What is the evidence that sound travels as tx/s w(i.1ab0nj+ j 5joj7peb a wave?

What is the evidence t3s7ugubw :)m bhat sound is a form of energy?

Children sometimes play with a homemade “telephone” by 6:;lcydm3qf pigme.fq 2p3(sattaching 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 other cup (Fig. 12–29)26cgqs 3q .dp ymil;ff3em (:p. Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air intof tn/vpv62 + advxtn5g(d/ kj9 water, do you expect the frequency or wavelendkn(/fj2dp tn5v6/xgvva+ 9tgth to change?

What evidence can you give that the speed of srgi 7q naxb a4y(j8:7wq6 ,r.e4gs iqkound in air does not depend significantly on :q64w , rk8jia a7b(e4y 7igqqr.nxgsfrequency?

The voice of a person who has inhaled helium sounds v8 :2tvyhdypr1ery high-pitched. Why?

How will the air temperature in a room affect the pitch of ore/ +y x6ld2hpbgan pipes?

Explain how a tube mightlg75 u:c*2j+pl w9q2p)g/j 7amwsr)y fgtarp be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An examp/)ga wlpr2p7tc fa5*)279jwy gp :ujgmls qr +le is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together c re47*cs j5a;.mptn l5:4ous b5vhf aas you move up the fingerboard toward th5*.:n7 ovr sb4afmcuct5h a je54l; spe bridge?

A noisy truck approaches you from behind a sbl dwb;z;l*3 building. Initially you hear it but cannot see i;dbbsw ;*zl3 lt. 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 11–15 on diffraction.]

Standing waves can be said to be due to “interference16vn:tsah;yhy s q4v 9 in space,” whereas beats can be said to be due to “in1vshyn69;qa: vt4yshterference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woulddx k(52epfrl/ the points D and C (where destructive and constructive interference occur) move farther apart or 2(l5pxf/ erd kcloser together?

Traditional methods of protecting the hearing of pe 6pk9(ema/ 2dtti- n, xhkss,hople 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 a/ dsh,6spk2in9 k tt(-,mhe xcould adding more noise reduce the sound levels reaching the ears?

Consider the two waves shownxt 2 rrg*st+;d in Fig. 12–31. Each wave can be thought of as a superposition of two 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 apargt sd;rtxr*+2 t? Explain.
(12-31)
(12-18)

Is there a Doppler shift 4ucrz ,un ik)kqn:/d qzap;l bnl, 53-if the source and observer move in the same direction, with the same q pkq ;bnnar,i:- lu4z/l5c uz k),dn3velocity? Explain.

If a wind is blowing, will this alter the frequenc54aez1 u:/ publn)yora fws4/y of the sound heard by a person at rest with respect to the source? Is the wavelen azf44 :w1noe/b5/rslupy a)u gth or velocity changed?

Figure 12–32 shows various positions of a child in motion on a sw:pha 5-zfo(4ny)va,9 p7jdhnen0nj t ing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the conn4f pz0jh)nt-an9ph:y7 , (d5 ja vehild hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of her sh;ph6hh( d2a ve9ao2td+cde/rout reflected by a cliff at the far end of the lake. She hears trad hot2a;h(+d 6e/cedp9v h2he echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his i( zzdfh-t5rebpic*,. :w0xpy htkkb+701 qd 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 significantly with depth.hy -1wii pb dz., t+r7*5kz:tp 0 (fh0bxdckqe    $ \times10^{ 3}$m

  (a) Calculate the wavelengths ilvr yrh9q t.*+lreb; 7n 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 driftinskn;7m.;:j6f:bhmr5zo9 szk l r0 aa koo/ k1mg just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How mooam5azr9s shl 0 k;mk67rf1;k k .mjozn:b:/uch time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the m*7 1e+h nnhhf --h9c1ebvdkrtop of a cliff. The splash it makes when striking the water below is heard 3.5 s laterhh9f1n + vmdk- 1e*hbrh7enc-. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete 6b rt7pqq(yvu2wu7zt g8 k*(rpavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did theu6(vwg z2turr8q *(y7t qkb7p impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distan gnko)-p o-kt-ce by the “5-second rule” for estimating the distance from a lightniktnp-) -k- ogong strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 1md2 f5(/zo7 ;ljwo2g 8ppihw .zcz2f b20 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 who wod2q/hx /9ptse intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired si.gt6b m,h6- b,kki xfgmultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not mgkfxib6h, t .b6,-kgdB’s.]    dB

