What is the evidence that sound f/mpkz-y24aro; ni;n travels as a wave?

What is the evidence that sound is a form of ener8vs* d:ng2. zgquc0 bwl3/yd fgy?

Children sometimes play with a homemade “tse+ zz.us(3 bwelephone” 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 the sound w seb+z.u(z3wsave travels from one cup to the other.

When a sound wave passes from air into water, do you expect thet8 n z-/zfno4riqr3.p )nu ,kf frequency or wavelength to o8n, fi /).uqnzt4 kzfp-nrr3change?

What evidence can you give that the speed of soundw4pke+ ajvn :r5 -u0xn in air does not depend signifi5 :r -wu ax+jnk40epnvcantly on frequency?

The voice of a person who has inhaled helium sounds very high-pitchfntft ) au+23ied. Why?

How will the air temperature in *+q.m zw u6fqzqp;(eka room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the am x1pqr/s 8qp9eplitude of sounds in various frequency ranges. (An r pp/qxs91e8q example is a car muffler.)

Why are the frets on a guitar (Fig.a9rpm ck o2c/)2z.aou1,vobghu-t y9gr.7 ko 12–30) spaced closer together as you move up the fingerboard toward the bvoz kmc 9)/u7a.p o og9th-kgra.or2,b2c 1u yridge?

A noisy truck approaches you from behind a z(,5dam lm *fnpj*-de building. Initially you hear it but cannot see it. When it emedn(pdm 5zm*,j - afl*erges 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 beatuyq. dvqeu; (4s canu.;dv(q qy4ue be said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, woqz. 4ox bn;xh 8iisf(+uld the points D qisonx8+.(x 4ih bf; zand C (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protectin*mq3 b4triht3 p;p.oy g the hearing of people who work in areas with very high noise leve3tqi br .p3o;*4yhptm ls 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 ik+d*un ;7 w6zpb4csg Fig. 12–31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, 4i* 7gdw+ ;b6nzu cspkas 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 observer move in the same dgtjw(.o68 5 qrl)t+ybv99wvt ygiw7 r irection, with the s+wq6( g8b wv.j9y vyi r7g5o rlttt)w9ame velocity? Explain.

If a wind is blowing, will this sfp y+d ota)2:alter the frequency of the sound heard by a person at rest with respef +a:do y)p2stct to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swing. A monret8 bf)ik-+u x6*tzc:(zba b(oriv ;itor is blowing a whistle in front of the child on the ground. At which postf-i(uvt + zk*babirobrzc:)8 6 ( ;xeition, 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 lake by listening for t9kfcs,99z vvhhe echo of her shout refle kfvs999vz,chcted by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just -: vcu0p rnhwu /x4c.ybelow the waterline. He hears the echo of thh. cn/urcuvp-xw4:0 ye 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 i 0; e ,nsl5p1(ek xmbu.r q;:mr +yvki,ljicm+n 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 abolha0a6cwc1nz e;04d ;* wgvlvve a school of tuna on a foggy day. Without warning, an engine backfire occurs on another;wlhacwd60 1;ev v*nlc4gz a 0 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 cliff. The splash it makes when s n /tkvqv1 un:f6o/(rttriking the water below is heard 3.5 s later. How high is therk n6ttfv( o/:/qnu1v cliff?    m

