What is the evidence that sound*hvhru: x nq-o h(c+w( travels as a wave?

What is the evidence that sound is a form h .-zp)*x9;d3w7fy kmp ki,fgt ilu.c of energy?

Children sometimes play with a homemade “telephone” by n52yo/uw:.,hcj5 w.t wz nwzi attaching a string to the bottoms of t5w wn2o/nwy5:. ui jz,c.wzthwo paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, do you e((uxcbymb/w, w0 ehs5 y-a-ql xpect the frequency or wavelen5w w,csl0h u yx aeb-yq-b(m(/gth to change?

What evidence can you give that the speed of sound in air does not detph+knc4v 9;vuqy; 5f pend significantly on f4vy u+5 ;fcn9hvpqkt ;requency?

The voice of a person who has inhaled helium k5(pdhp )qzio vu27i:sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organv0 s9mp ,. qdj;p( gomtg-i 4gy+2ezhn pipes?

Explain how a tube might be used as a filter to reduce the qo2oqz1;2n( dmc r-yh amplitude of sounds in various frequency ranges. (An example is a car md z hnq r-1o;(yocq22muffler.)

Why are the frets on a guitar (Figwl,7.hn8 qes *knon- q. 12–30) spaced closer together as you move up the fingerboard toward n*w7hk8eo,nl-n. qqs the bridge?

A noisy truck approaches yxpe/wz 910 illou from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, iel 0x/pz9wl 1its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “ipoy1xei(sl3ha go9oyd7vtb6ac,( :0o7x9 xxnterference in space,” whereas beats can be said to be due to “intxeb3h dclo(xyo7o:a y 6gs979,i opxxat01 (verference in time.” Explain.

In Fig. 12–16, if the frequency of thz ss0k3xpfk3, e speakers were lowered, would the points D and C xz0kk3sp3sf ,(where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectingm(-m2*( opwhhhpa wl1 the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noiseo p*h -2(wlhmhap m1(w reduce the sound levels reaching the ears?

Consider the two waves showjr;g +y1dl j:hn in Fig. 12–31. Each wave can be thought of as a superposition of two sounjy: hgrjl1;+d d 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 source and observer move in theskhvk e*t g/v- d9.v. vei3+wue4zm7e same direction, with the same velocity? Explain 9 k7t. eehs+*vv-zvm/iede4. ugvwk3.

If a wind is blowing, will this alter the frequency of the soun1r9ly 69mc. vw1hnptxsh+ui/d heard by a person at rest with respect to the source? Is the wave6mux/1ht h+1ycrn 9wvl si p9.length or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A o z68-m*mmaz1fz hwtadm)/nx o6;z9 fmonitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hearz;o-8zd)t6 ao1 hnz f6w9mmf/*mx maz the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the ly0tbs yw 6g 5l7.i-k.i xrwn3pength of a lake by listening 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 thp ygnr5- wx .isktlwby036.i7 e lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side 1,b-t* j blf4yewuul,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 signil4,1lb jt, fywuu*-ebficantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the waveleng,f4ng0u(vs 9-o4rwe a o tscpxbw01 7bths 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 just above a school o: j1vx)a0zpxcd( )jxdf tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elaps jd a)xd(1xv :jzxp0)ces before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clihy g4ulcu5*6 j; 3b3ur i0uhnqff. The splash it makes when striking the water below is heard 3.5 s l;urjn43 uq hiyuh0u 5g36lb*cater. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge sto76fv.lk ulc ;vne strike the concrete pavement. A moment later two sounds are heard frcl6 ;kufv 7lv.om 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 eaugkaywqxmm5(1 ,o: 9(8apl s-v gis(rror made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if tymskml 8-ova5a 9:g((q (up,xwi 1agshe temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level o(dk:(,fg4obl w eg2ru f 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 1 47+aqige2r/4chxy oqly k r2sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired si* tfz5 j ;sewxx9*g*kumultaneously at a certain place, what will be the sound level if o*zgx*95uxw*; tje kfsnly one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain4ht 9qq e2vo1z distance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this pq9qovz1e 42t herson experience if the captain 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 dB, whereas fokt nm. *bedz5 rj.n9t5s1 eka+r a CD player it is 95 dB. What is the ratio of intensities of the signtk5 tkj +e snzdab1r9mn.. *e5al and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power outpua5vviq56p : jmt of sound from a person speaking in normal conversation. Use Table 12–2pjqv:v5 i a5m6. 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 eardrum whosea x7b42 oy+dw d-yj*eawxe;0c0 gq/ us 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 ato. c9i ,d7j/y, qziyzd 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the soodj yz icq,.9yd,i/7 zund 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 mi3 njoyppljsafpzm32a. 261a3.m qmt4 ut r+3 in front of a loudspeakel2 3 .pz.2tq 3maaf+mp3pu smjrnj4oa 6yi1 3tr on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typicarsq)j1tez*a;: ji *w9revsy 60 s3ydc lly detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whoedqy * zrj6jt1s3a*scs rw v9 :);iy0ese levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the intens8 qkb 9/vzan3fityv3kz f/q8 b9na increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice xc94g4-dvatu the frequency of the other. What is the ratio of their integv9x 44- actdunsities?   

