What is the evidence that sound t jbt ;eu.58jmgravels as a wave?

What is the evidence thh1cd4.r 6jk mrat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to thw lb)yop56jv *e bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the so6)j 5l ypb*vowund 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 yvbm4bve9:tv k1if23 cou expect the frequency or wavelength to change?3 :bet1vkvv4 icfm92b

What evidence can you give that the speokdk3m2zx1bsy; l/5,jjs 1u 7f glpu2ed of sound in air does not depend significantly on 3k721,xlus/5j;2 zpg km dly ubfsj1ofrequency?

The voice of a person who has inhaled helium sounds very high-pitched. Why?/0i0l)0p v +3gnuzo xjuj af6k8- gzjb

How will the air temperature in a room :9sl slj:rp0 gaffect the pitch of organ pipes?

Explain how a tube m5ny; 8- gqnl j6r9 a4-dvdjuadight be used as a filter to reduce the amplitude of sounds in various frequency ranges.vj ar4-d89 dlnd5n uaj y6q-g; (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12)hn,fp+uxv u)23;v dw o4rxm + a6yzit–30) spaced closer together as you move up the fingerboard toward the bxnoz+i26p ; vu+dat3 fmyr4v)x u)wh,ridge?

A noisy truck approaches you from behind a building. Initially you hear it but 7cr ju af03xc2cannot see it. When it emerges and you do seeuxrc 70c ja3f2 it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfev0t *6u1;*u2v kgictd/i nvvnrence in space,” whereas beats can be said to be due to 6vc;dvgiu*v 1 / *ntvnuk20t i“interference in time.” Explain.

In Fig. 12–16, if the frequency ofibb* fu382vjj12-nw 0pum wg n the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther mfwvb-*23ubnjiu80w1npj g 2 apart or closer together?

Traditional methods of proteonw*3 fcdy 2x3cting 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 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 reachingw 33*xnd of2yc the ears?

Consider the two waves shown:*cf ;j bxq+sh in Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different freqf csxhqb* :+j;uencies, 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 source and observer move in the same directiots7. ieg u1m.d3,omyon, with thyd e .sio3mt,m1g .u7oe same velocity? Explain.

If a wind is blowing, will this alter the frequencb.-zm,-h/1p zrbsvnq. d d9wjy of the sound heard by a person at rest with respect to the source? Is the wave9 rm q-dwbz,bzp.ndhjv-/.1slength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing.vh-s4 f3o pni6dd2:lm A monitor is blowing a whistle in front of the child on the gri2f6dpd:4s nh3-lm vo ound. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the ec sh(d )xtpdh9;7 r;hsfho of her shout reflected by a cliff at the far end of the lake. She hears the echo 2ss7fd hhp(r)9t ;dhx;.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the watzsw3 6b0( s9k-hi ucoderline. 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 1560 m/s (T9ws(0ikc d-b6sz uh3oable 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air a owv18ny91k;c* x81swkmiczkt 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above az.1p a ,6wdbf0m whdc) school of tuna on a foggy day. Without warning, anwbdmfd0 cp ,wz1a)h 6. engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it ih. h +-y/ b5z/im7mtrlsitd;1 m ,znvmakes when striking the water belob.hd ; lmt i hmsz+vtyiz-5/m/17i ,rnw is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge ston g uj41ak /:dxj6(xyun gtoc1)e strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the ot:1u o(tn)xaj1k/u 4gdxg6yjc her 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 f4kf s z*xfsbn c+gl(zhd3 akk*/161fover one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperaturenz 6asdkshx4gk1f *+k bfc1/f*l( fz3 is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the 9 kwgdx fp4*i.yc wyhm 5+:*oapain 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 leo /x:fsc19dy8gln 5o t2p3aoba,o7g n vel of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when firjl j 7uq0 rxdk4+,zr*ued simultaneously at a certain place, what will be the sound level if only one is expk, jdlrr 7+40 ujuqzx*loded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noy: 1gu;)ltdb jisy 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 intensitiey):lg dtub;1 js, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB,bp n 0ddcu5)4b whereas for a CD plcn4 dpbudb )05ayer 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 eqr gdk:5b9du /i(zb1.l v*fvj req 2+a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mou bf9v+rjr2eqdg( : ku*e1bdi .5/lvqz th. $\approx$    $ \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 areds e 2zv1l3n*wrvip /1a 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 A7f3a7o q7gabw.ik ,dc is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at 7 i3gkfaq7b oa.w7 d,ca point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when plaa,6w1yx g0r h /qtk.vo2s(hf v-vzl ;yced 2.8 m in front of a loudspeaker on the stagelr gh s t.ovk(yy12 /w6qhf;v-za0x,v.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dBh48qcmwtm y 3m:f r; bl:qamo g+q;(ad.w8z7v. What is the ratio of the amplitudes of two sour m:.w th8b qlqyg qfco;m4aza7 +m8vm:3d;w(nds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the 3m *gp2tut3ua(n+n m mintensityp*tmgann+umut32 (3 m increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqnn7 2sxzsraynb)8aypm*i( 7g/*/ da fual displacement amplitudes, but one has twice the frequency of the other. What isa/p*y*zrfs d7ng8/ i(sb 27xaam)nyn the ratio of their intensities?   

