What is the evidence that mp +d/auow:t+pnqe5 2sound travels as a wave?

What is the evidence that sound is a form of energy? f*s3d u-ycwvpwi8/ t6

Children sometimes play with a homerqqu tckj pr92a4d o1enx6*+1made “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how thenkcr12 q6pd+1q * a49rto juxe sound wave travels from one cup to the other.

When a sound wave pass2q ojqpc12 k87w*ezznes from air into water, do you expect the frequency or wavelength kzqw8q12 *j p72noecz to change?

What evidence can you on+rog 7 u1p3ygive that the speed of sound in air does not depend significantly on fgro3poy u1+7nrequency?

The voice of a person who has inhaled helium sounds veryyf7an6( d jd9j high-pitched. Why?

How will the air temperature in a sys5ef:qq ual2;e q* 3-2a o)crmd5 zmroom affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds iu b 5le(i z7c)*f1obuhxw )3jvn variouse5)uf(vwl 3z*u 7xbbcohi )1j frequency ranges. (An example is a car muffler.)

Why are the frets on a guitaiixdxbl.6+jo.6 yj mbhd :o(zc05co:r (Fig. 12–30) spaced closer together as you move up tho (ly::6czc0 xdjb5.6+xdobii .jm h oe fingerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear it but .n1i coc. w.m/ei hjk0ko)wd-pz*g,lcannot 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 11–15 on diffract/ko i 1wmeh .*c.pjkozg nw 0dlic,-.)ion.]

Standing waves can be said to benvj ,d3ig,9nw :f ,rgr due to “interference in space,” whereas beats can be said to be due to “interferer,,n i3n v, wg:9rgdjfnce in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poisac:9 kwxy. g8nts D and C (where destructive and constructive interference occur) 98a cygxw k.:smove farther apart or closer together?

Traditional methods of protecti b (k1u5bdfq-lz*uzj(wb 8yb16f8d e png the hearing of people who work in areas with very high noise level(df 6p fy1j qu8uz(b1w8l k-ebdzb *5bs 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. 12–3g2f/5kalghu 31k1og * upjq-a1. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as i- jkaau ofgg*q lhug5/312 1pkn 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 i qijfg6 l z9nel; :y,3r;r;m(lvu0 tfobserver move in the same direction, wit6ez; mq f;jfv 9ylgu;til03lrr (i, :nh the same velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound h xd/nxwgvtx, *s+rg+8uckfe7as6 , s;eard by a person at rest with respect to the source? ew/+ca gx+r , dn87sxkv*;tf6sxu,gsIs the wavelength or velocity changed?

Figure 12–32 shows variousdqggni12 p:o, gym7a r1 1awc4 positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the souo1gcnqi g41: y2dagapm1 w,r7nd of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of hernen+*,n7xjq*9zpqc q shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. q7 *j+ xqnn*pe,9zqnc Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hx5rr9isab5ur0q 9z 9oe 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 (Tabqr a5 rub r995i09xoszle 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths2) zt2 g.hmk:u-oxymeg15h3q+kyr bh in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy v(v7 dtlye(,hdv4-t6f6 .atsc;aya a day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How v-6t tc,7ht4alda.( ;e yavd6yas (fvmuch time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top ofwgozwd y-1a g0wrkj-1) 8vug6 a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high k16rz gg awdg-ww0o1uv)j8 -yis the cliff?    m

  A person, with his ear to the ground, seesy7;hrlmg7 f )p a huge stone strike the concrete pavement. A moment l)g 7hymplf7 ;rater 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 error made over one mile of distance by the “5-second n)xhu26j8 glorule” for estimating the distance from a lightning strike if the temperature)nxljuh2 go86 is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level 1l fm/j c)h6uiof 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound wazna4+-b6sm jhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level i u)l,z se g0lhb6/q3tof 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add in)ub0z lqgti,63/ slhetensities, not dB’s.]    dB

