What is the evidence that sound trav f+ ke7+v)tai ru2hq4x9xhw)d els as a wave?

What is the evidence tha:ohm3nt,5)hrf/w x nql efohtfa.;, 5t sound is a form of energy?

Children sometimes play with atwl:mmo cy 0bsc417n+ brp*v; homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the othelw0 m14vcbys :rn+ tmb;*pco7 r 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 y31 kw,rbujs6 water, do you expect the frequency or wavelength tok,r ybj6wu 3s1 change?

What evidence can you give that the speed of sotv5kv -rw07m3 d0fjx-en2 wfdund in air does not depend significantly on frn7-jdfm vdvfk 053wwre20 xt -equency?

The voice of a person who has inhaled helium sounds very high-pitchefph34*k;l yrs d. Why?

How will the air temperature in a room affect the pi)cmzn. *2bsgzhm/ pw 2j0cli 2tch of organ pipes?

Explain how a tube might be used as a 3p r1mvz1i g)jfq1:cbfilter to reduce the amplitude of sounds in various p:jz111vbrcm3q) f igfrequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–3svw tgnt :4e )aa:2wz,0) spaced closer together as you move up the finge :z 4vse:wa2 )w,tatgnrboard toward the bridge?

A noisy truck approaches you from behind a building. Initiallydu432d npie2 hq8 5 jhppm,ot. you hear it but cannot see it. When it emerges and you do see i 3h.42on5epm8 q2upih,pdt j dt, 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 b khq9w- uwwth ;m.;uq5vicb+/ e due to “interference in space,” whereas beats can be said to be due to “interference 5uw-h+. k /i9bv;wmhqtwuq;cin time.” Explain.

In Fig. 12–16, if the frequency of the speakers no: l2x;:x2awzd m,u wa/ia/ml(n 9ecwere lowered, would the points D and C (where destructive and constructive interference occur) move farnza 9u 22;oexln/(ac:,l/m aw:mxdwither apart or closer together?

Traditional methods of protecting the hearing of people who wofj uc-pn/v 9opapd (/cz6 k 3yxb,2t,jrk 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 whickc 3p,/a xjtp, fzdbn/-(v u2c6 p9yojh 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 supp:ds veq3 sl.t+.f ym t+*ck1werposition of t1d.kf*w cs t l :vysq3epm+.t+wo sound waves with slightly different frequencies, 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 sota( t3l(wl66s cewj1 furce and observer move in the same direction, with s16jt( a lwce(tlw6f3the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound y(6ae:(pzpaxb 0+m+ ww5jlfer ,x9icheard by a person at rest with respect to the source? Is the wavelength or velociwbapy(e 5 ri zmxwjx9e:06l ,+pc( +faty changed?

Figure 12–32 shows various positions ofg/i*p zve w1m7 a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whi i7zgwp v/m1e*stle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her shougviu v7( :jur:t reflected by a cl u(viu:g7v:jr iff 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 side of his ship just below the waterlinec. n4gqw 0q:fv. He hears the echo of the sound reflected from c:0q vn gf.4qwthe 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 significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng n8dii)*7p+d)x4zd)laspkhlz 4ij ;o ths in 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 jusys v4xtdrb439 t above a school of tuna on a foggy day. Without warning, an engine backfire occurs on anotd4ystvr3 x49 bher 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 clif0v/ ba/git2zhf. The splash it makes when striking the water below is heard 3.5 s later. How high is the cz h//it 2bgva0liff?    m

  A person, with his ear to the ground, sees a huge mctad 1* ,fqn /1vzcu/stone strike the concrete pavement. A moment later two sounds zft 1cd n,/uqcva/* 1mare heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distanc w;n7e e6,2m jjju,yahe by the “5-second rule” for estimating the distance from a lig7j62 jn aje,emuh, y;whtning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound awx ypg0k ;alvqz*7 ,8xt 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 whose intensitk5b6ik5ij ,z acxj.v jco ,n1-y is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired sif1q n ers tzsp1ggpn*ta-9r 28*rf- /fmultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensitiep *-e / grtn*8as zr1f-tfsrp1gf29 nqs, not dB’s.]    dB

