What is the evidence that sound travelsd8u d5 uysyd6sg y8)1-p7p cpe as a wave?

What is the evidence that sound is a form of ene*ft+t b f9dgs8-qa:h yrgy?

Children sometimes play with a homemade “telephone” by attaching a string kcw84g*qyn ph omh( o5)0)kkjto the bottoms of two paper cups. When the string is stretched and a child speaks into one c p 4 k8m 0g)nokkocyh5jq(w*h)up, 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 passes from w:n / yh1bb4 fn+ftn f*1cm+2;anlzfh air into water, do you expect the frequency or wavelength to cac zf/4nnmhbffn t+:fyh;l 1n21*wb+hange?

What evidence can you give that the speed f er9,y gz-y+hta .u5cof sound in air does not depend significantly on frequ9acg 5.zryt+ eu -hyf,ency?

The voice of a person who has inhaled helium sounds very high-pit b-o 7b2l2wnzhku57 rvched. Why?

How will the air temperature in a room affect the pitch of g0jbnpqwdk(6y9x w7g* ps+n5organ pipes?

Explain how a tube might be used as a filtexp/n)c m2ot; zr to reduce the amplitude of sounds in various frequency range2p )/;mncozxts. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–6l4u. .oo/ro onk xjq, zlaa7:30) spaced closer together as you move up.a al q:roou,7o.x 4/nk6ozjl the fingerboard toward the bridge?

A noisy truck approaches you from behind a buildin7d;1j2 d6l 3sqf(o9 s0ysy saqik (btdg. 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 Sectqy0bjs ok3 sf 1diysd(d9;al ts72( q6ion 11–15 on diffraction.]

Standing waves can be said to be due to “aj.zbm c1m)jds)-)f9v vy9 ss interference in space,” whereas beats can be said to be due to “interc9m 1 )mdaf.sz) 9bsjvsy)j-vference in time.” Explain.

In Fig. 12–16, if the frequency of the speakerj. p uzg3 nb662owk8rss were lowered, would the points D and C (where destructive and constructive interfere b . 3konsgr2wup86j6znce occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people whoykg-m9gj4j:fs6 +s os 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. Instead, a device is used which detects the noise, inverts it gym 46fjo:+-kj s9gsselectronically, 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. imdse f ;7i2v912–31. Each wave can be thought of as a superposit 27 9sd;fmieviion of two sound 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 observer move in t(4 m,f5duid g ulmr6p5he same direction, with the same veligu6m dd5 fpur(ml, 54ocity? Explain.

If a wind is blowing, will this alter the frequency of h.ti qvy1f wg:gv1(4m the sound heard by a person at rest with respect to thw4ty (vf1qmhv:g. ig 1e source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion ond-n ttxdr sv oq+p )7,i*b+cg7n,i5hm a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the so-txs+,cnpnriqi57b mo 7*,th)dg +vdund of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo of sm (vz5d74eu( xks:q oher shout reflected by a cliff at the far end of the la 7((s: 4ezsudvk qmox5ke. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below /ukde;*u s;uathe waterline. He hears the echo of the sound reflected fros*u;dk /uu;ae m 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 a( 4i 33xdabwpnir 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 jun2z)vrcvk52 twmiek8/f5f r -st above a school of tuna on a foggy day. Without warning, an engine backfire occurs 28f)5m zwk/ve-krf 5 2rcvtnion 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 the top of a cliff. The splash it makes when strikin*, dqc:s ovzp+g the water below is heard 3.5 s later. How hidpv:+ cq*z,os gh is the cliff?    m