  A person, with his ear to th3o9eb))3 bss dujs()c- jlaewe ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.es)job es)39cjs-l)3u wb ad ($\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile o5nl mu 5bek9yj5 s7eg4f distance by the “5-second rule” for estimating the distance from a lightnign5 l7u9myb ej 4ske55ng strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sounxkv0s3 whw-rf 3y 0 -5,oysgxwd at 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 leve*2ilo uv.-ytcjw (3fo l of a sound whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sounjw*5 1pfu47 mx1eqnuzd level of 95 dB when fired simultaneously at a certain place, what will be the sound level i7xe u*wqz11 pm5fn4juf only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain dista8+;b/ pgjw :eq bpu7kb,y7z hvnce from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the capta ebv7p /hbyq78ugbwj:,p z;k+in 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 ,r fco2j+vc9b, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each devic ,2objf+ cv9rce? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal converswg.dgw6v 8) jhation. Use Table 12–2 w6h.8gd g)jwv. 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 strikytzbvn*5yf jy( ;eb61es 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 mor xkak( bdhn)h+s 4o/e;e modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.skodkeh;ab(h/ +n 4 x)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 wi f,sk-v oq0+placed 2.8 m in front of a q, +ivwo fsk0-loudspeaker 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 2.0jyc1x 12fwsn i:/ d*zz dB. What is the ratio of the amplitudes of twdfji:cnw*2z1sy 1 x z/o sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will 5xelr5dz5)1ij 0cj kn the intensity incr5 ek c)5z1jxlr0j 5nidease? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has *yz)g42*ihaxp0 m igu twice the frequency of the other. What is the 4 )g0ui*a 2gzihxpm y*ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds tlc:l. , wcmxx3o a di.x cx,l3wl:cm splacement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hz tone tvah: z1 xkdp,of0+3yy .j5uf usyf*o),bl3jdhat has a 50-dB sound level? (See .jf u yfoj dvoak3zs3 +by1,,h )ld:0uyf p5*xFig. 12–6.)    dB

What are the lowest and highest frequencies that an ear c9o-nfc9nrj7 jm+ ig 9ean detect when the sound lejeninr7-g omc9 f j9+9vel is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound leve zydq00-bk*.*fgxycrafru 5 c:0 bym8ls. What is the ratio of highest to lowest intensibr: g*5.c0qcdr-ybafm*8yfy xkz00u ty at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a vio cb (ekgrru1 qm. 3 z/eldu1b)vj7n(9mlin has a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must th )jmv7(rr lze19/1dq3 um eng.cbu(kbe string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first thz ( q0+rzcengqt x5u/1ree audible overtones if the pipe i+x5zg1tnze/r 0qcuq (s
(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 blowing across the top of an : q3ls+hl(d vcempty soda bottle that is 18 cm deep, if you assumed it was lh(+ vdlc q3s: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 opeq6jh)y;v/iy kj+1kdm*ya7 o k n-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the j+* o1yk7adj 6;kvm qyyk) hi/lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of )hu*+ alks i**z .bfmm540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a leng*uz ).mib+salf h* m*kth of only 60% of its original length?   Hz

