What is the evidence that sound travex :n p(vh0+d) w/avmtqls as a wave?

What is the evidence that sound iszc g.pwzv2(e / a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string to l l-moilz)yjs 5*n7p nyt+6k* the bottoms of two paper cupskylnp no5msl* yij)z6-t+* l7. 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 63 1i p4yrefzmf.j:xlyou expect the frequency or wavelengl.j6yzpi 4mxfe 1r3f:th to change?

What evidence can you give that the speed of sound in ai*sb q)s h+i2j8s; hgsw gbvb18r does not depend significantly2hh b; w18qg s)gsbjs*8svib+ on frequency?

The voice of a person who has inhaled helium sounds*p8e 3 k+ao;dc0ve2yca*.l8np jp knt very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ px49h1hcdvc/co 3/9qgqhyp v* ipes?

Explain how a tube might be used as amy c ob/ijla544b7 v6n filter to reduce the amplitude of sounds in various ylj b5o64ni m b/av7c4frequency ranges. (An example is a car muffler.)

Why are the frets on y(7 hw9y9iddv9ag*t4pvjcl ( a guitar (Fig. 12–30) spaced closer together as you move up the fingerboard toward the bridydlg9h*dapj9 (v v9y (t4 c7iwge?

A noisy truck approaches you from behind a built1 wl69f t.xd ug+/:5fkrsi pnyfe+l8dj :jt4ding. 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-frequency noise. Explain. [Hint: Seet +fpls4 gfj yw6rnt e /i8.x:5dldj+ 9ukf:t1 Section 11–15 on diffraction.]

Standing waves can be said top s -c3u3st0z-*j; (vlap nwhg be due to “interference in space,” whereas beats can be said to be due to “interference in time.”s-z (sgup03wlj ;3- tvhca *pn Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointad y6 5fm8nob md rbk3lqy(re5q fq0ps/-;e62s D and C (where destructive and constructive interference occur) mos fqarq(rbedo3p2y0en6 ;q /k mf y5 m5l86b-dve farther apart or closer together?

Traditional methods of protecting the hearing of peopll m )z tw.p1kjb6*vpg3qn0+zpe who work in areas with very high noise levels have consisted mai*w01q6 mpp.lpgbvn+ k t3)jzznly 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 reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can be thought of as-m )i ki,twr /4bz*yih a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which -ibz/mihr*,i)w 4kyt 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 samenjmr(roig ,xwq+ )*n( direction, with the same velocity? Explaiior,(+qx*()jnmwng r n.

If a wind is blowing, will this alter the frequency of the sound heard by a jzj adlzpy;hl+e;8s(/ i- , drperson at rest with respect to the s ydpj(jl;i+rd-l,8 az;es h/zource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitoy sr7hw /azu-0r is blowing a whistle in front of the uhsa/y 7w 0rz-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 l;yf ivr47( eavsy-g+j(a7qyo istening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lakegi;y 7+ (as4re yfyvo-(7vjaq. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the s t5dy ;m-wai3side 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 seawwiy3t5 - as;mdater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths i*9iofua)l26l ,.kjdmq c om-hv3va (c6e )rwun air 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 jusmk6er,)vlpul7i 2h i6 t above a school of tuna on a foggy day. Without warning, an engine backfie k6 6vul,i)2imr lh7pre 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 ozcg r(4qiyvr;a 9u2bt h)o.o 1f a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the cliff?rb(;or1 oh.y 4t2zuac9g qi)v    m

