What is the evidence that sound trn 4u3o;rt (dr.t lxaq;avels as a wave?

What is the evidence that sound is a form of pb6ye l ma9(w(energy?

Children sometimes play with a home4f v8j2ngy x60//eu ovn9s*8pflrm zl made “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a /lv9or*68/ n4 y8ml0pxszj v2 gnfuefchild 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 passes from air into water, do you expect the frequency or wavdm.d mxl rnu.9-c a1nj iq0k.;elength to changemxrc.ln ;n 910k.iuj-qd dm.a?

What evidence can you give that the speed of sound in air does not dec bs;- f p (mk0.,eooiw)yr q(v kmandi/94ty8pend significantly oqt4ky i oam m-0bn(;e ofc,r k8d(s 9ypwv.i)/n frequency?

The voice of a person who has inhaled helium sounds very high-pitched.si- xm01 v)lvf Why?

How will the air temp 7u s7vyt2 0h/u,jvoawerature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of 3 o 0:kucov/sjsounds in various frequency ranges.3 jks/u0ocv :o (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer :h,sd.s9woa 9mupybt5n *0nrtogether as you move up the f9td ,y9rn* m5bn.op wsa:0s uhingerboard toward the bridge?

A noisy truck approaches you from behindag z5ht3yr:s+v ;wx ,1 tm:jvq a building. 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 S,matrwvgjxs vz :+ :yqh3;1t5 ection 11–15 on diffraction.]

Standing waves can be said to be due to “interference in space,” whereas beazvac/b m:;ea1e4d e l7su4 nv;ts can be said to be due to “interference in time.” e; u:14e7; vm4/zncladsve baExplain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointsnpn xx-383j:ps (itvfa+:4atsia+ v 7xys h4l D and C (where destructive and constructive interference occur) move ffn ia:j x 3st4 +l+ a:xn(t38p-a7vih sxysp4varther apart or closer together?

Traditional methods of protecting the hearinvht90e 8txsn; (ywt.qz5h b)bg of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. 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 0;vws x(e 5bhbqy)n z.t8tt h9noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–ioj m/,o1z)oc 31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In whoiczmo,j/1 o)ich 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 andjcdw uwsg4k8/ cz+i3/2g+w xdyrzu9; observer move in the same direction, with the same velocity?9ri /jc z k4dwcw+xy+wu/3z28u;gsd g Explain.

If a wind is blowing, will this9d6kaz2.g wcv alter the frequency of the sound heard by a person at r9wac6dk.z2 vg est with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a jz+prihe 3e;p i -0t py:x4i(rchild in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whiij iezppr:r3 0ye -;x4 p+h(tistle? Explain your reasoning.

  A hiker determines the length of a lake by listening for the echo orc3 hepohzkb9h7m nr36t i(7u1ru2 r2 f her shout reflected by a cliff at the fah1bz22ru93i hu 7rh3rp6ernc ktm7( or 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 below the waterline. He hegng q ko05+7suqa)7cmars the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1o0n7s+qca g)g5mu k7q 560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in airmo4zq j8d +a87+fof kb at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day;0/8.0 qwodghg stroa . Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fishg gsr;h.dqtw0o /a8o0 ,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash 7 q63t : dx* ktjd6e9e)nmt,fpeu47 tjsoq8azit makes when striking the water below is heard 3.5 s later. How high is the cliff?7tu:d3 op,)a6qst*mte7ee 6 8zftj4nj 9q dxk    m

