What is the evidence that sound travels 1j*ci815r *- heajhznwv-l+in pylfou)), nzas a wave?

What is the evidence that sound is a form of energ01 wsig 3t2 qs,gf 9 xf-,v)dfz -e+jkiswao1yy?

Children sometimes play with a ho s7hx*z+k-v1ocgg /l omemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at thg/vozxhk -*7lgs1oc +e 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 ziswfdho .byl/46 7:h expect the frequency or wavelyoh.lh /db4fs z6wi :7ength to change?

What evidence can you give that the speed of sound in air does not depend sign3 p4bp6o-7scbhw h 1boegz0 1cificantly on frequsz 0p1bw 7occ hpeg b3-b64h1oency?

The voice of a person who has inhaled helium sounds very7 i, +nu9wji; xbwizv( high-pitched. Why?

How will the air temperature in a room affect the pitch of owr. 3+9ie opgvclr*p +jcyx(*b9 n8yxrgan pipes?

Explain how a tube mightdj 4c/c15c jjt be used as a filter to reduce the amplitude of sounds in various frequ51dc/cj4cjj t ency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 1id+fsp g 8nl aa)uyeg3u- s6;12–30) spaced closer together as you move up the fi+asf8;gd 1yue ni a3- g6us)plngerboard toward the bridge?

A noisy truck approachg,ci ya9vbcc, 4,6 zptes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [c4baz9iv,, 6ct,p c ygHint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas b:r x-x nn:bslcviioo4o;vx3ov 4 dsf) *, az+)eats can be said to be due tor:od )3n,ifcv:xz4xvn v;oxio) l* bos4 a-s+ “interference in time.” Explain.

In Fig. 12–16, if the frequeqyxrdmox-,r 04ps* ;ut+oo r (ncy of the speakers were lowered, would the points D and C (where destructive and constructive interference oc(o* poot dqrs 04xr;mur y-,+xcur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in w8o:pi3bxi-(dlk6uf areas with very high noise6 l-pubiofi w(d:kx83 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 noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave cxx2wun8+jb* g an 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 compn*8 b g+uw2xxjonent frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and obvf. l0z hs)yn/q46w9us ijs4.rdl9 zzserver move in the same direction, with the sam9 ufs0 ny hszsr9dw46)/zqv. .4iljzle velocity? Explain.

If a wind is blowing, will this alter thesw;gwpet2xit5g2 :tfu;h.c0t;xrg 9 frequency of the sound heard by a person at rest with respttprgtxxs 2w;e gt; 2 . ug;fwh9:ic05ect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a gjdj+dvtgrw ;)60;dyswing. 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 frequencygdv+w dd;;r y0j )6jgt for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the slp eh3 m4sge67h3j .mecho of her shout reflected b3e sh psg 6je.7mm3l4hy a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the42q);znwakc n.kryb 3 waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocqa;nbz.24r y) wk3 cnkean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in a9 0k;uz izh -)t.,3kq1lo:l,7qmvd ls bzd piiir 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 of tuna on a fogg -g2 tel5qsh6gr( td+j;e lks*y day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fi2je6s+(et5*stgdgr l lqh k- ;sh,    s (b) by the fishermen?    s

