What is the evidence that sound travels (a;0 w/hqwlxx62iv ibas a wave?

What is the evidence that sound is a fo6 xrio0e,z)i4 b+env 7nj 1bdurm of energy?

Children sometimes play with a homemade “telephoned *n xt1t lt;8e8oorj1” 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 xr8d 1;ltot8 e1o* tnjat 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 e k7de3y: p ;wfmgu,pm:xpect the frequency or wavelength to change,k :;7fuewpymm:dp 3g?

What evidence can you give that tnh l))yw;(q rua1l cu(he speed of sound in air does not depend significauc1)lun; y r(l)h(wq antly on frequency?

The voice of a person who has inhaled helium xsc+ lu7(7 ;pcir4uxusounds very high-pitched. Why?

How will the air temperature in a room affechbk,t:x 0+6kmso o 6d)tz(fu ot the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitu aevqn6-a1*tn de of sounds in various frequency ranges. (n vn*- ae6tqa1An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–b1/d 7f wfe rovg5:ij42sgu.a4l sht )30) spaced closer together as you move up the fingerboa fwv.ria:s ugjh4t)/ g21 4elfs5d bo7rd toward the bridge?

A noisy truck approaches you from behind a building. Initl+cdfkx(2,qkrnej -a) s q:y9ially 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-fr, s y- r(9ejlc)fqkqx:+a2dkn equency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be 9/h+ qx0*bu frqcblo9said to be due to “interference in space,” whereas beats can bex 9/fo0rc9 qbqu*h+ bl said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of;d 7x3d m7ikpf the speakers were lowered, would the points D and C (where destructive xf m7ddk;3pi7 and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of pc/w7t dd m9ecwpv 086zeople 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, headphpt/6 c7 0 wwedvzdm8c9ones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as a scj(10 (cyrrxcew-r lz, z d;5azrrrk7c* yl,/uperposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In wzer1ja(z ,,rcryzr -70ld c y(rk;cc/wl r* 5xhich 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 i45d3g3m -98f vd*6n,8owdmqx/k u txiuelq rsn the same direction, with the same velq4xrxkg*mev68 -/f dd3,lt3wuui9 qo85mnd socity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard by a unmkh6z7,( ey 5yo(zpa,t m 9zo8h,leo. l yt.person at rest with respect to the source? Is the wavelength oy 7.aetnkmz8hm ty6o5,9h(y, (oe. z zul,oplr velocity changed?

Figure 12–32 shows various q6ots/6eq 7(6dnarnd positions of a child in motion on a swing. A monitor is blowinqa/eqn r o6dst6nd( 67g 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 listening f xp81h7 qsrng*or the echo of her shout reflech8ps 17nxg*qr ted by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the siuo)51rruld q.de of his ship just 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 the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary signif. luu)o15d qrricantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air snmqh;dz .i6pi6/zn q1s1pbpa(m9z3uwi)1o at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above ao2* g:kokcx/i school of 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 before2iog:c*kkx o/ the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped fro mkdr(u8z0t7ir xk cqlr27a*, m the top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How hix,0 uz(r rk2cdm 8t*k7i rqla7gh is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete p5,8zgidutt0hh. 3j*k lc.rm i avement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concreti0l5.hht. uj *zigtc8 ,k 3drme, 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 vculkzfv 6z 76;a,+qd by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (aluzq;dk+7v 6fva,cz 6 ) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a soun43ay df +pu2apd 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 who6/gbw2 y9 f48pbrp4rfhx(mm v se intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB ta;ls6 7 b+ei:cqit(swhen fired simultaneously at a certain place, what will be the sound level if onl at6+ctel:( bi;7 iqssy one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equaait rm7- y.1ielly noisy jet engines is experiencing a sound level bordering on pain, 120iyi.e1trm- a7 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is saidwpa 9 tmcb hs1a3/dw:* to have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the baad/b p3a*s9mc thw1 w:ckground noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perl eg;w6z0j u8uson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly unigjw8luuz; e 60formly over 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 strikeswjy 2ld7r)ah- 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 modest40-x f.r xuc sa8yh7tb amplifier B is rated at 40 W. . xfu ay- c7rs84xbth0(a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when placed 2.8 m in1rnmugl+4oz j ,8.bjac.e 4hlhko.a) front of a loudspeaker on the stage. hgn 4.hzo1aj)mle8ol.b .c+ ra k,ju4
(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 i 9zuvh -veg8itx9+ sxyg+44xl8e g .blevel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose le bx.igt8ex- ve h 8ivg9s4guyz9+x4 +lvels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what facgckbwo*g*8k - mtwe7 0j* 8rvmtor will the intensity increase? Inbo*mkrcg 88 vmegj 7-*0 twk*wcrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudewanxm1, n9 o, e.1nhw+sqqh-w s, but one has twice the frequency of the other. What is osn h9,waq+ weh1-w,xm1 .n qnthe ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave i3xfr i)l/e (eln air that corresponds to a displacement amplitude of vibrating) fl3ir ee/lx( air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have 4n6oa9j3jaepa0l+/ c+td;n, icv2k2 t laxrewhat sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (S3nn0 vcc;+d 2e,aijp /x9a j at 4tll+ak6ore2ee Fig. 12–6.)    dB