  What would be the sound level (in dB) of a sound wave in air that correspond l jc/0u:a-bhos to a displacement amplitude of vibrating air moleco/l-c:haju 0b ules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sebq+1bjq 4yd:o em as loud as a 100-Hz tone that has a 50-dB sound level? (Seey1qodb+: bq j4 Fig. 12–6.)    dB

What are the lowest andsww0rdipw-ccq ; qk4tb /,: n9+gk*f y highest frequencies that an ear can detect when the sound leve0+ksc4 w/ g :tqdiqf ,;*c r9ywnbpw-kl is 30 dB? (See Fig. 12–6.)

  Your auditory system can accokk.-z ux7mec8cogz4px 6 (4 evmmodate a huge range of sound levels. What is the ratio of highest to e6v.e cx7m pzcz4ogu-kx(k84 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 h vl 5kk)fl/62f1 rvukkas a fundamental frequency of 440 Hz. The length of the5vfu fkv 1k/26)klklr vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Wh)hd6s; n, myziat are the fundamental and first three audible over ims6); ,hzdnytones 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 frequency would you expect from blowing across the top of an ezv:wnp5q plv4bhz3; 7mpty soda bottle that is 18 cm deep, vvhp: zw3b qn;7l p45zif 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 spanni9 ua(nfu)7oncng the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pipes require)nf u7a(9 cnuod? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hasog21 huwxwj.twhl(gh 56 x1i; a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its11 oi(w5;hg6th xxwuhg .lj2w original length?   Hz