  A person standing a certain distance from an airplae;z.tg.51ywue(j8 /xkw gizx ne with four equally noisy jet engines is ;xtkwg zgy.ix518(w u/eejz.experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-n1i4lcpui 2xy +q2-d znoise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of nxpud 1+2qyz4i-c il2 intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of s,g.jtwni0gtjl ep -,j :s:e2e ound from a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a s:,2 e l-te:esj ,wn.pijjgt0gphere 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 are u nvn*d m8bolp7.b5win.f70ea is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplijz+ l-.nn5s3(fn5sj wjk- ypifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.jn-n jnskjp( ws 53 -zl.f+5yi5 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 regisw7rmg+b0th 9sn1 ; n usuthc(;tered 130 dB when placed 2.8 m in front of a loudspeaksr97nh01mbc+w;t nth g u;us(er 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 le 61p yy0x2ie7rgp i8udvel of 2.0 dB. What is the ratio of the amplitudes of two soundy7g i61uepiyrdp 0x82s whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound ida; sn*a t-b3wave is tripled, (a) by what factor will the intensity increntad3bs; *i- aase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplic:k0v b) uv(d8y2invitudes, but one has twice the frequency of the other. What isd nv2yuki 8vcvb() :0i the ratio of their intensities?   

  What would be the sound level (in dB) of a sound qcd((x :wc8 ib7jg:p xwave in air that corresponds to a displacement ampl:qc7x pi8x(b gwdj:(citude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must hav ac +qvig5rd w) hsn73,vlgo,:e what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fi+s o g)v 3dq5a,cg7,inrvh:w lg. 12–6.)    dB