  A person, with his ear to thebdaodd:0 uq6; ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the im6;bu :dad0dqopact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dvxe2w +f3ebgh bt pya79j(k8(istance by the “5-second rule” b8 +2x( w73(9avg febtejypk hfor estimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of6ay1qk 1)m6fpf,cww4 or3 xav))vvf m a sound 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 level of a sound whose intensity is 10vtw 0r/1a bjmi*enb$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB wpzsgb4 u574j9 :kx1 fwk.jx sehen fired simultaneously at a certainzb k4sw x9ef47x5kj .ugj:ps1 place, what will 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 equal+a ytxc8/c) 3t7qi jitly noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine8qyc7+xjt ict tia3) /? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whereas for (0 eh/ywqao1ar8 w+y+biuss,a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for ow8/ +b s,r hws 1iaayy(+u0eqeach device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking inbrv. ;*5jumrz c6fn/ n normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mo65m/;ncrjzv.nf ub* ruth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an earzbj,scc3*d2-xxg 4 nydrum 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 0lx6dy(bhpm uy2p 7v 7rated 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 from a loudspeaker connected in tury 02yp7p6l(d u vbxm7hn 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 vs9fpka 7e/3pi 1b xg7130 dB when placed 2.8 m in front of a loudspeaker/pa igs7v epx7 1kfb93 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 typicl*usd4d3 lio-tf4, 2)ri kyxbally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amounx-b 2u*d 4o3)tifkyllr d4i,st? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave i8j k 2ywp,;ln2wav3yh v :glp3hd.l;qs tripled, (a) by what factor will the intensity increase? Increase by a factor oy.lwv 3w,; gy2l:lap nphjv; 382k hqdf    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has tlb7sm1 r/.v,p it;s /o;s0wd z1wvuqjxo1v0hwice the frequency of the other. What is the ratio of their intensities? zw r1 7u; vjoboqpsm.,t i0lxwh/110sdv;sv/   

  What would be the so:xsdeg b*j 5+7 waw7dtund level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 300:ge 5 x+7dw7dbat*wj s Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 100-Hzh0x(ksxt. -7s b ldk(0 bjihz9 tone that has a 50s0b (-txzl7ksh 9h k. xbj(i0d-dB sound level? (See Fig. 12–6.)    dB

What are the lowest an)ai-rl r8dc3wp n(xm8d highest frequencies that an ear can detect when the sound level is 30 n( w8rca38l)xdimp -rdB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range i :.;cd kx*g iag3h7 sndz)asmz 1;ietr;04vaof sound levels. What is the ratio of highest to lowest intenshe4 *acsx i1)a.d gt0k;dzri;;s g73mav nz:iity 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 fundamenta1;.wprjktow 5lkfw 1l8mu):k 8 wpt)c l 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 the string be plac.wkpcl18 wo;m k )k8w: )urfpt1 t5jlwed?    N

  An organ pipe is 112 cm long. What arnnoky ) 8fdgz( u dv8) i+92 vnwjvu+oy8(sg6je the fundamental and first three audible overtones if the pipes8 2w)v yk)(f ndoi8(8+zd o96nju gjngvv y+u 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 expect from blowing across ..q,e ftl:f kjthe top of an empty soda bottle that is 18 cm deep, if you assumed it was a closed tuf,k:je f..t qlbe?    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:y cdz3wo/v q( the range of human heazwyo(:q v/d3cring (20 Hz 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 ha mriacg.8s -/ds a frequency of 540 Hz as its third harmonic. What will be its 8ms/ad.-c g rifundamental 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 above+ zl--8 cx;dvt9nh0fyh5, u 8c rtggxk middle C (33+cf0c,gz ; l u8xhr5nv-d-xg9 tyt8hk0 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middle C (262 Hz(ttz:qn8+0jg (eq jw c2yuad5) when the tqa(+tg0 u(e2nt 5 yqz:jd8jcwemperature 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 2uy: ohzcgo8 0/dhu4z7 0 $^{\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 the one * wb s0h iyely*)5xr7i-s1hole be that must be uncovered to play D above middle C at 294e5n7 0x- syr* y1)leiowis hb* 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 616 Hz, but not.g r*nz/th,ss 5ih0 wqi2j,7t(eu )waxd (own at any other frequencies oda7i ge,.ww(0qnj t h i/n*t)5sx sw(,rh2 uzin between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonaty 1tl;5g hiv f,u.z )6 6bidu,grjetm8es at two successive harmonics of frequencies 275 Hz and 330 Hz. What ,.g;f r1 vt5t ed6 z,6bjmhgliy8iuu)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 h/q; -6tkbdy :gco i9fo(6rgr$^{\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 the9n*fdz fhr7x* audible range for a 2.14-m-long organ pipe azxr*f* nh9d f7t 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal isuhy5 6l6g do;2xny x+i approximately 2.5 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)2g6;lxy d+yh onui6x5 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 bqzo/+5clv w2nlc8h) qw 9 vo;oeat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How faoqc oc+)o 5/vqzl 2lwv9wh8 n;r off in frequency is the other string? ±    Hz