  What would be the sound level (in dB) c snv5wehnbz8)/d78y05 50xnntg ujqof a sound wave in air that corresponds to a dis s5u5)cnny 058qng87w0 zt xeh/db njvplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-H:h,m:q 9im 1k/vwywgquk5+m 8)qnwobz tone that has anv5bw:+o8 uq 9q:qmymk,/w 1wmgh )ik 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frno1- rwa0b l+requencies that an ear can detect when the sound1rlnawr-0o+b level is 30 dB? (See Fig. 12–6.)

  Your auditory system canj0b h0u:dunuvap,v dqgum wrd*l)6ak9 7++ ; z accommodate a huge range of sound levels. What is the rat6 n 7r+0u)9vgkjz audw;,qu hl vp *ad:bd0u+mio 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 fuxa ln5a; l7 u-+r5htxmndamental frequency of 440 Hz. The length of the vibratin 55xmx utl;ah na+rl-7g portion is 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. What are the fundamental and first three aur6rox:u j9jylx b29as+wapm.8mc8b4dible overtones if the pxl.ujx69+ :28 p bs wra8y cmaj4b9moripe 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 ajz tqu*xr2g2u yrb947 p4qeh*b++xt from blowing across the top of an empty9thp*r 2ej+4 t+ xx2b aqg7bryz*uuq4 soda bottle 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 organ with v2,iub mkwws78 cf/0 gopen-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes rewws,0ku 2 vm g7ic8b/fquired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a freqv:l 2nmvv0l: c2a (g1kg9 urvguency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% onrlg20v vggc( a l9::2 kv1uvmf its original length?   Hz