What are the lowest and highest frequencies that an ecg ,nw 9gk*lm6ar can detect when the sound level g,mkn* gcl w96is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range o;t 1adodv,2 tyf sound levels. What is the ratio of highest to lowe1yv2t;adot d ,st 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:v) gt,5onutbjd1 m7rz (n4gr Hz. The length of the vibratingzn d:5gnt mb4 o(rv7jtug1 )r, 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 9 w)pjmg6m cqu38x,wucbmi e0-j3d 6c long. What are the fundamental and first three audible over0p3xm gwm-6ju 3md c) juce986i,cqbwtones 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 blowinq+8fyfe6v1 dkg across the top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tubed6ffk yq8 1v+e?    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 spanning ufh;plshe* m--dl e,3s3 d-xho, mw w2the range of human hearing (20 Hz to 20 kHz), what would be the rangs-3f wme-w, , odxh2pl3dm -h;lesuh* e of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string habn/6o9ksr0zav3m 1rt3 kb y* is a frequency of 540 Hz as its third harmonic. What will be its fundamenta19 rnsr*ty3zm0ib/ 6b akkvo3l 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 a 3j3aa *n:)0arek xarvnd is tuned to play E above middle C x3rva 3eaa *rn j)k:0a(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 aw-zhgw7j:-z,nl eb2j8n,x xz n open organ pipe that emits middle C (262 Hz) when txzw -2en8hnj-,7w,x lzjbg: zhe 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 hvg:sad p7 c.ooy8oni/4 z23t20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of x+-q-t nrlh ;vb psu8f6;vj* gthe flute in Example 12–10 should the hole be that must be uncovered to vl;xv u fpht--8*bgn+r6qj s;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 uvkdwuf : ifww8*-q*,Hz, but not at any other fwfukw ,v*fu*8:q- dwi requencies in between. (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 lon p(dn 3)w3tyis6nd7* w,mmgy. j. yhwig is open at both ends. It resonates at two successive harmonis7 j.t 3,d*63gwimhyn.y )nmd wyip(w cs of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 haeho+ ;34l z vo t;o+fe;k4ax$^{\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 mt) jos-w :5ghaudible range for a 2.14-m-long organ pipe at m:t 5-ogwhsj)20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. cf exi;lcn)/( 6:lghd 0*v*imjpqgp;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 the information in txijvp c0lmg *gdf*c6);e:l n;phq/( ihe 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 adu/.a3ym hyx5 vjust two strings, one of which is sounding 440 Hz.hy3 yxa.vm 5/u How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) a/9/ei q1/usk cgwy l,dk:meo*nd $C^＃$ (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 23.51 +nvhjkf4h6 k kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are pl 1 h+jkknh6fv4ayed simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-H0+etumi;xdts vjoma/f ym8lh41g * 7 6z tuning fork and 9 beats/s when sounded with a 355-Hz tuningjhxe;dgtv6 aso/i 74l+umfy0 tm8*1m fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the saxr1u.k 3p v 6aji0rbs.me frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat fr jvk u3xapr.s60.1rbiequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two j8* n6o:wvitd identical flutes each try to play middle C (262 Hz), but one is at d *vtwjino86 :5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and -7p316qwe ff( kpy-rd3 daffh C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of37 r1fy h-3da(kf6fw-e q dfpp 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. A person stands 3.00 m from one speak :na1vx :7s4 etjdiqfp8k9g)8o * mpqmer and 3.50 m q)g8vdxnoqfi:mp e7 1 a9*8t:4pks jmfrom the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tun ysne 9s0ni t5u14wmdp r(6w;oer hears three bmn( tr dws46yp s9e o;wn1u0i5eats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelen obv2:fx;sx3gg7 j 71i6zcj jlgths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20:b cio7ljgv6x2 zgjf xs3 1j7; $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fi7izprh7be q/ ;re engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with 7b rqih7ze /;pa 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 fx 2,bh 8mp 2wcmmut4.yire engine whose siren emits at 1550 Hz moves at a xuh4 2ymp.m8 m wtc2,bspeed 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 toward you at 1e.cunk8;ojuot dc -7n so (7j25 m/s versu7;(c2 o-e8kunjcoo.dun 7jt ss you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. When *nvsf wweh)7l9*1l) 5efjajwone is at rest and tj nslwvwf*w j)ealh )f91e5*7he other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.01nm k 3h.,lqhuwx 95ha kHz and receives them returned from an obnwl3m9uh5qx ,h h1ka.ject moving directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits mh+s0y10 jjqnqy12(o 1uusflan ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the r1 ojhujmq10 s+0fy2(1 nyulsq eflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving fla; + 9uoz )o;f sg-tmeg0od.eipt train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train carzdo.9+pomi -ofu; g s)et;ge0 approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-f4dei )ycb(ev 5low speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in hi 4ee(d)c 5vbyuman 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 from the sound source?   Hz

  The Doppler effect using ultrasonki7y+(5iohi m.e 7n eyic 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*g k2 0;z2ai2hznvdg zxzwoin*. 2nn* Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are lovnih.n izo 2agxw0d2nkn;z2 g*z** 2zcated, 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 ws)o rl gy:g6d) w ttb*z2,0lqon land if its 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 of 5) ydv :qe20b lj 3ydny(y)rwpsound is 310 m/s (a) What is the angle the shock wave makes with the direction of the airplane’sq52n ()d r:3ylvj0yy pbey)wd 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 planbvk7(bphh83 tet where the speed of sound is only abop8k t v3bbh7(hut 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 ju)j5gcv9h54 u 8 pbq;k(c qpz8500 m/s strikes the ocean. Determine the shock wave angle it produces 5vzk85 jc;(9 ucg)h ub4pqqpj
(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 : )yjb-q at qhkzkcq54,l9+og$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a 7 zp r)wt67u)ma y+*a2 1ogmu wmyd8liplane exactly 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 py)ia*mut)2m6g1 yzolr8wmaw+ u d7 7 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 devicipm ql1:3zf1( gmewh5e that sends 20,000-Hz sound pulses downward from the botti5ghmp 1le:f1 q3(wz mom 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 water)?    s