  An unfingered guitar string is 0.73 m long/ )zeie1nu5 ek and is tuned to play E above middle C /eui1z5 k)ene (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 opep fotl w*;ub66j1u+*ktj3e/q o ls b:mn organ pipe that emits middle C (262 Hz) when the temperuu6ltkl 3;sw1jb**qpo j ftmb:+6e/oature 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 atpk ;6zdsx 5.ek 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpijgk e:q(x4e wwa)..txece of the flute in Example 12–10 should the hole be that must be uncovereg):w t jkx. e.a4qwx(ed 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, and 616 Hz, bxp0e//0)om on:j t plfut not at any other frequencies in between. (a) Show wx ppo) /n/m el0ojt:0fhy 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 w;zkb8/i, d fwimiz /1both ends. It resonates at two successive harmonic/ w fiizk1dw /;m8,bzis 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 0ke:jso*bv2 4jsj1nf $^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-long orgqj/3sgswg c8f s 29nd.an pipes. 8 jsgqcds3fgn29/w at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 3,-5sfspu3ujfftnn 0 2.5 cm long. It is open to the outside and is cljuf5t3,3s 0f-nfn spuosed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0dh13r eu++hbvkdj.f32tmz *j i sd6b1 s when trying to adjust two strings, one of which is sounding 4 iu z+bk6j *2.ddm13vd+tbhe1f3js hr40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequencyo tp :-8 gl)aw-8 o/afrlgi6pn if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kqb qh0s* qa kzx+;v9r4Hz, while another (brand X) operates at an unknown frequency. I q*xkb+4; h0qszvaq r9f neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produce5(bkuc gxom*c 5;pr6x s 4 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of * 6c55 (bk;rou gxcxmpthe string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Ho4t0 pk4f)kh vz. The tension in one string is then decreased by 2.0%. What will be the beat frequency hear0kfhto k4p)4v d 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 pla)ox+ uoxmc f.6y middle C (262 Hz), but one is at 5.0°C and the othcu6 fo)x+o. xmer at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Foq ju -gk7psg(s 4.d.crm1 )wygrk B has a frequency of 441 Hz; when A and B are sounded together, a beat swuj q4m(g.-g dkc7g.)syr1 pfrequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. b)er3 x1**gy6xlydes A person stands 3.00 m from one speaker and 3.50 m* elgx13 srb)6ye*xyd 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 :clkj.ci) m,x puuw2 487ngex132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 1e8),l2ck :mu7pwxix4n .jcgu32 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 hpn4hq3cr ,0 ain air. How many beats per s h4a n3qrp,hc0econd will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s sirenieo 54e),g apdaqm/j(fw; +cx is 1550 Hz when at rest. What frequency do you dfa;iog + /()ea4ewmx,5qcpjdetect 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 f)gbn/62jd o6 xp ezy*wrequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s *xw/gpe d)626 jy bnoz
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source i - e2p4gvpepu i8a6,ovs moving toward you at 15 m/s versus you moving toward it at 15 m/ uov4p 82p6-,egvpeais 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 samj+qdqy6 u2o .:r* erhhe single frequency 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 Hzyjr*hu+qq6e .:2 odhr . 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 b;*s5d;zslzl+h.aam receives them returned from an object moving directly away from it at 25 m/s What is the received sound freqza lbsd; zsahl* .m+5;uency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wah 2 t:kt6wk(sppw /y*ax 5.e6g omj(fvll at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflecta(5f6yvtop(gp 6/j. es w xk2w mk*:thed wave?    $ \times10^{4}$ Hz

  In one of the original Doppu6aa0w-3s vw jler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a seconw063a wvsjua- d 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 wav;qj6ju xo-r-qip 5nf (9m, alves to 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 flowing in large leg arteries at 2 cm/s directly away nmf(- 6 iqvoj9pqu ;jlrxa5-,from the sound source?   Hz

  The Doppler effect utyxewop10 )a7 sing ultrasonic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When th fa c:7ibc juru+.i0r+e wind velocity is 12 m/s from the north, what frequency willaf.:+ru +u7 rij 0cicb 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 its8m6o, +qsavd( pid7 a)ea/vlo speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed wab0 5/aixin78l-r9 e0bzvgrof sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airpla /lbg rz97w bina0 a-5r8ve0xine’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where p gsw-s;:k:e ythe speed of sound is onl s-wgsp:y;e:ky 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 ocean. Determine the kch89tcyswood6/ h5an)*2z p shock wave angle it produ5sp6 9*n od8oak) /cwh c2hytzces
(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 85zvkk (5i /dproca 0pfwny,3t5po:b$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and seeu7 fg+ t6z i*wdp-wmluc 93uz+6yg-gb a plane exactly 1.5 km above the ground flying faster th w9t +7*d yw 66c f+mlb--gp3gzugizuuan 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 20,000-c ak-y.xs+2mz6kr wu 3Hz 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 is the minimum time between pulses (in fresh wax-swc2+z6mra k yk.3uter)?    s