What are the lowest and highest frequencies thh9-)avqc 0.s v0ki0hrijck+d at an ear can detect when the sound level is 30 dB? ( )avii+vr-0ck0c 0dhksh .jq9See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whath0*3/ cy*)r a/5chh )obotiiv.yn. 6 ajx roaf is the ratio of highest a3 h j o0ya6c*hfi .arob /)civh/5x)tn ro*.yto lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The l 8qtp, g-)ekw l(9xiddength of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be plpt(,q8dldexkgi-) 9 w aced?    N

  An organ pipe is 112 cm long. What are the ,4 sb+l wz-ea*btjn2cfundamental and first three audible overtons*b + z,ta2lc4bej- wnes if the 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 freqd3 euzeks/;( nuency would you expect from blowing across the top of an emp;k3d(neuz / sety 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 open-tube pipes spanni/rdjtzhg-k 5wt9 ,wr; ng the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengthsw,th;-jk 5rwgrt/ z9d of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonic. What wille;,/0u6pqf5r goe+nsp uy 1cp be its fundamental frequency if it is fingered at a length o0r5 qpuf,ee p+c; np1ouys/ 6gf only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play Ei8sja,hc5 vp0 pqe(m: above middle C (sm a,h:5pqj0c8ev i p(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 emi7w.;y0zco efl ts middle C (262 Hz) when the temperature is 2zcelof0; wy .71 $^{\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 h,g w ld6lb+j)20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece offa3hxb*4gd -ij kut*x+ +(wtv the flute in Example 12–10 should the hole be that must be uncovered to play D abodav( hxw3+x4+i*k*tf b t- jugve 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 264 Hmb, vyouygh.j3j k:f(*n *4zvz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is anyo *yj,nv umf*3g z bj(:vhk4. 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. I)y g8*4hmugniftiwz 0a/x)-x t resonates at two successive harmoni4 ma-ix*h g))0twgynixz/8uf cs of frequencies 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 6 j/rht pzip15$^{\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 audm-ezks /**vx qible range for a 2.14-m-long organ pipe at 20 zmesxk* *qv- /$^{\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 t zpvah el3(z4m 1.p7hvmn6ca+(btl-khe outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing wav7zc (l vm .+-apzm6 eanbhlk13hpv(t4es 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 evdq6j1z/oyr +l: lhbm1d* 7fqsery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the othqdd7lo ryhj 1mbfs +:z *6q1/ler string? ±    Hz

  What is the beat frequency if middl/ h*lrt;, cxude 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 (brand X) operates arqn16wsebz q( -bj2 t8t 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 play-e t1r268w( jbqqbsn zed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning6xnb5x- bl/j3o 3ppho fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain yj6opx3hx/ onp -b b35lour reasoning.    Hz

  Two violin strings are tuned to the same frequencj:r7g3 vhg1nu+ hjx;my, 294 Hz. The tension in one string is +j: 1nrx hu7mgvgh;3j then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutu(c np 1dn 7 : 7a-3mcfic++indamcv1p1ujl2des each try to play middle C (26nv 3un-j+7 d pcad1mc ipcf 7+(ma21un:di1lc2 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Cuu h0 w:x dldfn,);l8i. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, :id u,x)l0 h nuwd;8lfthe 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 fr;3ujhge. y+x-. n u(+ ),csvfzoeonypom one speaker and 3.50 mzo(cvy) ,+.x- ;+fuyg3unp.so nhje e from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a yj5ae zeu:0 q7-ik0p cpiano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibratee u0y0:zqac - pki5j7ing at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many be xnqs36;l8eu yie*,fnats per secs8x6,u;nln *y efi3q eond will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 wbvc03 ua(c d3qn 6upggh6:)sHz when at rest. What frequency do you detect c bv0ws6(p3h:dna6qc3g)g u u if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequenml97yqga 11n v3nz9yj/h : pntcy do you detect if a fire engine whose siren emits at 1550 Hz moves at a speeman9pny n9gq :1tlvh1/3 7jyzd of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift im j/qn50j o9yjn frequency if a 2000-Hz source is moving toward you at 15 m/s v ojn0m/yqjj95ersus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When onew9u y9y 1)1jooi5n2djmu hsb g i*5x9v is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequen5g 5xoyjo2 9* 19w9s 1uuhdjyvi)nmbicy of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sbdkw,uy tl84iu +.g uo)vs9q :ound 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 frequenyd.ls4ubvq ot,iuu+ )98: gkwcy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed oflxiwm5, a/ ;s,zig m9f 5 m/s As it flies, the bat emits an ultrasonic ss,,9x;aflmw i/z5i mgound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat ggzgk4d3tw 8/u -m/9zhd-w vr)ct x(atrain car at a c m-gwh)d x(4urtg/tavk3g-w8/ dzz9 frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow smxka us2e28 j zub1*6cpeeds. 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 expectecemz bxju*6 2a21ku8s d beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using r, (xk:l2xb(7top8hlqw t3oeultrasonic 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 sound of frequency 570 Hz. When )4s igi;2 jqfkma f9.j+lovs;the wind velocity is 12 m/s from the north, what frequency will observers hear who lf 2o.vj9 j +4sigisfkq);m;aare 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 aquxpn l i80(of h7o0,tt 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 weaw9/l lp)38r7az sf speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane7lp /awrs9)lzwa 3 fe8’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 tvovxm* -o )6nthe thin atmosphere of a planet where the speed of sound is6xotovv -n)m* only 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 8500 m/s strikes the ocea /fd0exa :j l6fska*v;ttym(9 h-5o efn. Determine the shock wave angle it -0;efv/ eaa:9j *5tft(s fk xdo hm6lyproduces
(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 ;u6/,cdr q;*qnuthti$/theta$ 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) ,znvpuf8;u9 n+yfa gp9(sdt above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 9up)azft undysf9p, n;(g 8v+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 d+y3 .nd hl(zb20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what isd( 3n+d by.zhl the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible r npzw,nbi;(4cdx pdx :,8sx:o ange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consisth7w -0q sn*thms of many plastic pipes of various lengths, which are oq-s* 7hwnm0 thpen on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close tpb)e / 4kxnjb)x*n9ogy; my.io the threshold of human hearing (0 dB). Wha4;ymn x 9ebk)b in.jyx*p/o)gt will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are heuq5n 4etuka qr(8bu2058 ucosard simulta tuunu8or(k820beas u q54cq5neously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. r8*(h x3,1uwsygv t:hsiztg( lc0r-rWhat is the acoustic power output (W) of the speaker, assus -*chus 8wrt(xy v01gz:,r l(3ihgrtming it radiates equally in all directions?    W