  A person, with his ear to the ground, set++8jc ;m wc;1o hqapzap smcg+256ha( nooy-es 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 8p+tw+yqm-c5;asaho phc nmaj6;gzo2c(+1o the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by ti lj*q ,k(e92f ypxv3she “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) * 3svqx2(9kejyf l ip,30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dwuofsu,oaa..romp2 oq 8u. g)5 6:rxdg ci q,:B?    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 intedygz ck.y-d ck,hv3 j+yq3**2b;ywounsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB faq 8lm.tn; y9rig8 +i hmci/b*c;5xk when fired simultaneously at a certain place, what wii5 /+* ; iynf;crix at 9hkm88.mqgclbll be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noisy jk ( 5arn7ef; fdpgv3+get engines is experda(n5rfg 37p f;kvg+ eiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a ,(dghk ta:7g- :g ibnnsignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for e:( -gbat,id7h nggk:n ach device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person spe*m4k1a l;f.aqcj,nip aking in normal conversation. Use Tabkm,l * if;n4 p1acqja.le 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 strike/g-zlk 4f* od 8s3ddxss 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 y*qkyc r* g m*(3ssn5drated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m f g yynrss*(3d5 *c*qkmrom 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 placed 2.8 m in fronl+pbjtoagj 8;lo;x9-t of a loudspe9aplb-j;l +o;j 8xotgaker 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 ofl1zk3 ipi22r t9 t,ihn 2.0 dB. What is the rathl9k pz2t ti1r3 n2ii,io 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 tripled, (a) by what factor will the intesym4 /1atgc0znsity increase? Increase by a fac0z4c1 ts/ymag tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has t qmaf+ no :5p4m1chbn q97)s:tqhth9rwice the frequency of the other. What is the ratio of their intensitie7rahc s9+mtb pn):5nt9fqh:1q 4oqmh s?   

  What would be the sound level w 7ss3nd:-/f6pqebe p (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 30n-df6we qepbss 7/:3p0 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hqpis6f48(n i az tone that has a 50-dB so pni isqa48f(6und level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can dex94zn 6p4jx kptect when the sound level is 30 dB? (See Fig. 12–6.zxpjx 6 k944pn)

  Your auditory system can accommodate a huge range of sound levels. What is:+ za73a/du xw7dbo gz0cvpn. the ratio of highest to lowest intensitybx:wz/v 7gz3d ano.pd c7au+ 0 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. Tx) sixgowg ,67he length of the vibrating portion is ,gxxi gs o)6w732 cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cmh:2is04 jl scf:*6hx4k ltjro z2d0my long. What are the fundamental and first three audible overtones if the pipe y* c :lf itod:rx46hkjmslj4202hsz0 is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you;i,iw1hfm9jwe/f y- gy k/ *lh expect from blowing across the top of an em /-we 1lwh*gy kji hfi/;my9,fpty soda bottle that is 18 cm deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of nin 8 vjd3aryn(* cq6s/(2daq:jy +qxhuman hearing (20 Hz to 20 jx6cij 2(/qad vd*r+ qysnyn: n3 (q8akHz), 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 aqbw5p,1iu w 6a frequency of 540 Hz as its third harmonic. What will be its fundam w5bwiuqp,a 61ental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 ajha34fl k.9ybp/v e -m long and is tuned to play E above middle C (330 Hz). h4b-l e/ j3.vfpyaka 9
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middll:8c6c 9( ec(ovtssiae C (262 Hz) when the temperature iloeisa(c6v t c:8s(c 9s 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 ahew3q(n3.x7);r.f r rqb /fz8 szjbzy t 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute wu2ca z( gz.+ x.;ttixin Example 12–10 should the hole be that must be uncovered to plxzc (x2a ig;..wu+zt tay D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hz, and h vti/*pt( )gy616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a clos)(vt /g pyiht*ed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is ope7* qblke kk*e fmnz;8)n at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. qb)nee kkm *f87k;z *lWhat 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 l69:* ky 8-ochjuoypb $^{\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 the8q5 bpne z43+ q8os.kep qkrq* audible range for a 2.14-m-long organ pipese 4rp k8*bqqp+ek3o8z5.nqq at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 7p:em )mio s 8wxa.o*n2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the gras*m n.wopi:oem ) x78aph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears s+5zag9lf6ic s*m*wv q13+v ffz ;ap fone beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the otq fsp*c w*f a3v1zms++5laz 9ivg6ff;her string? ±    Hz