  A person, with his ear to the ground, sees a huge stone strike the concrete r,i5x).id9 fcce1dji pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far awijcx5i1 i9c) rf d.e,day did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the ojjr vi-qp /-0“5-second rule” for ejv qrp-0/ioj -stimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of fg36zhakc/6 wg1vr9 (fni03f jbr ei7120 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 whose into wg8aoi c1c h za0- 9kpj)-q(7(eynyoensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 9bjk7u 9 4wf0s5nk)at r9q8jrr5 dB when fired simultaneously at a certain nu5 jb9 r49qr s0rk8k 7)jfatwplace, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally nok 9i6vlad25 f 8-pxrrkisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the l rk-p ridv2a6x8 kf95captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 d9 -w lc,y ,zc(xgc)8.lwh simdB, whereas for a CD player it is 95 dB. What is the ratio of i mgs9(l ,yi c)c8zw,xdc wl-h.ntensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal convers1z bp9*qmurf*ation. Use Table 12–2. Assume the sound spreads roughly uniformly over a m * quzb*pr19fsphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an ezr(hfxwa4ovlmb o2u+8e; +7e ardrum 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 i-8 yime..+b1 xnnw tum;+tjt A is rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimat +bnu18ym; ijt.+ewmt.xni- te 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 d*zp nk+ vr /gsgy1,sv(B meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. */1gzyp r g( ,nvss+kv
(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 s5 o5tra )dw5f5yu8ideound level of 2.0 dB. What is the ratd)da5 5e ru f5w5i8ytoio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatq cy7,+;1iehe q(ie gr factor will the intensity,yhiee;+iec (rg 7q 1q increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bu pzao a9vvb8(+t one has twice the frequency of the other. p8(vvo a+9zba What is the ratio of their intensities?   

  What would be the sound level (i icqf:8; -zra.bi h,y-j/r : laphnse2n dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm:f,-h bpz/;8n l:i.ehra2- y crajqs i at 300 Hz?    dB

  A 6000-Hz tone must have what sound lev.6ldczsnr nv)r4, 8o mel to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 12–6.v.n cn d6r,)olr8s4mz)    dB

What are the lowest and highest frequencies that an eaz8 vxl)6rg nxoiyia ow6f1v+n90eb1xahm(( ;r can detect when the sound level is 30 dB? (See Fig. 12–6.)a;x n6wh1xynxoom1lz vi+6)gv r0i f9ea (8(b

  Your auditory system can accommodate a huge range of ozns ;mt+*j4j7 rpvz :x j:9v tosam.)sound levels. What is the ratio of highest to loas;jvm:on7 t )jo4xrvzmp.szt+ *9: jwest 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 44qx8kleka3mx 06-.err0 Hz. The length of the vibrating portion is 32 cm, and it he03kem.-rq6 8krl xaxas 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 thrqqfrb 9lq5e(9bm ll 4yoa8m. /f3ey0iee audible overtones if the pipe is m yb90mflif5a8 elqqo 93lrqy.e/4(b
(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 frotj 06q9j -ru-ewuub4zm blowing across the top of an emprbj-t69-4q0zu jw ueu ty 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 w9xio0l e glh ji0mjb-twii(cv9: ,z-(ith open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths0 wti i9g((b ill9h,-v xij:jceoz0 m- of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency oyz-* h,+npc r,5aotabf 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its ,-yba op+ca ntzr*h,5original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abohznlr4+ dehi4 k/nd18ve middle C (8l h/h4n1i +nze4kdr d330 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 middiw1 e3li 47apumb (a**p.mrlp le C (262 Hz) when tpap. 7*lpbe3 r(w*milia4u m1he temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune acu 480wwuuwk9t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 s)8gl81.v4 l0rhruw t rpy,akm rsqg:8hould the hole be that must be kry 4armt8lr80 rg g)1:8l v.p,wus hquncovered 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 264 Hz, u7)fvjf ir, i-440 Hz, and 616 Hz, but not at any other frequencies in betweer fii-)v ,7ujfn. (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. It8 n9*nr xl0gcb resonates at two success*nx0g r89nc blive harmonics 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 3e 6 w( kcnygs6nppi/kf9g)q b/dj8m7$^{\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 with9rdqqy p u kae,/txg3a ,/b:2fsf6,pchz/6g qin the audible range for a 2.14-m-long organ pipe gaqhq3u 9x2/prk: ezg,pd t q,b/s/ f6 6aycf,at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately aqu):rgx2 +mc 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 ofq : ac2xgm+ur) 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 a0nnf ampvq*ekzq0 z: :s+fn+s7-u: bwhen trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the ots afzqqf :+0nbv-+k0 a e:un*7 pnm:szher string? ±    Hz

