What is the evidence that sound travelswts.l a*56a pnnt9 z iwepjay5m;4-d* as a wave?

What is the evidence that sound is a form ofaq7i60uz b*epin (4au energy?

Children sometimes play with a homemade “telephone” by attab,hr ej+* iukopu 17o*ching a string to the bottoms of two paper cups. When b7uipe*jhu+1 * r,ook the string is stretched and a child speaks into one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave paswd3 h73bbt5jp2j3vp2 p3 tiplses from air into water, do you expect the frequency or wavelength to change3tbp23v3wl j it3dppjp5b7 h2 ?

What evidence can you give that the speed of sound in air does not depenc, 8zr fot+jos58n 6dtd signific8dno6tc jrtf,o z58s+ antly on frequency?

The voice of a person who has inhaled helium sounds very high-pitched. Whyfo-x9wfb /zmgam x(37 ?

How will the air temperature in a room affect the pitch of organ pipes?idy 3ge x6gmlv9g29,o

Explain how a tube might be used as a filter to reduce the amplitude of sounds i2) +uzuqwwl c3ivov456yx pk3n various frequency rau3v )w+xqyu3wozi6k lp4c v25nges. (An example is a car muffler.)

Why are the frets on a guitar (Fiw 0kqa*r+zj 0/1wft zlg. 12–30) spaced closer together as you move up the fingerboard toward/+k0*fla zrtq1w zj w0 the bridge?

A noisy truck approaches you from behind a building.4db/a ll4:drac ka 4(w 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. [Hint: See Section 11–15 o4wbal:(4da4a/l d crkn diffraction.]

Standing waves can be saidt.n muab7qe53mev7, v to be due to “interference in space,” whereas beats can be said to be due to “interference i7ebmq ,.v una 7vm53ten time.” Explain.

In Fig. 12–16, if the frequenpsau6 k(ae73b cy of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or closer 6kpsb37(aa e utogether?

Traditional methods of protecting the hearing of people who wombk 68 bj:cawp*l34cerk in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphonee p 68cc ja3k:mwlbb*4s 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 wak csw3yh h-vp:6+ l *sbp29cczve can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or w*zps+9bhl3v26: cyps-h cck(b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same directionj/2r9il 4c ox ahq.rt*, with the samai/2t h lr.r *xc4jo9qe velocity? Explain.

If a wind is blowing,.acrndn:flf13 a5+ np1-daw/b*fan7 cn: v aq will this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity chanwnraa cdaa- :vl+/1.1fabc3n nd:npfq* 7fn5 ged?

Figure 12–32 shows various positions of a child in motion on s26nqf)ls yfq1zgpoyo8 00.b 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 h8b 0sf1lynoz2 soy.f g )q6q0pighest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo o)xrh*u ck zu,mry4iuip7 +* x(f her shout reflected by a cliff at the far end of kzr4i( ,** uu+rcy7x hxm ipu)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 jaey d1j z0a2p5ust below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speadzy5j1 0 e2aped of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengz,:l0 m(bu) q7,fnbrlqa0 usj ths 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 tun:33t4gf*tn3mn *dudpbk ;h3cn5ga q* z et3cxa on a foggy day. Without warning, an engine back: ubknx gnct3e3 mh*a3t p*3gdtqd;f 3zn c*54fire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from th e4,apsu1 vhp 4wxsi.9e top of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is thsv1 ew 944pp,as.xihu e cliff?    m