  A stereo amplifier is rat xi90 x-ltul0med at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. W0i9 -l0uxtmxlhat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically weabd n 5h ep0yq 7**qszwuicx,.8r protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine7h5.uw ,dq 0qcp*b *8n xezisy?    W

  In audio and communications systehl1.oh8nrsa 0 ms, 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 violih2-bdf4g6g hp n 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 points with a funda:wo81d ,chy(d,ucg yhh ij 95hmental frequency of 440 Hzi1 5 dyg(,d,hh cjwh89hu o:cy and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled wx.ld)/a;;isckq jfk(w66(gd vlavi +y/x s* fith water (Fig. 12–35). The water level is allowed to drop slowlyi)6w/dlfax6 k l;(j adiq vsfxcvgks*/+ y; .(. 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 frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a t9x b(1muc3 jtdube that is open at one end and also 75 cmxd mjc9(b 3ut1 long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obso r3ogxhehe kx;5 77rp/sib75po m-2 ierved 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 from two source7+a uuke :amo3myq93 kbo-w6ns. 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 is the frequenc+a o 6y39qa3muk: nbu7wm-oke y of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. T z(31ag5j3lv8bapf bu he conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?la fb13j 3ba5pvu8g(z   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz.vb9yc wlq *dz.yb247t After it passes you, its frequency is measured *c7w dl4byyq9v .t2b zas 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars fi4b e,buom: ,i0:mi7epyx *e just by listening to the diff e :eyeiu4biix7bm,0fo,m p:* erence in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soun,p n0 zopo)e*b+e4 kgyding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long,)+4ez0 oe*gpnpybk o. How long is the other?    m

Two loudspeakers are at opposite/r,i7izt d i/+rcqq 8y 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 Hrii, d+c/r zi7q 8qty/z, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 dj)b8ck/t j;)3a0iujr).us xo ly 4xd m/s what beat frequen)0 tjck)jbjr4xao)/ u;8l s dyix3.udcy 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 moth hu8al 24(hv lzat speed 6.5 m/s while the moth is flying toward the bat at lua 2hz8l4hv (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 higm qjr/ mqo+t f/i/. 17y bhjck)y84acnh frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is abo/fy qb mrc. c1jimq/h)+n7/ y4kotaj8 ut 3.0 ms long. How far away can the moth 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 on :8t k.jjm6mldce 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,t6djmmk. j8:l 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 listeaka;6ip* 8 ykgning can be compromised by the presence of standing waves, which can cause acoustic “dead spo6;p8i*kgka ya ts” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called e,u0dvovsgho; y k78iuva9l(4y 4 e/b“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 emit a clearee 0sbd4vo8; 9v uyk,(ui/4ho7vlg ya, 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 u:t1qu/ti 0uvilh28q)a+deq the human ear at a frequency of about 1000 dehva 8 :t2qlut)quqi+ iu1 /0Hz 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 grounit1ycwh*ruch f0m(26 d hears the sonic boom 1.5 min after the plane passes dim(i fch0tu2r *w16 hycrectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat isdq h3q 3bkrne-3.ff azx;2da9 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