  What is the beat frequgxy; 0hqt;fv*w.ohn: zf:0bc,mt. g lency 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 opqlkusw l2 9(p,9r.slqmmffhv j89x2)erates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency sjlwl rk2m,9)qpf l98.vhuqx 2fm(9s5000 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 tuz7/uqitw3 u kp;6i. x:x ,ciyuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stri cp. uik7uuq i/wxi:6tx;, z3yng? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensis)1us40 tfz/wedaldi::i yz mxl4 v(, on in one stri)/lzei zm sai044tdfxvsu1:( w,ydl: ng is 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 flutes each try to ok0fv22jxgj0.-fr(vnp gui 3 play middle C (262 Hz), but onek2giuj fxv -3nvo2r00p(jf.g is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and Ce6m79 g;f8l/f .h0vvn a*vv adoe94o kwm*ogb. 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, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequence 9 h.mf9o6dk*ovw gb v 7e48*vloa;/a vmgf0nies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m from one speaker and6qxzvum1kzr(n34m s 9 3.50q(u vmz43mkxsn 6 z1r9 m 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 pi*u -/t67ng ycvjb4jo6m+ c1xfvw,hkoano tuner hears three beats every 2.0 s when they are playedj6g c16mv*cv xu4 /b k-wh+oot7fnjy, together. (a) If one is vibrating 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 2rwe q r)8 ut,8vlb1t5i.64 m and 2.76 m in air. How many beats per second will b wuir5q,rt8evb)81 l te heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of m.e o 4. *o9ydv qanhde.:v9gma certain fire engine’s siren is 1550 Hz when at rest. What freque.vv e 9hm. qydnmodg.oe :*9a4ncy do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sireak l:-bny5r*qv5x(+azn oimbu)* 1lin emits at 1550 Hz moves at a speed of 3uo+)v5b1*y kq 5r:ni znla-maxi*l(b2 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a.-w gq u:wj;b(cary.n 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequenciesyr;w . n.cjb-wu:qg(a 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 f) b)th0iem7n-vmm. vsingle frequency horn. When one is at rest and thei-7 )bme mm0fv)vth n. other is moving toward the first at 15 m/s the driver 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 out ultrasonic sound waves at 50.0 kHz and rei97xe x+h7+ra 8me+ek5 rf 7crceb9euceives them returned from an object moving directly away from it at 25 m/s What is the receive cu77r7ri+xe+e9exe c8r kf5h+ab 9med sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat e v9/:mg )rysedmits an ultra ysgrvm/: d)9esonic sound 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 te :thgnf h0k)f *3pa3experiments, 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 carn 3fephht* kt)0f3ag: approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blo6l 4hd0jpg r2h4xyep7od-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 x6 74h4ehpgjryp20 d lat 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraso 2lav rs,z;u;rnic 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 the wind2f.ee ez8 n/n8/j rznl velocity is 12 mnze8/8f. ernn/l2jze/s 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 land if its speya s-uwg-00 aged 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 sound is 310 m/s ,ca x +4 4ya7fm1vumaf(a) What is the angle the shock wave makes with the directi m4vf4au+ fx1aamy7c,on of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the t ysnk;x*:vrtn of h2wckzbdhw7 87),*hin atmosphere of a planet where the speed of sound is on )t:k; 7 hwb,fdh8nnykrc*xo2 vswz*7ly 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/ov,np q9z5rtg (wco.+s strikes the ocean. Determine the shock wave anglevtp5.9zon( o+gwcqr, it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ppucj,xqr zrzv9 lj728f 5b04$/theta$ 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 ab ndgf3ez 6alru7/ 2 )og1zhn-hove the ground flying fasta)67 z n hd13gro2n/z uefh-lger 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. 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 tpwt/jitu 72n 99wy/i:bgs 5v20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maxiiptngwt s:viyjt/b752 9 /u 9wmum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human aur5d8o 2z1g bnhdible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of ms lt:)q7keke3yy 7c-aany plastic pipes of :qkle3a7 )-c7tsykye various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes aj.euc62zf6n t sound close to the threshold of human hearing (0 dB). What will be the sound leve6enu ztj62 f.cl of 1000 such mosquitoes?    dB

