/v j uclk 9en81u9*o, fd a pipe organ with open-tube pipes spanning the range of human hearing 99yj c,feuo lk kvn *16tdu/u8(20 Hz to 20 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 a ,c6u8gjn) im540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original leauc,in8 6mg)jngth?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play cat,17kivhw 0g6 f4u3yn dir-8rk.lj E above middle C (33cr 71k3j 8i 4v,yfu0k6lrtdaiwg.n- h0 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-g ho4q3h 5z jqrv/8tk (262 Hz) when the teh/h-okq3 4j8v 5rzq tgmperature 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 5jbrd 6pib,d, d(qql 6$^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should theae kkiaeoy ogmx61d,bt mu 9s4m32,*4 hole be that must be uncovered to play D above middle C ab3o4gm 1sye iae*,maxktu9k4, 2od6 mt 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, d x10u26qxs al440 Hz, and 616 Hz, but not at any other frequencies in between. s16 ux0lxq2d a(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 bowm25 oxe)- k dcdtes6qd03ph(th ends. It resonates at two successive harmonics of frequencietwsd pk 6qoee2x5-3)0m(cd hds 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 u26:orfgie2y6n; ss r.0nz qa$^{\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-0emzgdh2oa 7o*7 v1sulong organ pipe70u g2o*shozdv7 m1ae at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appnwhzv2om 9 na3ld wvl iiuv((2*f7-5wroximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the ifwi272wz9 5uhnvwon l avl(d(v 3 *-minformation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two string7q 3lr w-g7piws, one of which is sounding 440 Hz. How7w3lp7 griq-w far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (21 :neklk/p/ jd62 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anothersxno;z) ev( i ,oc;)vqg2+de4jk( xmc (brand X) operates at an unknown frequency. If neither whistle can be hesmc( xz oxqv+(k,ovjdg)e4; n2 ;ic)e ard by humans when played separately, 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 om4qen cm b1y5t-+wp 4beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning. +45nqbew 4mm1yt c-p o   Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension.uxjfv:0 l++kd:jw jt in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are ptv+djj: +x:.wfkjul0 layed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try tcgjj u2i20mz th-lmfea0 1g9/o play middle C (262 Hz), but one is at 5.0°C and the other at 2e2j0t i2ac 10gf9mgh u-mjl z/5.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; when:go1mg b+2s1uot 9bro6zk pz y.85eie A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are soundes2yog5o kzem.:91ie ob ztg61 8r+upb d together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands:r(28vt jy, cta5do un 3.00 m from one speaker and 3.50 m frovt n cy85duj:a(t2ro,m 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 vibratingf1nl2xuurn7 nn n(0l6 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 be the frequency of the other ? r1un0 27l n nuxln(n6f  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 sound2pk/shb 5jt5sv4i +koijkx40w* h ba3 zkha: 2 of wavelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assukh skob*jh ti/a0 hj2 x55kkv3pa42:izsw b4+me T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency ofcmnk*l3rlj *k h,a: 6u a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a **: aklhucrk, 6mjln3 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 )z 9*mecxmzy*a fire engine whose siren emits at 1550 Hz moves at a spmexmz c9*y )z*eed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in 4rzvl 14fm rbb1*mle (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 exactly the same? Are they close?4mrzrlbm1 be(4 lf*1v $f'_{source\,movine}$    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 frequency horn. When one is a k,arleesysr 1 /w9,w:t rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat fre/sr , swr,wle: 91yakequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonitz;, 4t j n2eov5ytyxjd7;ox wj o7;.sc sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequenctn j;7tt.w o ezjydox x;7,j24o5yv;sy?    $ \times10^{ 4}$ Hz