  What is the beat frequency if hp65k.pba58cqoddte02w n1 ymiddle 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) oc*bjavl9. mmj-( 5xi5 uv 6uyyperates at an unknown frequency. Ifm9(5v 5j6m.xa*uy -jyib v cul neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuningj,o 4mq o5 dh1 /27aibg7pch3onl1rnz fork and 9 beats/s when sounded with a 355-m1o7onjg r47l/cznab1hh 2,3 opq id5Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tension in onv sixk6:+vpy* gx:t 8re string is then decreased by 2.0%. What will siy +*rxpg:k8 :vxv6t be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will bea nq v7+bdt ,t3;pbh1c heard if two identical flutes each try to play middle C (262 Hz), but one is at 5.0p;+1c37b anhttdqvb,°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frj4wvucbig e ,4 dim* 9dk)2tg3equency of 441 Hz; when A and B aregwtgd,*)ec42 udbkji 9v mi43 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. As)g .2* vtyodx person stands 3.00 m from one speaker and 3.50 m from the o)s goy2xt .d*vther.
(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 *lzvkhv w2gn )f)(sw6supposed to be vibrating at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (w k2z6n(* whvgf) )vlsa) 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 yp rrp. c2g*j0oda/ -rsld 5q(and 2.76 m in air. How many beats per second will be heard? (Aors-0.j pgdr* la5p2 /drc(qyssume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’*lsn- hkp;u k5t 9wuz1--uusis siren is 1550 Hz when at rest. What frequency dontz-s 9pi1 5u l-wkksh u*u-u; 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 stil829t tkxk t0gcl. What frequency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed of 32 9 kt8kxtg02c tm/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving towu(rzl5qn9sh)zpg q90f * ee;bard you at 15 m/s versus you moving toward it at 15 m/s Are tlqhzzqeb(s5r9gnu e f 9p) ;0*he 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 / cmg eam, 3lxx 4qb6y-gjgz80the 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 is the frequency the horns emit? Ass3-gb4yjm c ,a 8mx/xg06q ezglume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounh 1vxkvayup), 0ue2h/u4m) hrd waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the re2myx u40 r)h ,kvaheup)hv/u1ceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wal( n7vsu) ywtun+ cue*.l at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the tu ncuu*e.+y )w vs(7nreflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experimennyznul*d*v 5k* qb ,boglvz05-y:m5 ots, 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 tz0nl5b*5:bzm5y *kg vn ouvd -yoq l*,he train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound wavr)qt2w18 u5z qc gi,paes to measure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound acq8t1qrw,gz2i p5 u)in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves of freq phx,6xypk:0ncen(q6 3rx z r6uency $2.25 \times10^{ 6}$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 fry5s0na 8.t/rvfya 4 ;z4qz -a 7lgg 7c4tjbodjequency 570 Hz. When the wind velocity is 12 m/s from the 04 dz7-jj yca .vfbzsy/tgnala t47o 5 ;rg84qnorth, 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 kq ) robylj69scf5 4kf p3*eh0its 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 th)9bvel: wbvw) r 8cr5me speed of sound is 310 m/s (a) What is the rr lm8w eb9v5:)w)bcv angle the shock wave makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a plan;fwyor;lkg +6 et where the speed of sound is on6ky;+log;w fr ly about 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. Deteuz5r-7h4c gq ermine the shock wave angle 7ruhqg -z5e4c it produces
(a) in the air just before entering the ocean, $\approx$    (Round to the nearest integer)
(b) in the water just after entering.    $^{\circ} $
Assume T = 20 $^{\circ} $C

Show that the angle ;e/5ml r3iu9n0 x+fny hhux( q$/theta$ 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 eved .diy2q 2ks,aw2 7hxactly 1.5 km above the ground flying faster than the speed of sound. Bya2qs2 e27 .wdky, vdhi 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 tvot c91floqab 4)i5w, ek30ulhat sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimll4o9b5e,t1 0co 3fqkv )au wium time between pulses (in fresh water)?    s