  A person, with his ear to the ground, sees a huge stone stri4zq9wnua;x+ 0/van d wke the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air04wan;d/ qv xw+aunz9 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 ov 0il od6xiq;:ner one mile of distance by the “5-second rule” for es; xi6o:ni0lqdtimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at n p(rlv+cwsgoo+;s37the 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 inte8-bi y5kn ixv;nsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fij y5cw0 5pvrq+red simultaneously at a certain place, what will be tyjc5vw 5 pr0q+he sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frof.;r lx0uky8vp2,bcq m an airplane with four equally noisy jet engines is experiencing a s 2 yfb0pvcrx;.u k8l,qound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereast7f4da ,wgy vvofe*owaw01*r 2xw 1m ; for a CD player it is 95 dB. What is the ratio of intensities of the signal andvw1 vwymf* 1, ow aawe*fr4 o0td2x7g; the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound fjdxzx /x.e-/ zpvr;x.wo ;k( erom a person speaking in normal conversation. Use Tabd o.;-z xx( e/zpjxw.x/er; kvle 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 st d t2:hevn/hx -p2.qfcrikes an eardrum 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 amplifie1ngws6,oa6o fr B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m 1wgnsofo,a6 6 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 zj)4f(o+vw-ftn ) rof dB meter registered 130 dB when placed 2.8 m in front of a loudspeaker on the stag f tzfno v)fj(4+)-rwoe.
(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 lj so 09v;u 51eqkfxhbhr lbi.p4* ,s1difference in sound level of 2.0 dB. What is the s shqe1j ;ixp1rl fo.5l9 hv4 b0buk,*ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is zii,b fktb4 ,io4a f5-nlv,/ptripled, (a) by what factor will the intensity increoba 45 fb4ktli,-z ni,f, v/piase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, bua l s;fl*iym 8n6w.)cst one has twice the frequency of the other. What is th w).af8s*nl;s6yimlc e ratio of their intensities?   