  What is the beat frequency if mid -1)u kyut jdbkj1f:o+dle 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) operat lfya5x9q;9g1c+ t tpges 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 simultan+fyqta p x99l5g1g;ct eously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tunind6e0 y 5+ 6;pkbuz7u 7u//it/ gmphbjmryze 8lg fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the stringuk7+e uipz6z ;/ l/jt my u/r0mb7gp5yeb6h d8? Explain your reasoning.    Hz

  Two violin strings are tun8k97 qk/:tgxfih o8 wved to the same frequency, 294 Hz. The tension in one string is then dgxoq:fvwi tk98/8kh7 ecreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two id1jnm t -dg0p8.m;axbzentical flutes each try to play middle C (262 Hz), but one is at 5.0°C and tm-bm;g jpd1t 8.0a nxzhe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, a1m7 (hiw*r3ut u6 hj5ztsycs4nd C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possib(5t mswtjyr3uh* 46hz i sc1u7le 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 staq 7n pzij4w:6 eqk726:qe wbalnds 3.00 m from one speaker and 3.50 m from the 2 w:6e4n7waiqbejqz plq76:k other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibratimxb 1 0gr0x07zwz5m8nit8 wztng at 132 Hz, but a piano tuner hears three7gzx xb801izrwm0t8 mw znt50 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 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 wavelengthhnp 502ke36bdw yu*z ds 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assunud2bhk0 5 p zy*ed6w3me T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire enginengj 9xd/o7 7dy 1bpl1a’s siren is 1550 Hz when at rest. What frequenog7lpdbjy 1 n1a/7xd 9cy 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 yo1a bq*6e5 fqw/flxb:bu detect if a fire engine whose sirexb 1e5 * 6qw:qfbbfa/ln emits at 1550 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 2000-Hz source is moving tovm:31fkx* eu r )vsb*eward you at 15 m/s versus you moving toward it at 15 m/s Are the tueex*)f b3svrm1:v*k 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 equipped with the same single b,1v mrtxfp*sxrpl-+ fo. )(r 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? Assume T = 20 +lpr xvfo( fp1s)* r trbm,.-x$^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and ret0 me.jzznx6 kcza6+ 77ptz+s ceives them returne067en pz7zm sajk.x ctzt6++zd from 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 :df lusz 0+g:wa speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with freque 0+:f:ulzs dwgncy 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler eyiu:g 0 dq a;ade r v(plhph+)rme..0)xperiments, 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 at a speed of 10yequr)l:iremp ; 0v.h) (gaa p .hd+d0 m/s ?   Hz