  Approximately how many octaves are there in the human audible range? s x(alzgq: x(25*dce z$\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists k6zlqc620wcbr uab x fk)*n1: of many plastic kzwu0 6 b61a 2xlk:*n fcq)crbpipes of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a perso-- 0 j;hpndbmin makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 10d ih-jm;0pbn- 00 such mosquitoes?    dB

  What is the resultant sound level when an 82-tjxa)klv): t7 xif9u( rcd 6;vdB sound and an 87-dB sound are heard simultaneous:;cxt)ikjrv7t u(a6xd v) l9fly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the opd hlf8u bojht28fq(/e:si7,den, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in allhfo 7/ l82bjh:iqu d fs(e,td8 directions?    W

  A stereo amplifier is rated at 150 W out3l7w iz w p2:bjes0qneck+1 u*put at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 k2lw1c* bze npks :30qj+u ei7wHz?    dB

  Workers around jet aircraft typically wear protective devicv:gst w;.wj6 cc qcc2,vj ce55es over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of.6cj,cwc wqj;cvs2g:5tecv5 30 m from a jet airplane engine?    W

  In audio and communicatioa:+e49 dl aqy4mgk- z)okiy0 ins systems, 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 frequency 1y/uv .6(ovpot g b-j )b58tbzd$\frac{1}{2}$ 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 fundamental dkp -wlte7 z:2frequency of p-2: wzel7 kdt440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube filled;/acs q /,qj6 vlt1u4s:r hqrl-4 d8r3yrfj ov 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 th r qqf6hl4:vs/ou;rd qy rc/j 3s4rjt,la-v18e water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one)s8h hdng wkgpv *(q. pyj)v37 end and also 75 cm long. How much tension should be in the string if it is to produce resonance (i p)7pgvj*vh(sk hg) y3nq8wd.n its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to reson 2h ,ok18u0vh ,vwod qtcs*c1gate 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 cx2 zq(3a/ ug4iy;dru7bzp k27h) elg xoming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther fro/7;dpzaiuzq xxru( 7g4bgly3 2 e2 hk)m one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on tht:p;zgbkf .k0 e stationary train hears a 3.0-Hz beat frequency when the other k.kz:;t0p bgf train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whis rwxi2qe4ci44tle as it approaches you is 538 Hz. After it passes you, its frequency is measured a4wc x2i 44eqris 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the k+shc2 z ;k0t31eq lqydifference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How f qy e;hq3 0k+kz21ctlsast is it going?    m/s

  Two open organ pipes, sounding togol+66mjc -xe0y 3xt chether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How loc+-lo xjc 63e0xhymt6 ng is the other?    m

Two loudspeakers are at oppu*e- yieu;nz4bmjzg35i p* r0osite ends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency hea3bg5rn puze0*muji z4ie ;* y-rd 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 amrt-.t5 y9fsaorta 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 ref9t5m-f trs.aylected 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 6.5eoboq1(nup:ki 7r(* x m/s while the 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 detectedepnri 1( qkbu* o7ox(: by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound ph1 ari*(l735xypt qewulses as it approaches 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 chirp returns before the nexy*p5(a17w tre3 qxlhit chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals (bqs6zr pmlu *o9ba):3z2hjv 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 mo:v3blh qpb*raz6 m )su(2z9oj st 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 pre5( *v hxpljk7puito:t u+ib96sence 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 fundp5+:tjihp x(u9k*l v 7o6uitbamental 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, slender alumi; wgwnkgmux ( yxlg(, n9s7va* *t2:venum rod held in the hand near the r7 sewtmgw*xl *k2v(v;u9yg,:g(na nxod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear osnp4md90-gf)o tc-z at a frequency of about 1000 Hz i9omcnsd) ft -0ogz 4-ps $I_0$ = $1 \times10^{12 } W / m^2$ 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 .8bp )zuxjawom11-ffMach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directly overheaobf)af 8p jz1m.u x-1wd. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is e96cxyxvd(p,k w7 weuj. g 7o615 $^{\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