  What would be the sound z;j3;4lfq1*m(nahaq9mdvhle)z i /mlevel (in dB) of a sound wave in air that corresponds to a displacement ampl( mmde 1a3;il zvqq/;a9hl4f*zjnh) mitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem a .v2it.e6exhy xdd/16oh4 jcws loud as a 100-Hz tone that h/e doc.h4 iext. wj1dy62hx6vas a 50-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an eaooopnj (f n*;c +0prn)uw1l90qygke8r can detect when the sound level is 30 dB? (S k0ol n*)gp +;c8e9njqu 1oywro0p(fnee Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What isy b.ueda27in7d*-rj a -)rgvk the ratio of highest to lowest intensity atk nr7 2 -iyda.)djg*eb7rvua -
(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 lengt3ev0.pj3e p zhrnq (3th of the vibrating portion is 32 cm, and it ha3q3ep .j rzpv 30eh(nts a mass 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 first y46yqvdt a. 3xthree audible overtones if the6. 3qxtdav y4y 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 frequencyjg-4.j6u z:t( q4z hb 0hwfwta would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed tzw zu0b4-h. jjq(w:h6ta gf4it 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 t z:2s1ctxxor 8he range of human hearing (20 H1:x oz ts2x8rcz to 20 kHz), what would 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 frei+m7) z r1raia4vdhksh8; v)uquency of 540 Hz as its third harmonic. What will be its fundamentasvd)m7)8arhv1ah r;u kizi+ 4l 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 and is tuned to play E aq1up5l3qx9ln:q;;hoa ew +)yyfw2 d3kl lf9lbove middle C (330 Hzql wn1a 3wq l9l3;;2k95ly:df hxe q)upy olf+).
(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 pipp -wzjfv +k vlz5w)to5k *-)loe that emits middle C (262 Hz) when the temperf lz l+5zjkw-v5pv )owko-)t*ature 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 gn 7ol+z8fe a,0sqoqyhl9 2 ,;4teofs 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of t /0: amoex+kxg0j n5sqhe flute in Example 12–10 should the hole be that must be uncovered to play D above middle C q+xea 50jx/o k0 s:ngmat 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 pipecae 93wr: ha*m can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) h9:aeca* w3mrShow 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 at both ends. It resonatss itbu cs82i9n w:qc5ir5ia6c6vg7 ;es at two successive harmonics of f uw2i ;b 9 iatgin6iq:8vr67cc sc5s5srequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 v*fc okmf n;s+j3;f vec 6/krp;r5h6b)p +uar$^{\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 prese m-ux k:q,c;4 xuwciup+ (d /w(a)aapvnt within the audible range for a 2.14-m-long organ pipe at 20 u+wx ,/i)vkp 4( ua (xq:;a ducc-awpm$^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to thedpg+q/4r7xvhb 7/w8a)sxno gbjbi(my(+y x6 outside and is closed at the other end by the eardrum. Estimate the freq+bv(+xd/ixw4qy/pr)m g8asj7gyn box7(6 bh uencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s 58 6(2kcb:w,qy i axf+hcu4ix:cka du when trying to adjust two strings, one of which is sounding 4dw4fai5 ::x+c,a6 hc(c 2kbxkyi8u qu40 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C dhn5 .ftkk72 q.c):cxpyx 0+vvtkt6y (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 opalt:c; :2es zherates at 23.5 kHz, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, eahs:lt:ze ;c 2stimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sd g+2aho2 t(xsounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What igso hdt+2xa(2s the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in one rf.hfz9;.oc- .gznv ustring is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [ ..zfo 9uz rfg;-nhvc.Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identicd *vuc 8c8g0uk/i-en yy4lxf- al flutes each try to play middle C (262 Hz), but one is at 5.0°C anduy84/ ylve* 0ckf cdg8 xu--in the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 4v. rqi5+zk xz.41 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 frequencies of A and C? What beat frequenciex5q.kz+iz. vrs 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 hge 5ysf8es c3/s;3t2k k6wpk.00 m from one speaker and 3.50 m from the other 6 5t3wkk fkp2s;cey3sh8eg/ s.
(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 q t8go;asm zxm 2g+k29be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are p+m sz92k8x2tag;g moqlayed 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 wavrw wr5mkx,b; 5ez-sz)elengths 2.64 m and 2.76 m in air. How many beats per second w rmw,-e5k5 w sx)zz;brill be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequeuua 2;u/v/q uhlt*8nbu,i sx)ncy of a certain fire engine’s siren is 1550 Hz when at rest. What t q/,* v;8usui)hx2uuba /un lfrequency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sir/t9h qw dov05hl;g7 mbiw:7qlen emits at 15 hvmlwo/:95h;07 ig bwq7qlt d50 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 2 m3y-t9xhmg:v 000-Hz source is moving toward you at 15 m/s versus you moving gy:-xt9 mmh3vtoward 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 equ0iaqaji :g9cr 4 aeu9,h2l+elipped with the same single frequency horn. When one is at rest and the otaeca aqr+hi e0: 9lj il4,g29uher is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultras1-i bade99i ieonic sound waves at 50.0 kHz and receives them returned froea9b 1edi- 9iim an 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 of 5 m/s As it flies, the /c9huyg.dca y:j zf0 ao,o(n- bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the red jnyyh/(:o,cc fzu9a -aog0.flected wave?    $ \times10^{4}$ Hz

  In one of the originaojuddak 2)8),npx, ;o nz83to o;neael Doppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station enoz oop)8 d nkxuton28,e;a), ajd;3at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waveq,h *n/id 6qy soqli-)s to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat/ lo i6,i)sqdnhy- q*q frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using93)l6wy ,qr2f x kk6rowo6fp w ultrasonic 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. y36wj) rpgk sp 4tf9/)lpai 8;yc e;ssWhen the wind velocity is 12 m/pss; 3 wijs 8gyp6)r; 4epytcal9)kf/ 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 speed at (9pa wc4/wp1gacmon)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 whm.a1atu0k qq;ih nd ,32(clha ere the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of the a,q1 m 0aiu h(. cldkqh2a3;tanirplane’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 socj 4 np)w6ok*v0quws 1und is only abow 6v k)usqjon4p*w0 1cut 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 stri3zj t//b xhy9okes the ocean. Determine the shock wave angle it produce z b9hox/jt/y3s
(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 6le;ap8pb7 th,3hnrm$/theta$ 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 exactlyu9dnpo5gp3ejn23 dx qb lkr-bf8q -24 1.5 km above the ground flying fas qjx b2k 23ergfb-d4p9 5ol3qnndp- u8ter than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound e e 2twq/pquy 3/ezf7,h2knz6 pulses downward from the bottom of the boat, and then detects echou qek2ey 7q, t62nhwezp/f3 /zes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible rannf2/ sa)6jcffi47gz 2os l 2bdge? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pw7:e37awicziy-k om +g s*m4t ipe symphony. It consists of many plastic pipes of various lengt i4cwgt-7z oamwimky+*es 3: 7hs, 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 mak tk +xqt(okid8m .0y +6btqt3ees a sound close to the threshold of human hearing (0 dB) tmd it+ (+qoy.bekk80t6xt3q. 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 plszd9 l)r,2 ysound are heard simultaneously? ll)rzp,s92 dy   dB