  Approximately how maly7 otsd r2zq .u;qs)7trx- k*ny octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphoxw/cc78z5d1 nm g 3ebtny. It consists of many plastic pipes of varizt5w8c 1g7mbc n /ed3xous lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m froopw s/nz *n 8ml.7wkp:m a person makes a sound close to the threshold of human ho8 pw.l*nzmp w/k:n7s earing (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82st8 k6.j:l.jyo 1bnaoii n+7d-dB sound and an 87-dB sound are heard sd:i+ otb6 a.j8jn 7li.oskny1imultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open r1s(nr zoyhpdwf7r; ms*m982, is 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in all direc7wd rfsm8 2zshpyrr91;on*m( tions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz., 8io/of;/u bjx* gb0vg5cjwfq spp-, The power output drops by 10 dB at 15 kHz. What is the j 0;,8c up,o ps/5j/wi*- ffbxqvgobg power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over td g)2y.xt tb,fheir 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 30 m from a jet airplane xg, 2yd.)ftt bengine?    W

  In audio and communications3zf)za bnz,4aee( 9oo 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 ffrms pkin -um23x-z8/ requency 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 fixedizl y:* do*f0emla *s2 points with a fundamental frequency of 440 Hz and a mass per unit leng:fil ol*sda yez2**m 0th 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 / g1wcvh 8urrizhi(5qu74 cs(8 p pi/habove a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the aziqp(5u hrpcgi(h/ hw4 /svru8178icir 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 thj)hax48 )p,eojb s1ur boqi; 9at is 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) with the third harmonics91oa b)bjj ;,pru4eiqh) xo8 in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to r rgx2.x1ds;2et - xqj u7kq-zi); axpxesonate 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 500–1000-Hz range coming from two sou t*rkxac),o. erces. 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.te),o *a xckr other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train i,p9b6 hn6 nbxrh/3rcl s stationary. The conductor on the stationary train hears a 3.0-Hz beat frequenc39bc,6nhh rp/b6n r xly when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 Hz. mfw i/uj6ir4j,r53ypAfter it passes you, its frequency is measured as 486 Hz. How fast was the tmi 6,53rjrf pwu4y/ji rain moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to te s c,j:7wxrl2he difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops byc7jx sr2: w,el 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 frg;wrt2 p: ete-equency of 11 Hz. The shorter one is 2.40 tg:ep t;rew2-m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves pd 0h3bb ;y(ox+s c*y kd59slf5b7vuoeast 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 (ayho9kl s(sf vub5yx5 bcd7 ;*e b3o+0d) 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 0vbjrar:*52 ir s lobdcv8-,xin the aorta is normally about 0.32 m/s what beat frequency would you expsvbrr5jr- iabc, dlv0o: * x28ect if 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 m/s while the moth i r fm)jts(6nj;s flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat af6ftjjnrm) (s;ter that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approac/s3ivymjywq5ud) ,6 jv zx1 xi)hgv )ga-;m :ahes 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 detected by the bat so that the echo from one chirp returns befoy)z-j qmxu s)mj5)ia/ h:g3xga, vv6iv ;d1wyre the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one Alpqo 8ij ) x/qdhk5,9p6rzjl8hhine village to another. Since lower frequency sounds are less susceptible to intensity l8,ri 6dlx9)pq z8 / kjhjq5ohhoss, 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 comprok/fgb6sr1/9pcyci)( t 1k 0qud j-lajmised by the presence of standing waves, which can cause acoustic “dead spots” at the locat tsrj1/1kucp /-ld (09 ckgbq)ayjif6 ions 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,” e( r ad,l7zn(.1qmc9q evh9aw 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 practice, the rod can be made to “sing,” or emit a clear, loud, ringing9e7edlz 1v mw (a.qrcanh,9q ( sound. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequencyfdf kxk)a,t - mh8ix,/ of about 8mf-x)kx, ,f/ dahkit1000 Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on th+dqkt u+gf20 arg00wi e ground hears the sonic boom 1.5 min after the plane passes directly overhead. g fi0tdg0k2++r qa u0wWhat is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 1*bxeupxg kkzqf0.9 b)l a,bq* la /z725 $^{\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