  A person standing a certain distance from an airplane with+i- zk)wz0ydgw dfe6zm,j /. w four equally noisy 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 oidz6zy/z+. )-0 wwkmdgjefw, ne engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB,9krbf ( m* lb4wuh3*kp whereas for a CD player it is 95 dB. What is the ratio of intensitiklu kr**h(f93bw4 mpbes of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power es-gxjc4n b;//coxs/zs(tv 0output of sound from a person speaking in normal conversation.ctx-n//;4s(sb jx /veos0gcz Use Table 12–2. Assume the sound spreads roughly uniformly 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 strikes an earl 8g;0fqbru z*c b4a3rdrum 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 i+c dg :umubp9wyzko*z10r )z 4s rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you w4+bw*o9c rz:zy0mgu z1 )kp duould 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 ikw dt2s)u4)*k g rvx7an front of a loudspeaker on the s4srg2a) w u7*kdt kxv)tage.
(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 dB. Whaxvozv(xpyp,*enti9s :aup 6c 0;y5t.t is the ratio of the amplitudes of two sounds whose levels differ by this amountp:tz.(vonu;p sxyye05apiv, x 9tc*6 ? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) bgti9 za9gfv8d.b u.v(y what factor will the intensity increase tv8zv9if ga.ud.9b( g? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displym l1a+ 7uis(racement amplitudes, but one has twice the frequency of the other. What is the ratio ofl1m7y su ia+(r their intensities?   

  What would be the sound level (in dB) of a sound wams l/*)9gdr jbfmp k8.ve in air that corresponds to a di*b p f)sr.9mdmgk8l/ jsplacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound leve(ag6n6o fe,ru h9qos) l to seem as loud as a 100-Hz tone that has a 50-dB sound leveo6e,o6hf)agu q9s r(n l? (See Fig. 12–6.)    dB

What are the lowest and highest fre- t.i2i kxv)edt(;tdc*du. fnq vhe83 quencies that an ear can detect when the sound level is 30 dB? (See Fig. 12–6.23x8e;) du ec.t iq(idv kft-.dthn*v)

