What is the evidence that sound ul,ps 8dvn g;j:mqn +8travels as a wave?

What is the evidence that sound is a form of ene8-8gb6bvx7 l n7sxcy;0 otvlvrgy?

Children sometimes play with a hosm w) scz ce746 g6d*eqkka:.zmemade “telephone” by attaching a string to the b7es 6 .wgqk)c4zz m cke*sad6:ottoms of two 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 expect the frequency ordgursi,.bvmw,c(su; t; h 2q8 wavelengri. wm; t (s;gh2qsv ,u8c,budth to change?

What evidence can you give that the speed of sound in air does not depencxepirz4 9j/zy;/b: nd significantly on frequency?cy9zp: ri;4z/n/e j bx

The voice of a person who hasfxw a a*z5f1r5 inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of y8dtycl/f )y 7organ pipes?

Explain how a tube might be use7yane;*m8ym lutg 3 (ux:k91kbx)e rid as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mufflem a1 mg 9x )ri7eeyb;u3l*ktkxn:(uy8 r.)

Why are the frets on a guitar (Fig. 12–30) spa)b9wkew/(f) w qntnt ed8x. r;ced closer together as you move up the fingerboan(kq9ndtewe;) ) rxb/wt.fw8rd toward the bridge?

A noisy truck approaches you from behind a building. Initiallyoylr;i yx6pdzivcj ;(de7b , +-4kwv6tvry3- 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: See Section 11–1536 (wk ;z-yp + y6b-rejvxv4dicdtyvl;7io ,r on diffraction.]

Standing waves can be said to be due to “interfecujd-.y(y7 vrwnac8)m5 j9k zx 3b s5erence in space,” whereas beats can be said to be du.)5c( cjmuz x 3re5-awvyb 9y8jnk7d se to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points zix+xeaz. e1 )D and C (where destructive and constructive interference eza+.z1xxie) occur) move farther apart or closer together?

Traditional methods of proteceg3lvk5l7od 2,ypsa /fk5vt) ting 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 )/7es yalp5 23vt do5vg,kflk 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 iw7atnf 5cwa )0n Fig. 12–31. Each wave can be thought of as a superposition of tc7 0fww5 nt)aawo 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 source and observer move in the same diredjm8bv0n,wh zo i( 1scwl853qction, with the same velo(ni3 5chw0zoq8d8b1mlv ,sj wcity? Explain.

If a wind is blowing, will this alter t+lauu hyv41(hjji .y3he frequency of the sound heard by a person at rest with respect to the source? Is thlhu. a ih3j1j+4v(uy ye wavelength or velocity changed?

Figure 12–32 shows various positions of a child vi1 ;mjek (9hzin 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 whistle? j1(z h;9mkvei Explain your reasoning.