  A person standing a certain distance ab f*v-y s+bm*from an airplane with four equally noisy jet engines is experiencing a sound level bordering on b -af*bymsv+*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-noise ratio ofk+ hl xu 6wsmtd0gc4:+ 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise uh6cw4 g+t+0lskdm:xfor each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fromt8 +j)5ca3 qszkqh4u e a person speaking in normal conversation. Use Table 12–2. Assume the sound spre c3+eq)a shtzq8uj k54ads 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 area flf v6q,0x jpv5dl6k( 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 amplifier B is rx0xjrtal2 52u 2h z, m/pszj1pated at 40 W. (a) Estimate the soundsjputxjrp x0m12zl ,52a /h2 z level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a d0 l;.6*mtjv oig. duckohp(: mB meter registered 130 dB when placed 2.8 m in front of a loudspehjlm gmp *;0o:.dov.6cku( t iaker 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 typically4yx y9 eok-yx) detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levely94oyyex)kx - s differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripl/vfih9dk1)ly+stfsac, - : goed, (a) by what factor will the intensity increase? Increase byioh1-9 fa/ tsk,f:d sc g+lvy) a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twicepn.:1yl;rrd c the frequency of the other. Wpnldyr;r1 c.:hat is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds t6a/v*by l ghu+o a displacement amplitude of vibrating air mb+a/lv gy *hu6olecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as lom7i/tz* s;hz3v(5bm+i x*bemg8w;s uh r jil:ud as a 100-Hz tone that has a 50-dB sound level? (Sei :smr+iiu 7 esx5wb jmhz8/;*lt*hzg(3b mv; e Fig. 12–6.)    dB

What are the lowest and h 8t(2,0v0ma)p,9xhb f6jqrlmx3sa ppd lp6 ssighest frequencies that an ear can detect when the sound level is 30 dB? (Seers8t6s a (mp9a2jxv3pqd hfxs b m,l6,0) p0pl Fig. 12–6.)

  Your auditory system can accommodate a hugen2* 6 mg;1nezupts4fystbml83f- a g4 range of sound levels. What is the ratio of hi3- uefstmf t;bn4m6p12lg yg*azn4 s8ghest 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 fundakp+r h fs7;y:.sb/kft bye,p4b)fr k+mental frequency of 440 Hz. The length of the vibrating portion is 32 cm, a .fk+)kr/;:fss bytp4+b7hkr,pfey bnd it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. Whatww 5pf).g ye:d l6exdbt9 ,ke-v 1zqb* are the fundamental and first three audible overtones if the pipe is w9zew e gkb*yep:d,-v 5.dx)1bqltf6
(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 frep mu.j;i rams*4c y7f;quency would you expect from blowing across the top of an empty soda bottle that i; 4mcpu7j. *fs;riayms 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 spanning th)vv8 8rk/-kubvq 5hfqe range of human hearing (20 Hz to 20 kHz), what would88fqvu hk qb)v-k5/vr be the range of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harmonicptvo6q )8r- ;tpn+oolb ikq: zx5ur,1. What will be its funda 5uq:ilkxt-8 1o)qr+ zt6; pnvobro ,pmental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar fnic mqz)m;+.fiuy93string is 0.73 m long and is tuned to play E above middle Cc9mi un;zf m3).+yi fq (330 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that em xpk;,c ao73xaits middle C (262 Hz) when the tempero;p 3k7a ax,xcature 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 20-0+lg gntgr1+ cq)p lojgr5m ) $^{\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 shouwc/i9/g v i7omld the hole be that must be uncovered to play D above middl/ g iciw/ov7m9e 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 atfyt6l ye-.1z l 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in f zl-16etlyy. 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 long is open aeo k;.fqj .sc/t both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What /..os;cfq kejis
(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 .6nov 1+v:ekhif6vwlr p+r:$^{\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:iweic) y1 5pi for a 2.14-m-long organ pipe at 20e yipc)i51wi : $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is ope6n aty6h3 l6qpn 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 the g6ht lap6 y63qnraph 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 9gu-1 vhcr,p7os p6apyuo9e4 to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the o u9pog1s96p cve4ra,- h 7upyother string? ±    Hz