  What is the resultant sound level when a 8i9uhwrbbs8 eg 0rw:*n 82-dB sound and an 87-dB sound are hea:g b8i0ub*eh 9rrsww8rd simultaneously?    dB

  The sound level 12.0 m from a louds 1ot9:tqowry )peaker, placed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assumingwo)o:y ttr 9q1 it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. v tckw6tyj.1 f.+twny0l4(- a f j0wqzThe power output drops by 11(.q.+yj ky6ttv0twac zwnj4 0lwff -0 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircny2t (b noz98wfclo8 -raft typically wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an fw-8o n z98ocblny2 (tunprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems,a ujyy1z6 2i-e 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 t3p0fenpz4j rffi62 q*j +bhy8uned 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 poincg;fdt hpg.26 ts with a fundamental frequent g;cfd. 2phg6cy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fille/ my2s7fxsjr;g58 sabd 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 0.39525 7fx bj8ygr;ssa/sm m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thag/a8sghb r4 xzj9 *8nbt is open at one end and also rg*g8 b4 n/9abz8xhjs 75 cm 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 observed to resoim9qas6*ye9 49kfti0 jdj:wpnate 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-* e- bakdz:f7ian h7+rHz range coming 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 d h-:a*fb+akze7 in 7ra point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stqx xt go .3(*yl+wcu5vationary. The conductor on the s xyw5 *q+tvc3.l( gxuotationary train hears a 3.0-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 approa; txn 9bobclu6dq86 );o)hmkaches you is 538 Hz. After it passes you, its frequency is measured a o;m ;x8 )dqu6nbcto9alh6)k bs 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate thevlnlsr 2afr*y2/kiebk(80m0)l *y um speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose th sk*m8em0ari(vu0*y/ln blfl2kr )y2 e 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 b voa; +0uvp. wl;qg1vtogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long01l;ovp.wqv;+ aub gv. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad 6i u90 o.c;eodoki2 jhcar as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers haveek.hi0io;j 62o c9uo d identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally /e 04p99q5w b wrglgtlabout 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflect 9w5pl4 /lb rgtg9e0wqed 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 speet5:1 n 0 ewoetdozllbwy/ 4b7:d 6.5 m/s while the moth is flying toward the bat at spe4o:lbtyw/ zne: l1eb7wotd0 5 ed 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 apprc2ar3v. ,p/n)dnc 9nz xu, adhuww(*b oaches a moth. The pulses are approximately 70.0 ms awvdhrc,/ bna x,w9ad.(n*zcu nup32 )part, and each is about 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) a3qx09( cu5 svp2cjrk:1tg ad was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in suchc1 r 9kap3g0vu2atq(j c:5xsd a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening c7i2o87t bxh msan be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, ant72ox7i h8ms bd 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,9: q/jb fsbwg,” involves a long, slender aluminum rod held in the hsbjq,g :/bw f9and 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 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/iq,jc a-p7 vf9f9bl m dpn5)qy of about 1000 Hzf5q 9lafj9qmbc-v /7 pip)nd, 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 thej:h4qnfjhng b.yjoq;8 56g0 u ground hears the sonic boom 1.5 min afbj4u0o:q ;j6h85ng.hf gy qnjter the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 p r+gxo0-gr*n $^{\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