  A stone is dropped from thj sbb xkkr:9s3;m5.r ye top of a cliff. The splash it makes when striking the water be b.y;:mr 93sbsxr kj5klow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to 1la z .lcyudunmw9r:r+p: 3+kthe ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apartr9+ad:k+1u yl ruwznlc.p 3: m. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile oa3hff jr i3ak:h,u7u7u 3rbm4f distance by the “5-second rule” for estimating the distance from a lightning h37:kaau ,3ifhu7 4ubrj fr3mstrike 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 120 dBds x .)inbr)5t?    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 svx-+r3,v. ieddy (issound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously at x1 kz5 xz3q5v c9c5qfja certain place, what will z5jkcx5qx9f5v3c1 qz be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain d9kkh, 3s;taeree3b-o8nu6 :v : fiyzt istance from an airplane with four equally noisy jet engines is experiekv-ra8z;tee9uk3 iyo:hb:, e sf3nt 6 ncing 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,rx,;epv,gq04 xz5 gh8*my e 18ouxu v8ujzd v a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is t;8 e,1ru,hg*zdogzvy xqe0,x 5xu4mu8jv p8vhe ratio of intensities of the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a perk 2hp1 z*kvl: hz-uu)spr 9o9hson speaking in normal conversa uhsk:9kz1 2lho pz9h- p)r*uvtion. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrun qh; h(r5 xpya enczbg,(7);gm whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest ampr)1l,aswio5z +x .in 3qqnbp;lifier B is rated at 40 W. (a) Estimate the sound level in decibels you woulx+;1n5z3o, piq). wbrqis nald 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 c3*qz9ls u .z9c f*+gv hvkgt7placed 2.8 m in front of a loudspeake**9zuk hvfqg. cl+ ctg39z s7vr 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 ler 0ojyw4 3b/fxvel of 2.0 dB. What is the ratio of the amplitudes of two sounds whose3rfy4o x/0bw j levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a soun0vyyua:a7 ovqe +wn19d wave is tripled, (a) by what factor will the intensity increas 1nvywqa9eyu:v o7+a0 e? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have q(8oar3phy 7u+5 gpzy(w;ecsequal displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their intensities?y;hso q(y 3 7eapw5 upr+cg8(z   

  What would be the sound level (in dB) o c5bxw 2dmtry*9q5hj8f a sound wave in air that corresponds to a displacem95*mrc tjyx5dh8 qwb2 ent amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone 23eak/t3fw x sthat has a 50-dB sound level? (See Fig. 12t2s/efak33 xw –6.)    dB

What are the lowest and highest frequencies that an ear can detect 74unqd .c g9blv9 zld pzn:e0)when the sound 9dl n.le uc:n9dvq p )07z4bgzlevel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hu.bn-vhcse .f: ge range of sound levels. What is the ratio of highest to :-eh.vfc. snb 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 1 onwica-xo mxem)/w 6s-4mp*of the vibrating pex)*wn1-s4/axomo m pic w6-mortion 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. What g:+oiv+.y16 wmi3ohrnr, pi t are the fundamental and first three audible overtones if th6 mp1o nr3iw+rot:+.v,igh i ye 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 yovd1phx44p qq.u expect from blowing across the top of an empty soda bottlv 4qpxp4q1 h.de that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes s ha s*6h +x3k+j*.z)bbqnjdxhpanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lengths ofjbxzjab xq+k sh6+h).h*3*n d pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has aat,dxwmp r0fdu.+gb*o d/) 3y frequency of 540 Hz as its third harmonic. What will be its fu.)adwu * ,d mfg+trpydb0/xo3ndamental 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 andtg +s8g:t z3j *wy8pku is tuned to play E above middle C (3y u +88w3gzt sjgk*:tp30 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 oguko r2r6 zitk880e;gf an open organ pipe that emits middle C (262 Hz) when the temperature iso6egu i8z2 8 rtkk0g;r 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 atjmmau:m) v-e 5 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 sh* ca(i3t1lnasi kkb52ould the hole be thabcts a1 ki 5lk*(a32nit must be uncovered to play D above middle C at 294 Hz?    m

  (a) At T = 20 $^{\circ} $C how long must an open organ pipe be to have a fundamental frequency of 294 Hz?    m
(b) If this pipe is filled with helium, what is its fundamental frequency?   Hz

  A particular organ pipe can resonate at 264 Hznqvk04 l 9m 4h;2jfrca, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an 4 4 2 9nv0cj;qrkmhflaopen 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 resonate.,hh c1kemb+ zs at two successive harmonics of frequencies 275 Hz and 330 Hz., k hhmebc1+.z 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 );o:yt-4s0 r.uan)fh k xsose $^{\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 rangboq -f:uh9 hyoyb0o.9e for a 2.14-m-long organ ohyu.bfq0o - yh:o 99bpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long.iys;8g albl* . It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the aas*iy.8;l blg udible 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 (u slu amru5pq jtd6;wq06-j3 beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otheuqluqps6mr 5wjt3(0da6 ;j- ur string? ±    Hz