  What is the beat frequ pz(f6rhyd7g*srm4n//b uw*kct5 mx5ency if middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operatesg7 c5wo(f p;nb at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whb5ofgn7pc ;( wine 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 whenxl t(agx6c052 q f6qvq sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. Whl(56qqva2ftgcq xx0 6at is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, .(ltx f1 bl+gu da sq6179gbqh294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heard when the two strings are playft7gll aub19.qqh (b+gs d16xed together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each trh7l)/p-m yq)ex.sx lbc.gnm5 y to play middle C (262 Hz), but one is at 5.0°C and the otherqgl5-)) s.mn x e l/xym7pchb. at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequer 7wls7:w7dzl3 g z)qzncy of 441 Hz; when A andlr7qz 7dz )lsw wzg73: B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A 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. ,dd;0v ltq.b:pvii j+A person stands 3.00 m from one speaker and 3piib :t0+ qld,jv. vd;.50 m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tunve0xedb fnffu7zr 5-gi jh8 *v *;10pwer hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 1325 f; f v-rdb*w*pu i z8fe7hnvj0xe1g0 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in air. How many beats pegmz qck9 61a-7vf9is-ks4iaau; );rlti lb/mr second will be heard? (Assume T = - i7-krzs4a/mv;s bqait1; um)ig afl6c9lk9 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren islfm*w tor3t z8v hj9*/ 1550 Hz when at rest. What frequency do you detect if you move with a speed of 30 m/s h/fo m j*t8*wlr 9z3vt
(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 sirpb)*lko,o3kp6hjeh4 c k ta()en emits at 1550 Hz moves a6*a)c43oo )bhk (ekpplkhjt,t a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in rex:k 8 o b1,omsm5;p.3mzntu frequency if a 2000-Hz source is moving toward you at 15 m/s versus ok,1nxmrs3zo bm;u8t5 me :. pyou 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 one is but l(2(ehl9s at rest and the other is moving toward the first at 15 m/s the driver a(ll2 h( bs9uett 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 50.0 kHz and r q l)e2rd1( 9ln:uvuol 3clu61fl1rwneceives them returned from an:l cnqvf 1ll (rlouen13wur9 )6d2l1u object 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 ofa,:l;-c4gdn *dm, v altyhbbt4bhy,( y,r9 ji 5 m/s As it flies, the bat emits an ultrasonic soua d (,lit4 ydv9ct,ba:gn,-,4hjb;myb y*lh rnd wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving -x 7j p+qb1ilpgzp(;xflat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at (q7g-+p lx1bp;xpi jzrest 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 measu7-2mm f5cqup y4*egf0q+wnq o re 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 m0c+7 quq5* em24-ng pwf qfyoin large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves .1aj5j eo8bsvof 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 570p .;6, jrgw 7c8ks7f lyhq3ypq Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,wps qh;y73 ylk,8cj6gp7rfq . 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 movi, ut 10ckunve2,l pfz6yei ys)q05i+ang on 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 soundosbf z4u,s i(9 is 310 m/s (a) What is the angle is,u9f z(bo 4sthe 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 thoz:/fem e ak 55 51n0skql-gvoe thin atmosphere of a planet where the speed of sound is only about 35 m/ssq :/15kom fl0aveo5 5 zgn-ek
(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. Determbsz5z0 hp6mh1 ine the shock wave angle it produsm1hb 6z5p z0hces
(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 -e*v)pfs+92infjz lo $/theta$ 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 above the ground og- iwu(,r dh0flying faster th ( ,d-wrh0ouigan the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses downwarn 3p,h a:oq/vr nl7u jtf(bt).d from the bottom of the b/.)(n fporl aj:uth7bq3,tnvoat, 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 octavesd 2c5b) 8 o:wqvla2h 7ectjv8t are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ofg 8z2jr tdnf*op(*u4m many plaspg*n j ufz2 84r(dt*omtic pipes 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 person makaml r:9150uhn:thq:hdxp6 mbes a sound close to the threshold of human hearing (0 dB). What will be the so5::ulma th1xmd nh q:9pbh0r6und level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and a e69qcnlb18g/- z ut1jq8dffvuoa 7(a n 87-dB sound are heard simultaneously? ae9o(af d8gvc7t18q/ 6u -fu nbl1zjq   dB