  An unfingered guitar s.jtj9z5l, iq wtring is 0.73 m long and is tuned to play E above middle C (330 Hz).jqw ,lt.5ijz9
(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 opendo vo9gfp+8 en(.;jq d organ pipe that emits middle C (262 Hz) when the td8q no;d jf.o+gevp9 (emperature 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 atf0x/6wyeowq4v v qy)b y1c/* bflt;a, 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should the9kbrjry;2ym4 vvnrl1 : gnk6* hole be that must be uncovered to pla 1gvkmj4yvn*r;lyr62n9rk :b y D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonat5;-ihhwdy ;w nid:i(oe at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why inoi:d; 5w;hhw- y(idthis 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 f*44owjer osfze,h 8)long is open at both ends. It resonates at two succesrwf o)zeej4s *4fh, 8osive harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 itf 8jsqk-/ i,2rlm z,$^{\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 l98z 9 exb6l7o m4grmfwithin the audible range for a 2.14-m-long organ pipe at 20l9 m6zo7 el98g mx4frb $^{\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 the out2grv+d3d( sh q rnn-n/3j d heg:j4lj)side and is cl-jrnvqgsg3 +lrdn3j d/4 2d n(ej:)hhosed 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 graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one bo/ 73yu h(mudqeat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequed/oymqu hu73( ncy is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) ance)1 8cddl7kt6o( ui.z4 luvfd $C^＃$ (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 kHzotr*0m a a bxo/*c5wi9, while another (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a somabw cxa5ir0/9* to*hrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 35mc . w9 dkfcv: 1u(v/k 5o06nihem6ked0-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the mo v 0kdf id:. w6(ec59cmkv6eku1nh/vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frj; s s.5.fmw0zwwwkbij,g -g2equency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency heardkmbw0.j,i; -jwf2 gswz g5w .s when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each1t,dr0if 5xb +ebsqg+ try to play middle C (262 Hz), f150sd e+bix t,q+bgr but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. s1/wkq; .ily1ju+:,4a2 h xfnhb rw ajFork B has a frequency of 441 Hz; whenhj/xbhfny1: j2 4q,s w;ak+.lr1ia wu 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 frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A per q-8w 7*orc-um.yvzop6ox,fm son stands 3.00 m from one speaker and 3.5 7y,xo-p mv*- .rwzc8oumfo 6q0 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 sq vh hmm1lg;u7u rxn)t);w,x:upposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the v q:lxtnhx1 u ;;7 ,w)r)gummhother ?   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 2mvkr 8qkv4iq226xem wavelengths 2.64 m and 2.76 m in air. How many beats per seconqk8xri q mk242emv2 v6d will be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fr t95+kjtj zvvbi:c.*ire engine’s siren is 1550 Hz when at rest. What frequency do you detect if vj c:t*kjv.9+irt5bz 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 fi8 md(fyd.3eru :z; ewrre engine whose siren emits at 1550 Hz moves at a speed of 32 merd; :fyuw 8mdr3.e(z/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frf *mtsa 7c.,qxequency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the tfmxst7q *a,c.wo 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 equn uu (ap )+fp(p,okqw9xo wg((ipped with the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What i o((fw(,puowa(+ ku q 9)ppgxns the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound i .:ahwlu6qa l,2r ee8waves at 50.0 kHz and receives them returned from an object moving directly away fwr6lui:l2aae. ,8e qh rom 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 fmrpmtp6bd89m/ *vu ;, the bat emits an ultrasonic sound wave with m* 8fm dvtrp ;mp/bu69frequency 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 flat t, zk+lgvn 5)zxrain car at a freq zxz, g+)v5lnkuency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blrpj;j1 -e1m6nyggh; 7by qyi/ood-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 thpyy;/ bj-hjgy;n16ge7 rmq1i e expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic wavesv.0 au xl,ihk4 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 e.u3r1wmr z / t mwht:zry1*/bof frequency 570 Hz. When the wind velocity is 12 m/s from the north, what freqw3rbt/ emyurrm :/ .zh1*zwt1uency 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 objecteuo4hn4wh qedqh1/h7 :ie6d7 moving 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 sound is 310 m/s (a)pwc;s.p. +rurtr*z9n+ k 5 spy What is the angle the shock wave makes with the di r.;*ypnt9u.rs + crpk+spz5wrection of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where they ha6xmi+4dq7krwp7 3 speed of sound is only abo6ywr+xkap i77 mdh34qut 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shock wa b+i hf6 7sc; /idkk;a *zr56wqlnxin9ve angle it produceszisl;q xnc b769k;dai+/f5rnih6 *kw
(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 tth*elxrab;h x/;tw*,u. pp, $/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a iick k )- 6404*qp xko,c cyhu-uoww8vplane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane c8c4- u*4xi pc0k-wwik)uho ko y6vq, 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 dowzz,iom w6n b)+9,fkcb nward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, who+zm bfn)bik6,w9z,c at is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in * :ckvv9r+/-dn fa oqathe human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists of mauu (qe eww7a 9c9ld s-gr-v75ony plastic pipes of various len 7- lr9ue( 59v7d cs-awogewqugths, 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 close to the ii, lzlyw6+yogu qj hf3.m -n7/n*5eethreshold of human hearing (0 dB). What will be the sound level of 10ygl 7woznl he ym ,j+f-3inu*q5i.e6/00 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sou+g wib ;:2y eiafl40cmnd and an 87-dB sound are heard simultaneouslbw:a2 mfy0g4 ci+ie ;ly?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 p 6ru9tj) 3*rd- jejyf dpl49fdB. What is the acoustic power output (W) of the speaker, assuming iy4)rp93 ju6f pd-rfej9*jl t dt radiates equally in all directions?    W

