What is the evidence that sound travels 5q;fcv1n(l e; bwm v2)yp ).nkn4nnwbas a wave?

What is the evidence that sound is a form of ene6h( ; qsutgg3krgy?

Children sometimes play with a homemade “telephone” by attaching awocgmj t hrv 9t-4- *s8t:)/6zq 0majzb nvr4x 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 ho ac6o4)8 v jtbn-rsmwzm4t9jtr0-q h gzx*:v/ w the sound wave travels from one cup to the other.

When a sound wave passes fozy)/m z0 /nbbrom air into water, do you expect the frequency or wavelenzy/)0bbo m/zngth to change?

What evidence can you give that the speed of sound in air does not depend tzo/d tmm 6o;-signifid/- 6tmzo;otmcantly on frequency?

The voice of a person (+rzha vak 4a:2/7k at*xm1s h;dq vurwho has inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of org1qf.p0j 8n urzan pipes?

Explain how a tube might be used as a filter to reduce the s(ivc+z5o(jvl+crsr .k333bc8m h msamplitude of sounds in various frequency ranges. (An example is rbsi okm8m5c vj3rs33 +.(hz(s+vl cca car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move:-1f jr6npwie up the-:n6 ei1pj rfw fingerboard toward the bridge?

A noisy truck approache oy.q;42kva5lfr- ntks you from behind a building. Initially you hear it but cannot see it. When o;n2-v ak.ty4k5rqf l 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 “interference in space,” whereas ;,oqonlq / x/ vk:v a,n/uikk8beats can be said to, iq;/ vkv//oknaqk: xl,o8 un be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the p0v9.9mgpch m n: 8sicse;jf 6roints D and C (where destructive and constructive interference occur) move farther apart or closer together8 6;9js .rcmphgn9fsv:m c ei0?

Traditional methods of protecting the hearingyi /:v)rwkme ;fmc8 ft3q)m7z of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise.8;mfc 3fziw)y: mq 7)/mevtrk 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 can be ap /m. 5lhim2igv;a8s)w ;qgmthought of as a superposition of two so /hl 2 ;sg)5mpagma8qm ;.wviiund waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and * hxd:3.45a fq usaijeobserver move in the same direction, with the same velocity? Expla a4.dh5e qxfsi3j*a :uin.

If a wind is blowing, will this alter the frequency of the sound heard by a2gr+0k;jy. heuh5 v ab person at rest with respect to the sourc+ 2hvr0. e hbuag;5jkye? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monitot9+vgzox*xpt rg+p8 y1n u*5j r is blowing a whistle in front of the chiyg8pr+9+x vtn1 5*ugt xpoz*j ld on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lak2 .)/ egdzb eq*d:dbmwe by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Est: db) gwq.mde2b*d/ ezimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the sidph9ovh- p )e nkkx)a03e of his ship just below the waterline. He hears the echoo )39nvkh0phap)xe-k 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.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at5wfbi (7orvg 1v9+fcn ue, hm1 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 gfji d5ekw6a0 23+d kcudg(g.a foggy day. Without warning, an engine backfire occurs on anotgg d5kuaj cwgd2.0+kei36d( fher boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a clif bcu0qikizv*22q-7rb f. The splash it makes when striking the water below is hcb0ru2*kvzq72i - qbieard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a h ,w.pqxf rvv56uge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the 6.p5,vxvw frq 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 ovabtzl p8-9hv .er one mile of distance by the “5-second rule” for estimating the distance fv98apt-lbh .z rom a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound 4zz)sb: h3wohd951 qppvr)opat the pain level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensityk vwdy0, ;4dsc is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whenf8w /7 tfv(tmf fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not dB’sffv t8/mf wt7(.]    dB

  A person standing a certain distance from an airplane with four eqyg dx 53.4x8 jxytg)cdually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would t4xgy xdc8d .gt5yx)j3his person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of te2j/ z/dsu.d c7r. /rywcui1 58 dB, whereas for a CD player it is 95 yusrwcu//z/2c1. i7j ed .trddB. What is the 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 person spe q19anpp z9q-paking in normal conversation. Use Table 12–2. Assume the sound sp9- 9qpa1pz pqnreads 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 eardruo kz4yvjox 8:tos*0q 4u l;4,kel4plkm 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 a)ccfot+z:m bc-1 h .h250 W, while the more modest amplifier B is rate-.cca hmh+ z): cbt1fod at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when place 9ys43:hll;.(acd vqj2e hjald 2.8 m in front of a loudspa4jl:(hayhs;qj. v de2l3lc9 eaker on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0 dB. Whatgcb 4n;dk)8uh4zc 5 hu is the ratio of the amplitudes of two soundsku5hbunhcg8) 44czd ; whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trip+i k,hfu2o 8ury- p+nbled, (a) by what factor will the intensity increase? Increase,uupi 8y+bn+-o2kr hf by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eq6e: 9iknah s3kag /f- 9hfehk3ual displacement amplitudes, but one has twice the frequency of thea/ak 6nhe g9-3sk ff:ki3he 9h other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that -)pd1s,az sdys 1g;ei+x fyp5 corresponds to a displacement amplitude of vibrating air )fe ;y1gp xs5y+pzsi 1 dsad-,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-Hzm1isweq )-)0vzg b /9m2cvt8h5xg qas tone that has1bt mqg x2s )wv/9v eg5hca s-8m0iz)q a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear5-k7gjr/gi tc can detect when the sound level is 30 dB? (See Fi5cti -g j/g7rkg. 12–6.)