  A hiker determines the length of a lake by lis+qkqgpbudxro3 + e+9+oi8c8 )bb8 oqgtening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.xo gq pqu kbc d8+ oerq388+++gobib9)0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below tbd;2olw 9w9ni .q )sgshe 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 (9n wq ;.ib dgoss9w2)lTable 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wave* /je6 ,sz hvdpn/my 023zknlelengths 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 drif 9ija9z aekk)0ting just above a school of tuna on a foggy day. Without warning, an ekekaz9 i9 j)a0ngine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the o,m6myl -f6xetop of a cliff. The splash it makes when striking the water bem,x f 6y-le6omlow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hu j, vrnwn/j j:p+6ebw5fnp1-w;u 4nzlfoh/ (rge stone strike the concrete pavement. A mow(np jjnfzfrh/ vonp45 /1ure, j: -w+lwb6;nment 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 away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erro fw6vy*a xdu nct,s.6*r made over one mile of distance by the “5-second rule” for estimating,nvdu*y. xt 6* cfaws6 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 a4 t-capm+e*qie0b s *r sound at the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level o u+ c6a.7h+dp xzpnobsk( euc6j2g1he3+d 1ewf a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB w0 n-nlvishu5g wz42g6hen fired simultaneously at a certn-gh2iv n6l 0zwsg54u ain place, 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 foury*o.dpqru 2w) )qh+fg equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound pw g*y )u+ )ho.fq2drqlevel would this person 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 foryl0- *vhv ju0h)br rj uo8jt97 a CD player it is 95 dB. What is the ratio of intensir0 -)jv o78rvy lhju9j*h0utb ties of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frot 6vk )cqk cl0x8t cb1k9t, t9emm;1svm a person speaking in normal conversation. Use Table 12–2. tkb ) ls;1ekv9mk ct1c mv9xt,6t8c0qAssume 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 whose arehp)ro8r ,gca,mr,cf0jwvi:u on1w h 61p b4 r)a 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 ru5bfb7+fnd1 lated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker conneu5lf1n bbd7 +fcted 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 registere lo+gah vu2h5(d 130 dB when placed 2.8 m in front of a louduov(g+ la 52hhspeaker 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 typically detect a difference in sound level of 2.0 p+-)ugfnn:4eoz 4 ebmuhju *4 dB. What is the ratio of the amplitudes e 44+geo:4mn ) *u-hunbpzjfuof 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 what facto;5wgn b lm4xvv2d (2snr will the intensity increase? Increase by a (2nw25x;lmsv b 4 dgvnfactor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice thexs.ny dt6jl(g uk*c. - frequency of the other. What is the ratio of t t-gcsu6jkn(x.d .* lyheir intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds to0 e6 o)k6 5*bjczdzhui a displacement amplitkzio60 h6zcjb*5u) de ude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to sb hqs+8fhv(2o eem as loud as a 100-Hz tone that has a 50-s(hhvofb + 2q8dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequ;*gvwz ff (;urs6 l/zsencies that an ear can detect when the sound level i *;/ vrsu;(ffsglw6zzs 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hug.b40laof z,d8kq* o7xe*cj is e range of sound levels. What is the ratiok zxd**o8so0,lf4iq b ej .7ac of highest to lowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental frequency of 440 Hz. The length of4*p-at*wd ldl,foh t7 the vibrating portion is 32 cm, and it has t7l4w*dt, p- o*a ldhfa mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 9k*967b kgpnc.cl2ft afkd:bpxfd 5; cm long. What are the fundamental and first three audible overtones if the pip7bpd k f:ccpf9ad bx; t29*6kk lfn5.ge 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 a9bca mswhw519;1k.5vtj7hue l jt c n0cross the top of an empty soda bottle that is 18 cm deep, ucmtj7l9.0s c9 ;1h5ekbj hw1vntw 5 aif 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 withmbh: p+;qo plr(/donx,8m a9 o open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the 8bm pn;ordm a ho,l9x(/ +:qoprange of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequenca)8i :+ vbcgpby of 540 Hz as its third harmonic. What will be its fundamental frequci :g8a+pv) bbency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long 7umyg l8au7s8zm/- yband is tuned to play E above middle C (33a-yum 78ym8 z7/ lgsub0 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 middle C ,;mb)/ib1uog ku 8xlprf(z6fi7+da-+ofwlm(262 Hz) when the temperature igmplwd7/b)1oo r, la+; fiuk8 ff -(uz m6xb+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 /akmh.jaq/sju07 b yh;i4 re9at 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 Ewqz(c v4*6 mrmxample 12–10 should the hole be that must be uncovered to play cm*4 q6m zvrw(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, butxv3xwgzn:+8 c5 lpk;s9vgs4,fdd pf 7 not at any other frequencies in between. (a) Show wc3lgn7 v5vf, : psz8gskf4;ddx wx+p 9hy 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 resonatesjtsq,v7d b.s r jzk*)9 at two successive harmonics of frequencies 275 Hz and 330 Hz. What is .7 dzt*bvkr s) jsqj9,
(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 .-hwhvp(a 1m6kwz mz+$^{\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 fols 3uwksvi yyw30yyvn+5)/ :tr a 2.14-m-long organ pipe at 20yy/: tv+y5lvyn) i3k u0w ws3s $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2)zm)9g0ca;sqn: hs fa.5 cm long. It is open to the outside and is closed anag mh0: qaz;sc9s f))t 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 7*ji (/zcmod /aqyklh5 .4tfsevery 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequyqzdso i 4(/hk7cal.t mj*f5/ency is the other string? ±    Hz