  What is the beat frequency if middle C (2 1;lqr92k.21kg a0zunuvomv i62 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, w8eburt1 -, xbkq 1z+ :c dmuq0x58fykshile another (brand X) operates at an unknown frequeq+x5qt1u zydbm bk18uef8cr0:xsk , -ncy. If 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 produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 4c:vyupwd f 3 930rlcrbeats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stringpf9c0rlc w3dyr34uv: ? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension im6ueh.9s+nqd: 8e t ynn one string is then decreased by 2.0%. What willmuqt:9s8. hye dnne6+ be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heardmhm.k afg *.2( mtj.ol if two identical flutes each try to play middle C (262 Hz), but onefm agt h.km(.2*j. lom is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning fibvhot c 0:3/v,4qyv zdopj: *orks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded togeth*4v3 z0vo, yv:j:b/icqp tdoher, 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 sp, t3q tt7uf7ubtgxl:5 eaker and 3.50 m from the 7ltuf:3,t5u7gx btq tother.
(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 vibratdpo.d0pyyz:m:uzlt 1 ik-l9q i) d (l*ing at 132 Hz, but a piano tuner hears three beatsk(izu:ytid z*lp l)o1 mq9y-0p. d:ld 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 wave+7ck; f7p aefmlengths 2.64 m and 2.76 m in air. How many beats per second will bea kf+mcp7 fe;7 heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqimz)m vx*)4kw) 2vwd guency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect imw4) d) v*mwgvkz2i )xf 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 enginain j1vkdci55 r 0tj86e whose siren emits at 1550dkii an8t6vc jr51j 50 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourck) rv 5;hew8ngxo *:kee is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two freqg8*e:e)hn;x k o5wrkv uencies 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 :yg ft(p+z i(lone is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume Tz:p( lt( g+fiy = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound wavu ehysm6u/44dn12.k 1kd jvtdes at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the v4sdk46 utn.dju1ye2k d/ 1mh received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall ats 7*m + qp-v,--f+aybbsm wnmq 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 reflected wasab--p wnvqf+ *b m ,mmqs7-+yve?    $ \times10^{4}$ Hz

  In one of the original Doppler experimentsi1el)y-oi , o/di+ egi, a tuba was played on a moving flat train car at a freogi i-yi )d1 /oli+ee,quency 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 car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to mhpyu 0 b+xr pl:)o;/moeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speedr+ 0/bh:py;) oolxp um 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 from the sound source?   Hz

  The Doppler effect using ultraso4+udo -gg de,inic 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. Whencgpf;;lg . 5ufqfe 85i the wind velocity is 12 mfe lu;f55; pfq.gi8gc /s from the north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its ; b-2jpys uzpuq2r7e/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 tu.3/q*f( thwfrp 5 ze,gu6gsvunnq: ) he speed of sound is 310 m/s (a) What is theupfu,. hfqwn:5se3gtqn)g z*6 (ruv/ angle the shock wave 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 planet where the speed of sound is);.+uumbh sze e/kzj ( only amh )/.s(zzj ukb;ee u+bout 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 shocn-m . .;fra+ oxvzkhk;:x 42mcpsr t/gk wave angle it produc r;:hkc;+xompza g4tvxm/. n -2sr.f kes
(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 +8awaz; (jzs ,z e.ont$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km abx/6 od(5*gam9 /miuf skpndj6 2ijv+aove the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane (um+v o/6fjmi 9d id6* j5nsgk2x/paahas 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 sen8 8w7aqzdg-t2grgah( ymz 6u437a zj sds 20,000-Hz 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 s268h7zgwga t-jr(8aq yd g37a4zuzmis the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible okq+ :)s cv6l- z-qbcvrange? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displarc-v9:g:uqu z ky. ;yey called a sewer pipe symphony. It consists of many plastic pipes of various lengths,vue.q ; u9: -yrzkg:cy 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 frght yo /7kl..6s8thka om a person makes a sound close to the threshold of human hearing (0 dB). What will g ha y6k.hs.t t87lo/kbe the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB 4i)wx1:4kmzlf 0v n:dtjim 7 zsound are heard simultaneously?:mm4w) zi7kfdjz x:in 10l tv4    dB