  Your auditory system can accommodate a huge range of sound leveyj+5x7 le3)qp u(pse2al c0xrls. What is the ratio of highest to lowest ia25sjec+ lqx r) l pupx3(07eyntensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin hal+vm lomhu 9zq +;m31as a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it haum+m h+zl3lmva9q 1o ;s 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 , e q+cj*ih4aeaudible overtones if e+ ahij ,c4eq*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 frequency would you expect frn0 a,k qf7ytrsdq: gnv+2 rfp400osgq:p9as0 om blowing across the top of an empty soda :f 0q+vqtn qrn00ksp ,ss94o0p d2ag:rg7yfa 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 ssi8l 6l/ r8 ;l;mw1zjxeykdz 5panning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes requ zwl8jx1;si k;/ez rlym56ld8ired? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a fb8pkzfvcpn4fb8 n): bl b 6v9-requency of 540 Hz as its third harmonic. What will kf vvp8cbfz:p )bb4ln9b6 -8nbe its fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E l4lfd,dyt2s.o( xz6 *,nu ncp above middle C (330 Hz).(*,24yc s6d, xzdlt.u plnf on
(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 opeg vhy95atiib *125 jisn organ pipe that emits middle C (262 Hz) when theiy t5ij9s 15 g2vbaih* 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 at 2)xv /2xhqb8yfo8ar*s( z9qs y0 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute qsr/+ o oeeu6iiu-f) x ::4znhin Example 12–10 should the hole be that must be ni:uz+fiu o e4s6 rxhq)o-/e: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 264 Hz, 440 Hz, a kvhn:p, d/d sl6d iwb/t1.gj4nd 616 Hz, but not at any other frequencies in bet/lh sw4kidp db: djg,1tv.n/6ween. (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 resonmjba:;(3t fdg29xuk bates at two successive harmonics of frequencies 275 Hzdj;3x( ftb m ugk29ab: 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 -k(1 c x86ewzfhi*v+m 0fw) etbbnf s3$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14 fnc2e+ 0u5oid-m-long organ pipe at 2neu +2i0do c5f0 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxima scgx+ni6.j0 ltely 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to th6i s0.lj+cx gne 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 adk 9b,/vgjzj iq.+t8k,fk/ye 9ywe7 vzjust two strings, one of whi.yikj t/wv q ,9/e98 ekjkzf7b y,zg+vch is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) an fs/* gdv4va2dd $C^＃$ (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 665+tl.,qool jeqnphX) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they5pqntqh6.l ole +oj 6, are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces wf4tn206yb) ,itlg h()lkr co4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s lwtb2g kfinto 6r()c0 4 ),lhywhen sounded with a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to tp g)h h1i)r3r60wuisvq+ 0 czlhe same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency3 cw0liq+)0suhig)6pvz rr1h 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 tmep h2 hoj)b9q+1gj/m o play middle C (262 Hz), but one is at 5gq2 /b +h)9mjepmhoj1.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork Bd6pamcik: 8 gkxxee-m- j/)i2 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 edxa-j)k i8pg:k-mc 6x e/2imand 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 apartd ) okjbsw2h+xky2*oe/ 3q7xw. A person stands 3.00 m from one speaker and 3.50 m fro22/ +yodk3jo7q esxhx wwb)* km 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 suppk +m /z-*+jsq*+ekcf3h upiweosed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the othh pk+w*e/s cefq mk+u*-jz+i3er ?   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 ma3x ccs,4 c/fdu3;iivr 9 ft bnmzy:)h(ny beats per second will be heard? (Assume )i4crdvu/ ( 3nx3 if9f:bc;csm,ht zyT = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire (zhcn mbhe.6a,d ry9: engine’s siren is 1550 Hz when at rest. What frequency do you detect if you zrm9,yb e6:d( n h.chamove 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 engina0v.ts2djcj 0e whose siren emitsa j0 tsjc.2vd0 at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towe64ixco;hy*; o/i o0(dk da b4u6 raljard you at 15 m//04d (do4 r6a chae*ojuk6;oi;yxi bl s versus 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 ejy:3 v. qzo)a-0nrng horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T =v -r0za.ny eg3 n)qoj: 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receh:y h9nw sry8g 9m-g:nives them returned from an object moving directly away from it at 25 m/s What is thes9h wn y-hmyn :r:8gg9 received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a vb)pgjghgwzf:870+ ,l j /to 7u:1vx f+kijdswall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave witthj0 l+vk+ p8j/vf: )jbwsgo:77xzd,1 gugfih frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Dopplef9 qk.71vndd or experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tonek fd1d7vno9q. 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 t(t -y*1g.w jhi hhx)cxo measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flt 1c.hh )jh i*(x-xwgyowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency f2n*gi jb5gypsvpfg 62). ,y2gohd7/a ts*io $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velocity is 12-m bppk8mjq /+puxf -2 k- jbup+x/p-f2m 8 pmqm/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 speevgln3soujb: iego58v s) .1 5fd 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 i,rhu.i, odjki 26zr3urc c(m ,s 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’s rj 6,o,mz dh( 2,kr.uu ircci3motion?    $^{\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 otmyi4 7f/p: b(wag5o- e+;pyti+avm atmosphere of a planet where the speed of sound is only about 35 m/ egam+/:a+ 4om 5ot7 (yiifwtp-; byvps
(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 travelingsz49, c-svag vrd4w xyw,tv(7 8500 m/s strikes the ocean. Determine the shock wave angle itxa4gc -zrvs,tvw,4d97(y w vs 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 iaik;z8* x8wd$/theta$ 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 exacu /ha(;eg x b)/ixm8;*enfhiw tly 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 horizontal dmi nxeah ufw)//gh; ; be8x(i*istance 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 sooc brm87vru-:nar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes- crourb mv8:7. If the maximum 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 audiblmy8,t uxfh kqm325e/ ie range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.r y,xd:6cn6at It consists of many plastic pipes of various lengths, which are open on both6ryx c:nt,6a d 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 to the threcpcq76o* 5ah qt9) cqmshold of human heari7 aoctcpc qh*9qm)65qng (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sounde sup8(xi rzaq )yw200gh+wi / and an 87-dB sound are heard simultaneouy8uqrzh0wi0ga/ ( e pix +w2s)sly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 9fe1 936hhjjsa)xay gv1xiv;105 dB. What is the acoustic power output9jx)h; 1 agehj3 as6vivx9yf 1 (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rajfes /w)8zaa fgz3l82 ted at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in wat jw)fa 8z/z3aef2sgl8ts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over tha ip(9ixf0a/ ,jx qn4ieir ears. Assume that the sound4j apa,0i(f qxi/i9nx 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 engine?    W