  Your auditory system can accommodate a huge range of sou ; bf5tlclm8;rnd levels. What is the ratio of highest rb; c8;lltfm5to 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 ofm4 3dtzp/ +iwwbb0qz3xg8hncjw41.a the vibrating portion is 32 cm, and it has a maxwz1pzt 8 4j bwnwgc4b3 .ih3m +0/dqass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and -: b rcah0 ;ut.wr7me8gsdwz9first three audible overtones if the pipe i h; 9usgwt8bz :cm-0r.darw7es
(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 blowin6 5bckzh(gh u79;dcuua +4azug across the top of an empty soda bottle that is 18 cm deep, if you assuu+ 76 hc5khzc u;ugz9ub d4(aamed 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 span7h.e1,mkm( 26t fcb lgplnu./ab ax5ining the range of human hearing (20 Hz to 20 kHz), what would be the range of thptf. i.c ,( 5u1b2agk /6ae xmbmhll7ne lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string hapms9,c dy2nfsz :48 zss a frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it iscss2: 98nfzmz 4sy dp, fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.ftoyf.9p6urx 8; 7udq73 m long and is tuned to play E above middle C (330frq7.6yd 8uf;ouxpt 9 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 thusetls (1j7 r/at emits middle C (262 Hz) whenr/7sj u (1elts the 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 2 ps7 qql6qu:wf5chj( pr:s27s0 $^{\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 should t.rj3.q+m ho k5sr qcjo6x. n(the hole be that must be uncovered to play D abovqtr ho+ jk.x.sm(5q.jc63 no re 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 avy c-4u;ttpj4t 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show wjcvu4tp t-;y4 hy this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It reso27y. kkyxw y* tw7k6rinates at two successive harmonics of frequencies 275 Hz and 330 Hz. What i2tkkrwi7w y y7.k6yx*s
(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 +3cyglq8 7 nh*gjk oqfkj;epxzp)+:(j .x y4j$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a 2.14-m-l: beb4qcy. uq9ong organ 4by: c ueq.q9bpipe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is opyqe*h+( zl5apun- /rpen 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 answr-/p*eapyln( +5z qh uer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to ad0swz0ru o9ts/ze*kuo cen18* just two strings, one ofw0 o*e zn0tk98rcseuouz/*1 s which is sounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency eq(;(e8xo n9ul/ u-xg, mvtumif 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) operatvcymw3 ;zacnj13 (i*e es at an unknn1a3cezjw;c3*mv i(y own frequency. 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 ng 6se(y1cjx,z f*a, hwith a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of ,sjea1n,zg6 (h yfx*cthe string? Explain your reasoning.    Hz

  Two violin strings are tuned to the samef594r/c;w lxbh ma kwgvj1 ,g- frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be th lf9m4j5wb,wv gxc;h/r-a gk1e beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each / h+o )/5:fgdd*v z xnvyxsk;ptry to play middle C (262 Hz), but one is at 5.0°C and the other at 25.; +vd*5sh p x)ndkv/ofxz:/yg0 $^{\circ} $ C?    beats/sec