  What is the beat frequency if middle Cu6 pjs,g *x*ssttn6dskd +5i8 (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while anotzdq:g*6s3zw w3yk4 l dher (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separat4 3d q lg6zkw*d3zwy:sely, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded wityk; c:ud+c.yrco,lco 20j cpu:4(xk: o-titwh a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of t xol(,r.+cocu2o: kk itw-j c:0cy;u4dt: pyche string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 bqv1kc ,z 4(pcHz. The tension in one string 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.]pbz ,k(v4cq c1    Hz

  How many beats will be heard h 61 bzasp;9kjif two identical flutes each try to play middle C (262 Hz), but one is ajs; zab9kph16 t 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of l dtziff i:y,/ (wz*j y8yl86y441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together,*, y yij:lfifwdzt8 (/6z8yly the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person /offlt+4g gs9 stands 3.00 m from one speaker and 3.50 m from the ol gs+94o/ ftgfther.
(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 piano tu 33rv/q8peu zhm 1pz*cner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what mustcpzr q3m3h uz*v8/ep1 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 waveleni ksy4 a)cu,,( tk;iqx7rxirb; 4c-wr(uv f4 sgths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assu rrsxc uvqtwb,a;r(x 7-4 i4fi,() yk;4kcisume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren .j e/kkem: 7c) ae)hyhis 1550 Hz when at rest. What frequency :kke hyh 7mj a.e))ce/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 uq/9 l ce-;ve uy11gd x;bzfv3siren emits at dyxz-/luq3v1 f; ve9u; e1cbg1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freq4)g,dh6 h0wov,vtq4:q ; fizs;b)s+j cwqqoy uency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are tzg+,h ws 4tcqo:whq vo6jsi)b;4v0yd,) ;fq qhe 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 ez 3 f fk:5s;dsz/wm9nwith the same 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 Hz. What is the frequency the hornsznfz35;/sekm : s9dfw emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonicv*og ypko(9 f nxjjl8br *8/l ,vjjg0- sound waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received sound frequevyl/nv- 8*jg8ob9xr*j kg0(p l,jo fjncy?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ult pac;,b;4qrju rasonic sound wave withbca;qu 4; pr,j frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentzyz3w2 3; 8gjy( kgkems, a tuba was played on a moving flat train car at a frequency of 75 Hz, and azy3k y3mz2 w(gje;gk 8 second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wags p;y0md)*uy/z 2nn nves 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 u0;nyzdy/*pngnm s)2large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of frequency 5tr* m(m3gusrkkuei m.8)g f* $2.25 \times10^{ 6}$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. Whisnx.hl5;: jk;zz w- men the wind velocity is 12 m/s from the north, what frequency. ;;5 sn izklhmjx:w-z 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(tl +aw )i aoj*7ov;flw-lzx2 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 q+l*a ac4f jdef06h e:of sound is 310 m/s (a) What is the angle the shock we+jc6fe 4 a *0qfh:dalave makes with the direction 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 thin atmosphere of a ph(c7ftznm.2zq kx e/as di;;) lanet where the speed of sound is only asxq;z./i m( h ft)azc;2 n7dekbout 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 shoc)y orre7sze s4nt8 k4,k wave angle it pro y4eo 8n74ksrz,r )steduces
(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 3.fq3b qt5 w8nr9pvjuh8 k7/i6v ovyk$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plap yi)vf z,3ip2ne exactly 1.5 km above the ground flying 2izv3 )pipf,y faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 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 seu 2qte l;8dp,unds 20,000-Hz sound pulses downward from the bottom of the boat, and 8; el2,dtpuqu 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 water)?    s