  The sound level 12.0 m from a loudspx/w fgb*2.5nf g jxdw0wj:im3eaker, placed in the open, is 105 dB. What is the acg xwxjgd/fw w5f.0 :j3ni 2m*boustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The pyt h8h-g 1ead*ower output drops by 10 dB at 15 kHz. What is the power gah8h1 - teyd*output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear 5apy ocn q;b1vh5xf o3v9db+)protective devices over their ears. Assume that the sound level of a jet aib3v; phvo5b5qc 9ay+)fd1nxorplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications se/wfx3p:l8 h fystems, 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 r l-gwrg-p11t (4um jvfrequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamentk5; 04svpwnc val frequency of 440 Hz and a mass per unitsn5c;kvp v w40 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 vibratio8u m grt8d(npxjp+j-i 3pp-t9n 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 pdi gn8(p93m rpj--x t +u8pjtwhen the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that is open at one6qni 7c 4jp m :ii/cm/gsxy3.o end and also 75 cm long. /njqsg.ioc746y c ix m/:3 impHow much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one f5 8c wjqdr. ,pauda:f)ull 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 dje:71).wtn7s gi/oxdvs t9 a t4m.cf coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the perw ei7t9 s)4s/jmxo.1n:v dtg 7fd c.tason 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 sta 8 /cw:elv+)14qmh4kp qglqyztionary. The conductor on the stationary train hears a 3.0-Hz beatpv/z48 kqm+ gqw:lh1cl)4qy e frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. Aftez )4fya dv 2qla4;(xlpr it passes you, its frequency is measured as 486 Hz. How fast was t4l)xdy av2zal q4f; (phe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars j/8kok+c19ckqmn *ifp 0fgnr.h1gw 9p ust 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 (frequ ik.f0nf*9m 9q/gw8ck+h 11 p pgrnockency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat frequency of 11 Hz. ,lp8xd-dpke0The shorter one is 2.40 m long. How long is the otx,ddp0p ke-8l her?    m

Two loudspeakers are at opposite ends of a railroad car v+3 ulzn 2j1ryas it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the 3 nu21zv+rlyj 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 abouth4roegv)y)5 9 fba;p ntyh/ l- 0.32 m/s what beat frequency would you expect if 5.50-MHz up te)a;vrnhyfy 4h -9ol/)g5bltrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flya,d qrz* k(0 wj;*zbqo5o zkb4sm t54jing toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after zkrqj4bqod z; *ab*to4 (j5zws 50mk,that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses asq g2l4b ebl/;dmo*n(t it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. H/montq2l; e4gbl*( b dow far away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once un0hk(dnylt+ *h8+b dt sed to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create 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, an nh bd8l0knd(+tt+h*yd 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 standibi+r a-i8o 2e9jr .waxng waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this rooma ir9a- 2+woibejx r8..
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, caw-0msksmz j )2g(j g;nlled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a mz;ngjgs02j (w sk-)mlittle 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 at a frequency of aaxf t-f6sbq (+bout 1000 Hztfb+ aqs6 (fx- 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 o4m i)qdyn tibyxl-m6.e5y,1ssr /k;hbserver on the ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altitude? sb4 n 6)msyy ld/keyx1 t qh-5mr;ii.,   $ \times10^{4 }$ m

  The wake of a speedboat islsbsz3lh g /5+ 15 $^{\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