  A bat flies toward as o,oyp8f *)2; xp;vylc:mxdy wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. f:2p*p,yosx old)c; x; vmy8yWhat frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exp)ku*h-0av yl fi,n 6mderiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached tm,6d0-yakh vnu) i f*lhe station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measur:3wdd u bec3l;e blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and thdw e3:l; bcu3de speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect u vdx9v)p 1 oo-dku9da(sing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits souu:d zrt5e vr3i:5 u)pnnd of frequency 570 Hz. When the wind velocity is 12 m/s f:zirptu)5rv e:nd 35urom 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 0a(g5*gbzxkx6 u g qf: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 thtm,y us 7gg/rr*4s3 hfe speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction o/3gmy,rsrf4*g t7hsu f 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 thin atmosphereykftg i t/++6c of a planet where the speed of sound is og6+/k cyft+itnly about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500pkgce. )a,,wm m/s strikes the ocean. Determine the shock wave angle i)a p w,k,c.egmt 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 ,nm 1cqcq*q 1h$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km above t/q xfk0 t bg;bw0e;md*he ground flying faster than the speed of sount/;k e0gd*;x wmfbq0 bd. 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 that sends 20,000-Hz sound pulses down;)-ohhz jugc -hy-2,khuez4nward from the bottom of the boat, and then detects echoes. If the maximum depth forh -h-j h-uc)o,uy2;nz e4zg kh which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how manybpm02 pl9 6hst octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display calledna/d 3/1+uvgmw yd s+q a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both ends. / 1 amywun+3g vdq/+sd
(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 perso-zl)17eras8 wyq j mf5n makes a sound close to the threshold of human hearing (0 s8mqr l5j 7)-wze1ayfdB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82- 7wh25y mqr6emdB sound and an 87-dB sound are hearme6 w2r h75qmyd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, i48ght y7u-bghpgd9, op94 cik s 105 dB. What is the acous ,4p-uhk9d84citb7 o9pgy ghg tic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rate5wnw *kwnp y hkt/f2w8(wi5pj/82wtkd at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?5(i2*85kw tf2 p8 kwpwjtynw/whw nk/    dB

  Workers around jet aircraft typically wear p/bet ,3m 67-ltgfpw8s r- iaxmrotective 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 eartt/ ig ,m7r3a sx6b-plemf8 -w at a distance of 30 m from a jet airplane engine?    W

  In audio and communications sy9we:meun xx.u/k k9(2t-h rbw stems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin (.s4z hhp0xrg( jg-rck3.hc eis 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 fi iw:nel0m4 ax1xed points with a fundamental frequency oiexwm n41l:a0 f 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 7cus5o j3 w3obu yi9p1vibration 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 again at 0.395 m. What is the frequeuw7 u bjp3os91c io35yncy of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one sjoogft nv+9:c wltm3d 44, ,)yrsq,bend and also 75 cm long. How much tension should be in the string if i:4wn)s9octr4v qyt3 +ml,f,g ods,j bt 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 r)yg685) .o )1snnncekhumcm 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– +p 6co7r;ot cf1oj8ehwh,sci75xzz / 1000-Hz range coming from two sources. The sound is loudest at points equw7jtz ;/1cpohxoszf58 c7, iec 6+ro hidistant from 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 whistles. One tr1y0k .j0myqf g)kvti0ain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency wq j0i) f .0v0y1mkytgkhen the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam cpwr0uun+v9- vo+* whf; pgg, train whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the th +,*v;cpwfpguo u w0+- r9vngrain moving (assume constant velocity)?    m/s

  At a race track, you can estiew ackt9qo 1 g ndz7(9im36pv1mate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppwq 61ctp m9ae9v3 idgn(zk7o1ose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency gt:qp m)pvb,h0.pbp. wsv2f) of 11 Hz. The shorter one,p. bwbfvh)02pq ):pgtv psm. is 2.40 m long. How long is the other?    m

Two loudspeakers are at ouaynv(+/t t d4pposite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listensva/dyu 4+(tnt 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 0.32 m/s whatb)w;p7k57 bzqw;b;o jy.yzjo beat frequency would you expect if 5.50-MHz ultrasoun;oy; ; w7zw jzb)q.yojk bp5b7d waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying towarexbnl t(o; g 9 a9.drtp5. uc77xranq,d the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the,cu. raa9r tx .eb5tp d7nx9nl;7g(oq wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses r2mvifloz :d rau46 ff9* f1,pas 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 mot:* f4rdp1v9r off 2z, lfma6uih be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from on0ap,(cet zp w w8iv*i h0(ifr2e Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Tawt2 (ihw0*ec,z0a8pfir p v i(ble 12–3.) Model as an open tube.

  Room acoustics for stereo listening cank20wuzq s:-+*pg3f rskv luf4;wq)mm be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locationq)u*lk4 mq0fkr;3+2wumvf-zps ws : gs 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, callsti1u 2t c,b;hed “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 rod can be made to “sing,” or ;i sc,u2 th1tbemit 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 frequenc:pgp w rf. /nrnd2p8m6y of about pp2:n r/f dgnwr8m6 .p1000 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 hears the utm 1*yn 5+mqfsonic boom 1.5 min after the plane passyq 5m+nt m1*fues directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 gn *ij+c:5 ayxp: w9yk$^{\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