  A Doppler flow meter us;goiz5 maxdq82tl rd :fol3 kil.b7*;es ultrasound waves 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 frequency if *qad b z5;g l28t.rfdo3l7iolxi:k m; blood is flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves owf-ahy d0 07i,colsm *f 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 souv,o8cs)s ks*gb*4dk s nd of frequency 570 Hz. When the wind velocity is 12 m/s from the north, what frequency will observers hear who are located,d*k)gb svkosc4* ss8 , 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 ita4m4 yp9 me8 bh*;bvoz fj.d2f 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 w.z klnkxt.m 3tdi )0.is 310 m/s (a) What is the angle the shock wave makt .kxd0.ml)w k t3.nizes 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 tx /jpcd a :9nib0a,6npf7d ;oghin atmosphere of a planet where the speed of sound is only ng: 7dn/ia,xpob d;j6a 9fc0pabout 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 mvk 2i:uyzkgt 28hp (;a/s strikes the ocean. Determine the shock wave angle i2ahv kyg zt;( 2p:ik8ut 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 : 0yn6xbvrho8$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.9;udxz gu 1 3emrk4rr:5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizont4 mu1rkr xzgd3eur;:9al 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,v8hb)9,u te:kx 63 sljln.caq000-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 minimum time betweenqs:ln9 cujt.e3),akhb6 8v lx pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audibla ;5x1 g0bi yqolv)cs/e range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a si yqi1smt-+zdir ,6 5fix2 v2rewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on both en6rii1i s2-ry t+vfmxi5,q zd2ds.
(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 thresho6 ;v-7cad3kymhy p + s5xw:ty,u(.lq cw 9exbcld of human hearing (0 dB). What will be the sound level of 10v;ch+ty ca,ex6k mqb.ps(:9y 5l7yuwxw3d -c00 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB sound ar 4:tx:dfd (zbce hear4xbd:( :zdtc fd simultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the5*dxf)jq9k8jjf3dz5 eo6 ug p open, is 105 dB. What is the acoustic power ouj 6e5ouk5dz*d8 jxgp) j9qff3tput (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 powzef70 5s6qdp-euf /pger output drops by 10 dB at 15 kHz. What is fpsp50gfq /u-67edez the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective db st)t+ u0hp8yevices 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 anubt) spt+ yh80 unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, il7bb1hm4e2d 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 tunedd0t8v-3l:rtt( m3xipdf fq;r to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fi/j 4+v h q-l./kzq-vrkg 3 .0kxgzsyrzxed points with a fundamental frequencyr s z/rg lzy+hxv-.kj43qv-gkq/z0 .k 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 into vibratych)p/ mn1 ,d7ief om:ion above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to re,i7oyemf:nhc1p)m /d sonate 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 iber .i(8p4lg as near a tube that is open at one end and also 75 cm long. How much tension shoule8airg p.( b4ld be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full loonm l2t p 972kj1a3lprsfc6c5 l)gi :tzp ($\frac{1}{2}\lambda$) 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 tz izpkb3x3,i s*+-h ;6ho-czp8opg i wwo 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 mioh;3ixp-iog6zzz i3+h8*b pw , c-ksp nimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. 4*+8o uew -;xspt lh8wc(udvoOne train is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequen 8td4hw-xw+uo 8ol(pe*;uc vscy 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 izf o.+3/ge0 mgxto mn.nc4 yst86lm9rs 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was thm +4eofg 9s/ .m8n 0z.mxg3l6cntyt roe train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars jus.ud(tqch5mr t4*. i ist by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightawad4 ..* m(t5hqitircus y. How fast is it going?    m/s

  Two open organ pipes, sounding together, produc.gqim ar w,verft,;j: o).o:oe a beat frequency of 11 Hz. The shorter one is 2.40 m long. How low).f:a o ,mevrojog,.rq;i :tng is the other?    m

Two loudspeakers are at opposite ends of a railroad car as.9hhpak 3br .z it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frekb9zh ah.rp3. quencies 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 aboutz 78 dj*pc.g d(gb)e(o en3uirp0tqs / 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the w)3(e*q p tnebz u/pgdrsj0d7oc.8(g iaves 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 +re(zu 9.8xay ua, judmoth is flying toward the bat at speed 5 m/s Th +z.aayujur ex8,u(d9 e bat 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 frequency soun0nw v( dz*erdne6 lp)2d 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 detectpnrdv l e*ewd6) n(z02ed by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 11wtz t6ngxd/ s,lm tc b.,+bv12–38) was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, 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 sharl vs .bw,zx,t+d1n1/gbmc t 6tp? (See Table 12–3.) Model as an open tube.

  Room acoustics for ster4va a3 1yn9bvpeo listening can be compromised 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 standing waves in thisp3 v9y v1a4abn room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a loa3kf ;1g)mb,do.p qqmng, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the otmmdbq )p;k,1qafog. 3her 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 tp3;ge)p 7dh 2x/ ur/opvzkk1a)r0ruxhreshold of hearing for the human ear at a frequency of about 10)u2rkagexkpvp x 0 ou//7rhz1 3; p)rd00 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 the ground hears thw fo cd/kk)nr/:qh/8te sonic boom 1.5 min after the platqkdo/8fk/ wr )/ :hncne passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 zzd 0 -r98oa +0mt0nt+ c7tty;ldgzcn $^{\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