  A stereo amplifier is rated at 15*rprtdp-g3kvwmd9b: e 9i y8r:k5 f(h0 W output at 1000 Hz. The power output drops by 10 dB a* yw rrrhf8:b p-k5i3(9kpvd m:td ge9t 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet a6a/ -x y3qkkipwwff/ *ircraft typically 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 distance of 30fk/6/ k-3 xfpiwwya q* m from a jet airplane engine?    W

  In audio and communicationn:ulfmf8lxiyq :k aqptk2p,w6t3z0 87 +k a9ds systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequea/u1 l7eavg(jl (i: pbncy 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 lr8 )qf mudddqtpj,y..(ka a9;ong between fixed points with a fundamental freque.;d jmp.9qa y8 dd qr,k)fa(utncy of 440 Hz and a mass per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set inxm;ptw11aj , , sn0h* jx/vnjq06doh nto vibration above a vertical open tube filled with water (Fig. 12–35). The water levex,jj0qsnnv,padj ht1 n*mx o ;6h0/w1l 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 ti2r17x ja p(y; t ulwzv++tz4fube that is open at one end and also 75 cm long. How much tension should be in the string if it is to produce resonance l4yp;xtv(+71i2rftz uaj +w z(in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observe ti kjz f0)34ep39ophud 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 pure tone in the 500–100.- zygaeizv - x ys9;5/kf0j-i jf5zoq0-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 from one source than the other. What is the frequency of the soug i/of -qzx9y.k- 5z5;jfisvz-y0 aj end?   Hz

  Two trains emit 424-Hz whistles. One train is staxzs g 0iwzw53 q n9zu.b(4(jsstionary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed o xiz.wjss s3(04(qgwz z59 nbuf the moving train?   m/s

  The frequency of a steam train 28uk i-hdj(n8m/hz uq whistle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the tra/hzd-u8nujhiq 2k ( m8in moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to th,hp(6ij tw ueynu-6 a9e difference in pitch of the engine noise between approaching and recedin(jh9t ui,- u6peyn6aw g cars. Suppose the sound of a certain car drops by a full octave (frequency 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.wbt ) fl b /xsmqb7 0(s9lgvi5449giaz The shorter one is 2.40 m long. How long iss/9mb4i0z ax 5lis7b (twvl q9gfg) 4b the other?    m

Two loudspeakers are at opposite ends of a rgxwl/; sm (zi3bwkle0yah -8(ailroad car as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency 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 tsk b gywxla i-0l8w(/(m; he3zhe speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.3 kts rv3r;t0y 4 ghlcb*j9g+,n2 m/s what beat frequency would you expect if 5.50-MHz ultrasound wavesh94jtc t3 r*,;0b lgnvsgyr+k 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+kygalpmu6(rba 6xz1q8 5/ o o 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The ba +x/a zp mb5l6rqoy6k(8 ga1uot emits a sound wave of 51.35 kHz. 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 frecc.(fy0sf 0oh quency 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 . yc0fof0hsc (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 signals fropw riu ;s3 1y7p8m1lrw:yvl2wm one Alpine village to another. Since lower frequency sounds are less susceptible to intensity iu;3lmy1 rw871wrp:2yvsplw 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, 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 comproak7h i-+bl5,c5yy szr mised by the presence of standing waves, which can cause acoustic “dead spots” at the loca+yr55bsilza,-k h7y ctions 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 demonstration, called “singing rods,” involves a long, slender akir-d gz didb:1s6aii3 0wz+xud6f12d0n bw )luminum rod held in the hand near thebk3gididuz bsw: f26i za1 d) n6+1w 0-idxrd0 rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human iyf d(* g4z u0pw+m+hhear at a frequency of about 1 iu0fmd+zy(hh* + g4pw000 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 ov; egv p4vmnyyfqa/5)6n n* sn;t3-9ljia n9mn the ground hears the sonic boom 1.5 min after the plane passes directly overhead. e/a9mg6 -qn 4nn9p5 v ty lf3n;m)ijvnsv;*yaWhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 j ifb9twxvl7x 13l;f1$^{\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