  Approximately how many octaves are there in t-5zbyfvl d l4-he human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displayi j1lwf, 5r/yt+syc7j called a sewer pipe symphony. It consists of many plastic pipes of various lengths, whiw i/jyc+ry stj,f 51l7ch 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 perfw6 s-rfe* h-5p 59 az3rrpxhnson makes a sound close to the threshold of human hearing (0 dB). x 9eh-srw-*pz56 53rf hpnfr aWhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level 9jnz :sxfd+g fht7j6.9pvm7s bd3 :ko when an 82-dB sound and an 87-dB sound are heard sif js9kntmz6d:+hp d3f o. 9sxv:jb77g multaneously?    dB

  The sound level 12.0 m from a loudspeaker, p*uswh g 7qp3uyf(n8t.laced in the open, is 105 dB. What is the acoustic power output (W) ofh8un s(73.p* fwqg uty the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The po5py kjwlyx1:wxi cl6 5 l*+swf a-q15rwer output drops by 10 dB at 15 kHz. What is the power output inj ax6ywlpw5yilx qk*flr:5s- c1 +w51 watts at 15 kHz?    dB

  Workers around jet air 9 : ubl7o/tq * qcl-xweh-rc;g;;uvvpcraft 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 unprotected ear at a distancq:gocu-l* /b -9v ql thxw v7ure;;;pce of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gai; 4+ysgyco:li4y vj: fn, $\beta$ 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 frequqck i ohlex rl,-/ u46;ln40ozency 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 v 9g +neyqf;b2cm long between fixed points with a fundamental frequency of 440 Hz and a mass per unit length nb2yeq;+9 fgv 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 vib.iu7xpxe6/yy ration 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 0.395 m. What is the frequency of the t7/x6p. xuyye iuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at7 swd,( zbvc;u one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in iwcd, zb;uv(7 sts fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate4fb 38orq +)sar1umnh as one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources. Tbm 1i: i* kq6j/jmz868mjg*vuq oq*cuhe 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. Whq *u8bmq *c6z1i6imj:j/qomv*ug8 j kat is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One traz05(u5udk1q1c xi ewg in is stationary. The conductor on the stationary train hears a 3.0-Hz beat frec(gxu1zi5 qkd15w 0 uequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whisb l8;9ly g4whutle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast washugl; w y49b8l the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of 9zl sv)l2jo -kun ptla* w32n:cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the s:) 2k j9nt3lovln las-pwu z*2ound 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 a8y;h /vtlu,6ic8 vf3 kw1sbqek62crtogether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is r yeu 28 1kvccha/6i b; 68w3ksltf,qvthe other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves past tw.6 i(kjo gg7a 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 speakers, at B,j6to(g7iwg. k and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is nor s al,1zh.vas*mally 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 taz a*.sls 1,hvhe 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 is flying toward the r, z6cl8 ioes8yp1d3 pbat at speed 5 m/s The bat emits a sound wave of 51. cl6 yozdpi1 p8r3,8se35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaches .r9j.a( uaqe da moth. The pulseajdqru.(e9a . s 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 chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was oncyq1e) t +;c0iaf(-yh4ipj jg ze used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible yc;-z(jy pi fg)jq0+ae4ht1i to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of sta rr.z/ iv 5 z3n9oxqp/6flevb:nding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0/.nxe5biv fr6 p3v lq:zoz9r/ 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 (wmb0st u46ab jh u,,qa 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 c0m,b,j tu(qhwa 6u4 sban 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 at9opta gak,- wvq l0.r; a frequency of about 1000 Hz is0 .,glw -;qa9ov raktp $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boo2 /s/ve szh:q vll20j7fyix)v m 1.5 min after the plane passes dh /ve2zv:s7q/ l2v)j l yxs0ifirectly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 /dmn:cwchaq5117bi q $^{\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