  You have three tuning for7(taqa m8h,angm/xzp5 m:3w yks, 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 together, the beat frequency is 4 Hz. What are the possible frequ5man h /(ty m,qxm7ag8wza3p:encies 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 ap7cbylvo jba s8 t;q+.)art. A person stands 3.00 m from one speaker and 3.50 m from the other. a+b)j s7;tq8 cov .ylb
(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 .q*jbiqqj w*82zr* ptto be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are pi*zw .jq jb 2**rpt8qqlayed 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 wavelengths 2.64 m and 2.76 m in airlqxy/oc 1o97 q;uc6j.z mu .sl. How many beats per second will be hear/syo76om1ccz qj ..xuql9 ;ul d? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certl(tlgkl h 8j93q- ce8main fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a speed of 3k9jg-q3 m (8tl8ce hll0 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you ))6wipvyy( r vx/zc -jdetect if a fire engine whose siren emits at 1550 Hz moves at a speed ovv/6)(ci-z )prx yyjwf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is movicm cjufy+/,,xrlru6 +ng toward you at 15 m/s versus you moving tmfuur/ cryx,c +6,l+j oward 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 sinb7nl+5 cba7h tgle frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hearbt7c7n 5hbl +as 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 receivbo:u1hdq n +hfh 9 k,/4de*xpces them returned from an object moving directly away from it at 25 m/s What is the rec hfp/:okh qc n4ex1b ,h*+d9udeived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the b4h.t/8km t rsuat emits an ultrasonic soundrshu. mt/4kt8 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 exptk/awu/y n -k6eriments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a wy//6ku tnka-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 measure blood-flow spee mi)jz+ kyfd6h ,t2pg3ds. 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 inpt+f3h dg ,z)2ikmyj6 large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasyz(frec n4+m4onic 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 5achp//k g2noji .r:22) zd6 mgi+oyfa 70 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located, at rest2kcigdj+oan:a)m/.2 /z6 o hfrpgi 2y,
(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 moving4*igg o k:qt0tpw*s x7 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 sou 3ztfo9q baz47nd is 310 m/s (a) What is the angle the shock wave makes with the direction of thetqzb4 3a f79oz 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 atmospherere8mvtqym /:i a, 07ui of a planet where the speed of sound is only about 3y8:i rqmvet7/ium ,a 05 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 shock7tjmf; 0)a6o0 znm4 6rcvesxk wave angle it pr xsm0o e a4jf0m) tz7cnkr;6v6oduces
(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 ubsa cu .n d15s7tz/s.$/theta$ 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 grount .ho7,m *uinfd flying faster than the speedfh,. m*tnou7 i 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 downwapl fcn9be6vc;xpb:,42 f0pmd rd from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum ti9ldpvpn b fc0fb;c6 4px:,2emme between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human aud );3r 1twoiples .vtx2dew4d-ible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ookvn.,t.no: 5 p9dbuwr5t.b6 bp*svhf many plastic pipes of various leng:n5. vt5tv6,pws*bd k bunr. obp9.ho ths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound)u 4l da alfz-kl,qv9+y/oe +e v5v1tk close to the threshold of human hearin 9oae+ 5vly,4z+qa) v/k1kvuftld el-g (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound are hra1 e tv;7,; in(kwdbheard simundt;, 1;vh akewbi 7r(ltaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Whdml kik-4e7f; p 6 wphok78ea1at is the acoustic power output (W) of the speaker, assuming it radiates equally in all k w8mk4oih617;7-papfee kl ddirections?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz.g,h*;vg :lx.pap wbqy;y gt;6 The power output drops by 10 dB at 15 kHz. Whavp a,bhp;lyt ;. xgq:6g*;wgyt is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devicesvx)f18ibhpc: over their ears. Assume that the sound level of a 1:)xb8pf vhci jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, )3lbp*)z,mlagevg7 h $\beta$ 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 vio*7 w*ovt rxff6g ; ldtbf:l lmtc3l);wa7-b3rlin is tuned 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 fixed points with a fun(ugw yc7o,m1qjepo -o c9sj*.n y 4aq;damental frequency of 440 Hz ace u(sn- qga mc, ;j o*pqyjoo.7yw491nd 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 verto9mfc8b0138 72pym3)flhgjgm k8o wqn;lb zyical open tube filled with waterlf1pf9 yo gwoy7gmjb k3ql28zm3bh)8 08;ncm (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that isk.)1 ecjp 4+vkf+b5whn99jb aeh q-gt open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) w wfhk+1b9gnc v94-+5eaejh j q.)pb ktith the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was obsnl4yf q 2ax+in-;w+ar erved to resonate 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 pur i rqy.mltq b3/t j4ibsa3h(;9e tone in the 500–1000-Hz range coming 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 q/ij;rt9la b4(.y i3hs3bqtm m one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. O p,n7cvr la1m6ne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the movivcmna1,76 plr ng train?   m/s

  The frequency of a steam train whistmt .ol/xliqf cz)7;c use)6w2le as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume conf7 cxe6)i .lw;ot2sz/ )culmqstant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by lis1yv a35 xvti/sobqx2r9+u-xftening 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 it gyq asb9x/t3v+irvf- 1xuo5 2xoes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding togef;e f-ace9kvg+ (1 -b9srgb;e/un e iczs0y+ wther, produce a beat frequency of 11 Hz. The shorteyu (ase+-enbe 10cgif/c+z 9rvgw-kse9 f; b;r one is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a rair*9/wzg2opp6yc b 6 8znxfu;ilroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have idenu *fczyx/oibpzw8 66g9 np2;rtical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what(a ytlo ot1v+ ekk;+*v beat frequency would you expect iftl+v(ky o+a;t k1o*e v 5.50-MHz ultrasound 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 t;l 6ymk)8cmf 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 of68l f mtcmy);k the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequencya8pvxe8ott2kq 0; .ym sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How vpmtk.q yot8 0e;8a2xfar away can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signk8ml1m2hpfc1c1i7 djals 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 op1d1hk78cfj 2ciml1 m ne of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromisedzp.jnf,1jc+n -.y.sb d sd5ke by the presence of standing waves, which can cause acoj-sdp5szcn .kd ,.fj. ye1 n+bustic “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 room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrationu:i r0yg* y8 *:pct9ndy4ta mn, called “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 little p4 0n*nay y* ytp: du:9c8tmigrractice, 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 az*zp kca3i: 0 5kj1bix*yhe :w frequency of about 1000 Hz is 5pb* :zyi je1z 3ki:hak0*xcw$I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears the sonic boomr ,9 ya a:9jcu3nu s*vgv4hv4d 1.5 min after the plane passes directlvj4:3uunsc4,v9ad* arvy 9 hgy overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedb f9tbk15vu4w 9 cwhu1goat is 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