  The sound level 12.0 m from a loudspeaker, placed in the oputzsnp t/un+t1 *mqj pl 4; 6l8:5lgqai4jk3m en, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all directionsnzp: pkum6 si;14lqg jt3umlt nltja q/8*54+?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power outpwyq4, hrud7ib5ys99 nut drops by 10 dB at 15 kHz. What is the 9r47 dyq5 usw,9bhyin power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectiv*p5 i4e,kx*adofib59i fh b 4 uszn-)ue 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 atpiun4bkf4*ub5,af )h-d z5i9ex * i os a distance of 30 m from a jet airplane engine?    W

  In audio and communicl86 3d.rf, 9yxultwjo ations 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 tunes6dk9pt gmy 0yg1 y/p*d to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixedww5)4d fep jv0 points with a fundamental frequency of 440 Hz and a mass per unit length 5)vpj wwf04deof $6.1 \times10^{-4 }$ 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 vu8y2nof/ pf2ugx4x exfz ,b95ibration 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 toz52 xu/eyfbpxg,2u8ff x94n he tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one i)2 frj +y(1umxc;kj kend and also 75 cm long. How much tension should be in the string if it is to produce resonance (in itskxyc; j (k fui2mr1)+j fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one fuqs8uqd lvp9q:s 0vb: csi,ddp 9f (6s8ll 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 pureal jiib(q -m(/ tone in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sourceiq i m-((ja/lbs. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conz3 4d 76u3kqsagnzq/rductor on the stationary trai a3zsug 67rd4n/q3 qzkn hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approa-d1x5j/v ;07pdni j*kfmuxca ches you is 538 Hz. After it passes you, its frequency is dmad pkv0ci 1;jx/-5nj ufx7* measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars j6gk9 is8p,abhz7y4wq r -x: ilust by listening to the difference 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 iw:li-q x9asip8r,k7g4 z6bh yt goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding cf masedvuda 4b3, (2-together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How longd3 v,2uamef( ba-4cd s is the other?    m

Two loudspeakers are at opposite ends of a railroad 6g, r61db,jq2kom syci 9uaa9car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) h6 jda9q ,9,km 6aosrcu1giyb2e is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/ue*r),dgvbcady *g5:ak 3bk/s what beat frequency would you expect if 5.50-MHz ultrasound waves were e*yg a :a bkk5 3,u*)gdvdrb/cdirected along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flyin7mi e)0sc w)x.)-z 1yx 2nguwg6sluv wg toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequenc0-es)wl.wu x6m)17 xgvc n)wisy gzu2y 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 a moth. The5fc . tb,uf d nk)ba2qeq*f0s: 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.* enbd:,q0t) fqfacku s5b 2f so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals 745m yb iy-j .rmm 0h1o(bl m,vwfj7rcfrom 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,m7robhm. 40 j m7rj 5- lwfcmv1yiy(b.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 bvcoj -f*mat; 4y the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room *am;t4 o-fjvc5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstratnsxii1h zd+31i i -hn9ion, called “singing rods,” involves a long, slender aluminum rod held ih+ziihd 9-isn3in1x1n 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 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 th 38 j1j0+h,c/qebpogpj pkd h)reshold of hearing for the human ear at a frequency of abo )o,pdpkp+h/1j 8ehqbc g3j j0ut 1000 Hz 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 therz eyn40x;cihj;: s um(hui7- ground hears the sonic boom 1.5 miu-sc7in u4;i;mhx(e j zy:rh0 n after the plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1 rzndf47up91u5 $^{\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