  Approximately how many *ir.w(wr opkai ).:mkngbw.7octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.ao7)amoeuiq 5y97q m: It consists of many plastic pipes of various lengte) aoq5miq9 o7m :u7yahs, 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 a sound g5x.na1a t*k 43c uhiiclose to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquiuxkcit an3 g*iah54.1 toes?    dB

  What is the resultant sound leve(bu; -dkj d1 xu6/vheel when an 82-dB sound and an 87-dB sound are hea khu-6/ ;b1uex ddvj(erd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, plac7 t ln70bgigf.ed in the open, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equg tlg0 n7.b7ifally in all directions?    W

  A stereo amplifier is rated at 0u91 njpdoi :y150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is n ypoui9j1:d0the power output in watts at 15 kHz?    dB

  Workers around jet a4ebi6o3h wvi, ircraft typically wear protective devices over their ears. Ah4 ,eo3iiv 6wbssume 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 engine?    W

  In audio and communications systems, the gain, :x;e(m :7 kujrjow ox9h(f7jd$\beta$ 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 frequenmbd eiqk5.6qru+ +9iicy 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 xswl)xn +193 vsy2 tr7e1vqhi fundamental frequency ofx 2ysw31srtv7 vie+ lnh91)qx 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 intjg.r2;)cdc i do vibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.3 cjrd)d.c;ig2 95 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass hr8etfbm jj44-*2/ a nsdd0ih 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 resonance (in its fundamental mode) with4edh-f bsa/ 4 t0jhrm i2d*j8n the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonau6, rki8jfyraeu864b. mcb+c te 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,v8)dmav)4/ nd+sv5t9x m* uo lvmayy 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 yy*mvs a4) +mxdonv )da t8,9mv5l/vuminimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. 3u ddk/axe:xe 1p-zu*x xr-e-The conductor on the stationary train hears a 3.0-Hz be*-p:ex uuk-rz/13- dxaexx d eat 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 apprv+-1n vv mbre3oaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was thmv+-e1 brv3n ve train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to tg 0d)e km7te3lfd2a.h he difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain carlhk.aet) 32e0gdm7d f drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Ho0ts oy(e/pi3 qu3)k tz. The shorter one is 2.40 m long. 3( ueqooti0k/3yps) t How long is the other?    m

Two loudspeakers are at opposite ends oexws1s 0hlm 9 ma08o)7wlr 5wdv4ux -df a railroad car as it moves past a stationary observer at 10- wuvd4r 8w 9esams0x5 dlxm7who)1 l0 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 speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the a*bgdf 8al i(k6orta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that ak68flb *gi(d 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 f ( svq5k6h)pfthe moth is flying toward the bat at 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? f )vq 5fsh6p(k   kHz

  A bat emits a series of high frequency sound pul;zcybt; 3,rr aqr5 t2pses as it approaches a moth. The pulses are approximately 70.0 ms art, rzcp25 ;t b3y;aqrpart, 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) was once used tou vcnox+cy qk+b*).1f 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, 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 asvcbcxou+.fq1)+ nk y * an open tube.

  Room acoustics for stereo listening can be compromised by the nc:9jpu ;d89 v*2palzmdao2mpresence 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, and 2.8 m high. Calculate the fundamental frequencies for the standing wa:* 2cjpo a n;ud98 la2pdz9mvmves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a8x oiqz ,q0u0m8 32dhm2q pkb.rv:dxo 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 emm30z0 ki xq:vqqr8m ph,2ouo.b2d8 d xit 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 p.ka4 gp 82bd2ppzpy.iz 7;xd human ear at a frequency of about 1000 Hz .i 4p.z7pp;dad y2 xkpbz8pg2 is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground f1 n simh7(; rn0 an8k9u)zlqzhears the sonic boom 1.5 min aftin9)l7q fkumz; 108(rzhsnna er the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15itjd2x d p:/)d $^{\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