  The sound level 12.0 h8. 82w2(8le dikgn z0e fl kt7/koasmm from a loudspeaker, placed in the open, is 105 dB. What is the acoustic powernokm fis28we 8/e2gzl 7t .(8dakl0kh 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 power mo+y7x.t;s vq output drops by 10 dB at 15 kHz. Why+ s.7vxq; motat is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typicatshpqn,)3ws5,z 7 jyllly wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a dihpwq 5sz7j ns3y, )tl,stance of 30 m from a jet airplane engine?    W

  In audio and communicati5. -n5nmv uk;yvtjin : zv*0szons systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to aou-fs: sj ),w:ra 1ruc 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 violck9o5k8c- ikt qke u2.in is 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass per u ok2k.ce-8 u9tk5icqk nit 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 vero:8 zae jd.lyao i59-3r o7zrztical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does 3lrj 9 7oizdoz.a8e o5yr-z a: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 is op vdd)+c2/lhry)8 0p/ dgm)ke+m ruuqven at one end and also 75 cm long. How much tenl)rg dkdy+evdq/)8 m0/)pvuu+c 2h rmsion 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 ounq o9( zx m2uuhr((5kne full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range com13n2 e+enm rbizn37laing 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 farther1ezr3inn 23lm+ a7 enb 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 conducponj91xe1 7;u/lhgiy p3/slt tor on the stp7; 91s //1lp uhlexgnity3ojationary train 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 a)/ t3w+ju wcf n;qedw6s it approaches you is 538 Hz. After it passes you, itsw /w;u)3 qfctnjwe6d+ frequency is 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 just by lis(wc -ddfk0-vlo;oxd .pb6 ) vbtening 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 fw).6obvxl(v cpo0-k ;-b ddd it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, soux1 kd.npzbf9 )nding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the other?).znbk19 d pfx    m

Two loudspeakers are at opposite ii ,ue)3vv6ag.r7oubends of a railroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical av br.v, 3 )uegoiui76sound 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 9i (9ghdubk4w/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and refl9b (khi9g4du wected 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 l4 x5m:szy0tygnaoz-+k ui0 qpv7:k-is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz t-g m:opz5i0snuqk0 +yx4 7vzk-y:al. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequee f/ lc9y(fe,kncy sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be (yffc9e/l,ek 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 signals from om(m-lxf ;6n o-c+hh+up bgx)pgb u1a-ne Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to cregn bmh() x fhgpcu--6xa1+ umb+o;-pl ate deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be cou0ex ux74 dxgazw7vd q.:*kt-pf j 11smpromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standdv74exuax: 1z1tsdu.-kqwx*g 7j 0p fing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender aluminhkv2s. tdx03amnu(/z um rod held in the hand near the rod’s midpoint. The rod is stroked wxdu3h.k(z 0 a2tsmnv/ith 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 thr h9qzcb 8me5)reshold of hearing for the human ear at a frequency of about 1qch zrb 9m85e)000 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 npw pv3n91n i(on the ground hears the sonic boom 1.5 min after the plane passes directnpwv3i(1n np9ly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat3i ;tn x(r6lgp 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