  An unfingered guitar string is 1ypw;ic7s dnip. *5d ) sefim8;- ld-,gfrw hr0.73 m long and is tuned to play E above middle C (330 mi8,srw;d5 yd7es*f1 w c)ril;g- p-.hpi ndf 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 ofzyy90 a,rl q1o an open organ pipe that emits middle C (262 Hz) when the tem0ol1a r9,yzq yperature 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 athw k9 ddk+d8kin)x :n9 j,/jpt 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiep: --j7gvn jkjce of the flute in Example 12–10 should the hole be that :k j pgv-n7j-jmust 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 pipe can resonate at 26e 7-g.a7ag3 kez gel/o4 Hz, 440 Hz, and 616 Hz, but not at anye.ge73oga gza e-/7kl other frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at two w w jjay*yz08wq.-pg7successive harmonics of frequencies 275 Hz and j-y0ww aj 8 zp.*w7gyq330 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 o1g b:n;s 6vd m fl61p7cfdpd:$^{\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 presentofk;jev)o2qp2 i8 xn5)hvb6-g+p mj o within the audible range for a 2.14-m-long organ pipe aqvi+58g2jf ;ho6pv )2 ko-en)xo pb jmt 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 outsiokecdir0pk ef ) ./5g-*6nxhmde and is closed at the oth km)ch0 /n6 fk*oi.e5xdep-grer 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 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 strings, /cnc(ngg- 3i/zl6y vione of whic g/ic/y3vcgzn-lin 6(h is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat fre*l 7k6o 4s66ab 1b-zr zc9qzmsjvtmp(quency 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 whistle operates at 23.5 kHz, while another k4ec lb +gjh9m+m8+bb(brand X) operates at an unknown frequency. If neither whistle can b b+mh8l4be j+ckmb9+ge heard 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 beats/s when sounded with a 350-Hz tuning fork q g/ (,ra qd7yxgszcy2w 1/ *gnpgyyg:0ktd *8and 9 beats/s when sounded with a 355-Hz tuning forky:nya0*dc/q7 pw(xsgz8dggqgty / r 1* y,2gk. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. Tgbu8*y 9m vvg9he tension in one string is then decreased by 2.0%. What will bb8 y *guv99vgme the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if tw--e+dno a x-hpo identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and then-pa+d-e x-oh other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, aot8.0-ryy ujdf; gpf4nd C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequef;.og yj0 dup84rty f-ncy of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m fxs8 7(psa vzd,wryw8 .rom one speaker and 3.50 m from the other v,r7wwsp8dx yz.s(8 a.
(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 vibratea 0(tvk2o.2 vqv7d6 x(sjsav ing at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating vv(v.tsasv dkeoqa (7 jx2026at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.6:y,;b 3vqexr k2pb3zz 4 m and 2.76 m in air. How many beats per second will be heard? (Assum :,k2pvxr3;z be 3bzqye T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a cerj g8bf x:6u7zntain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30z7fn68u: xbgj m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a 3old2nj o-,oa fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s doo2oa3, nl-j
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz 2d bjd*7/ p7pcy5mrx isource 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 j/dcyp7 27xipdm br5*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 th- rf6qm5e d0gr9wm2f te same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the dmdfq9wfe6tm 2g r50 -rriver at rest 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 oq uxer3 y92 mapqdr vy2)h(28uut ultrasonic sound waves at 50.0 kHz and receives them returned from an object mvrqh8qmdy229r)u puxa( y23e oving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emitqj*s0nl /a-a)n:vpovs an ultrasonic sound wave with fr/ v0*q o-n:npvs)lja aequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tulaar- l;yxddp)r k .-10uxs+ hba was played on a moving flat train car at a frequency of 75+hur k.1; lxxdp-s aa0)y-lrd 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 ultrasound waves to measure beiv8r fct+f7,8nzg fp+l 95xulood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from vl7ruff8 8z9 +exc+5fn,ti pgthe sound source?   Hz