  In audio and communications system0.cwpw xiu5 cwcn3 iq+6 mh+2xs, 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 frequencyg b2 (1lrzed)n oog;g7 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 fixedvj-z(2 : .eurbzzlg zjewx 9)o.y14nv points with a fundamental frequency of zy(l wrj.9 ezz: jzn14 xbeg.vo)2v- u440 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 abov8g7hijnjn:c1 6fm44hc 5ws /rv 0fdswe a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube aboves44 jm wn/fc1iwsh0 fjnv8grc65 h7d: 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 dzhp)4*pi38a x mlyb7jos a2 4mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resoix 4jha*8d4 2papms7 olb3 )yznance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as oncaj 6r0jxneqv a(cf31 zew(94, u9ueje 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 sou/obskpn0nebb5cb*7w 9m -8zyrces. 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 frequency of the sound 9c7b wm85s b-be/ko0z*npbyn ?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on thezdy05ax-/m o q stationary5z x0y qmo/ad- 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 approaches you is 538 Hz.t gcxr5qp2*dan/(ki( After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume c( rqx5p an2tci *gk/d(onstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listenil ; (zhaeld3l/ip1p1q sr ;bew38ns6ung to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drse; a3pz(q 31 u epd;swlli1rh8l/b6nops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 1/st26djb)jf7m 1u 5wex - buon1 Hz. The shorter on7/o5 wd6jumut1 sfe b)n-b2xje is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad ca,zlj pxn z7+*u0m6qg yr as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speak70qzgj+um*pn, xylz 6 ers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what bea bu bo1, .2unr(.fq gm/hebo,nt frequency would .b (1 h,bfun,/o qmeng.ruob2 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 at speed 6.5 m/s while the moth ikk.g 4 fgwh y4o7r+r6ds flying toward the bat at speed 5 m/s The brwhd7yk. +g f4g4k6 orat 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 approa, fr e:3 q;srtq /l:mbso;t;etxie,x-ches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so that the echo from one s ,t;q r:r;3 mbitle / t,;x:ofeesx-qchirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was onqbn4fe3*r*y.opo.o oj wdu8 2ce 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 deepr*8o4n3ubd.oq o e*f. 2oy wjp 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+cr/ vdn.*r ky listening can be compromised by the presence of standing+vc* r.kr ndy/ 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, 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 “singing rods,” involves a long, slend .ntym00x;w . gispd/mer aluminum rod held in the hand near the rod’s midpoint. The rod isydp .xm ;tw/mg 0s0ni. 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 for0 85tvuj2b29w gv ;c h9iyejxn the human ear at a frequency of about 1000 Hz jnxh2vt9ejw0g cu;i589 v by2is $I_0$ = $1 \times10^{12 } W / m^2$ 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 Macwy 1b/n w z9b mt)v-tr7sgxkniha(8,:h 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitugr yna wi,b bkt9wt(1sz7n:v8)hx/m-de?    $ \times10^{4 }$ m

  The wake of a speedboat is fv 1rxfle jo.1t eo91115 $^{\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