  The Doppler effect using ultrasonic waves of frequencyfd4 cg. la15wi-sfhi2 $2.25 \times10^{ 6}$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 57 wfzr*s:*:vnb0 Hz. When the wind velocity is 12 m/sw *::zsb*r fvn from 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 6 (8n u2 lt*peuoaju;4na,g*erx nk y*land if its 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 of soums zm qqc 6xg92r0ynd ;hn:m*/nd is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s m6rm*2q/m scq d0 nz9mnyg;xh: otion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where the speed of soukff 4sc ,v)nq,nd is only a4,vns,cq)k f fbout 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 strikes them p(w60cbcd t7f(hl6 d ocean. Determine the shock wave angle it proc67mpw ltdcd hf6((b0 duces
(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 q7lai+ wafw 6.f0r 5iazck2f($/theta$ 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 exackxgw d:w+ oc.-na js)0tly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizods)+: 0wkajnc-gw o.x ntal 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 downwardhzu4k bii 30am)8au +9lk/ ynn from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minl y 8+kbn u0u9/an) aihm3kiz4imum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible range?0me(h-ppcc9 v() rrc)w d6 fsy $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mans 82h ow;bx8hky plastic wh28x; hs8okb pipes 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 pw(:qkslg p)b4zq*q:n erson makes a sound close to the threshold of huzb:sq nqpg):wk (*q l4man hearing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-gwz 9val0a15w w+q7p sdB sound and an 87-dB sound are heaww91lq +7w 0avg5s apzrd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, iw+s j-gdu08 uy/r.79b hft wnks 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all di .g 0 rkfwd/u8twb- h7yu9j+nsrections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output ddb;53tsh6 h z;fjlx jye ut:)rt 95b2crops by 10 bfhhx;ltr59b5e3 2y d6 z:jtcu) sj t;dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over tv a )-eh nrtl2h;jjntt06x9o1 heir ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dr e 0thlvo1)h2t6t n-jn;jx9aB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communicatii::vw 6:nnu437zrte+ w4 hkaowib br(ons 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 violin is tuned to a frequen0f.v:jxxgeeb(2o8c+s 6k s bpcy 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a funj. zem8cd b6tc)dq+ 0wdamental frequency of 440 Hz and a 6cjd8 d0) mzt+qbwc.emass 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 vertv mgj *egs,+zi g*0wm4ical 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 wit e gv,+s0gjiwgzm*m*4 h 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tubme( rx9hdkosub; 9 t ,o5gzm76e 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 fundamentagxm5ukzm t9o;r e , (9os67bdhl mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observts mhsz7*c , (92j sr4blxpiq(3u sl-v(4vx xped 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 co bro .or78,gqlming 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 is minimal at a point 0.34 m farther from one source than the other. What is8.7obo rlq ,gr the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on k1n0w whzd0 p/(n,)anvbrfu * the stationary train hears a 3.0rwnn*nk w ,1afv00u)h/dp(z b-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 you is 53k .fw/nebx:n(1 xz b/i8 Hz. After it passes you, its frequency is measured as 4xf:.xwk bien/(n 1z/ b86 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 oikc yf c+f n(m+rf-6;gj99qato the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain ng m+f(a9 k-+9yo i;frjcq6fc 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, so5s5itr c83a.jv,n bk funding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the othersj8f 53nikt.,5c rabv?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pastve8 /7ftx o5 l)xf0rjc a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequf c5tfr8o)ev07jx l/xencies 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 oe-s7uj1z3 o q .d;8oxwgsk1yflow in the aorta is normally about 0.32 m/s what beat frequency 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 a7.osg usk1jyw zx83 1 ;dqo-oe 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 vk4 pz(yul jmb+q+b6;moth is flying toward the bat a+jybk;zl4v ubq( p +m6t speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches a moth. T4q )fcttzg) j7he 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 ech4)zqfj c)tgt7 o from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpine;e(a0zr.s3mzt fo 5ug village to another. Since lower frequency sounds are less su(tu fes5zzgr; .o3a0msceptible 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 Table 12–3.) Model as an open tube.

  Room acoustics for stereo lisqnc o,.ur z1+btening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure c,u1 orbn +qz.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 “sikvb5g+sfu d0v/5 bs fy 3fo 3;ks0rl0inging rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is kvflbs550ov+0 ds03br u;ifkgfs 3/y stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human earz jd :4o9fcm,yvs8 ;mu at a frequency of about 1000 Hz is4o;uyv8 dfz :j sm,cm9 $I_0$ = $1 \times10^{12 } W / m^2$ 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 sonic booe vw5 i3zav;cj) ql2)gm 1.5 min after the plane passes directly overhead. What is the plane’s al lce )iv3v;jq zga)25wtitude?    $ \times10^{4 }$ m

  The wake of a speedboat mkp u,9dl.spgt. tw k)w35y(gis 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h