What is the evidence that soun1 8fl6aq/ 7dlk0xwza qd travels as a wave?

What is the evidence that sound is a form oocehmbs65ha)3+x-jux4j h5b z 9cqn +f energy?

Children sometimes play with a h6vxq noo3fxr*x* gx/ 1omemade “telephone” 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 wave trarvxxxg*/f o3q n* 1ox6vels from one cup to the other.

When a sound wave passes from abmv94-i4qeta/ a3whair into water, do you expect the frequency or wavelength to chq-at ev/aaw4bi 943 hmange?

What evidence can you gi/zmny 2fx(8 vrve that the speed of sound in air does not depend significantly on frequemy8f/ r(2vn zxncy?

The voice of a person who has inhaled helium sounds very high-pitch 0: qopqmxu*m( zdf4pobgb 713 htl5p0ed. Why?

How will the air temperature in a room affect t awy vkzul/ hc6 g:rh(4lv siw2,x:qxl9g6 7(lhe pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of sounds ,g0h m:l e5xmxin various frequency ranges. (An example is a car mum05g, x el:xmhffler.)

Why are the frets on a guitar (Fig. 12–30) spacedf+bq4.r3d tnfzq7+* z kcm,eo closer together as you move up the fietd4m ,b ko3r*qf+z7.+fncz qngerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially you hear isi7; m43h wqn ;pe 9bvvkqec -c0q5:ybt 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. Ex cq7bnc;y qhe 04sbm:-vivk39p ;qw 5eplain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be s)ky (qy)8 w b:f; vx12(vzhabirk.dqj aid to be due to “interference in space,” whereas beats can be said to be due to “interference a 2qj(kqd f1hy)iv:wyz(8r. bv;k)x bin time.” Explain.

In Fig. 12–16, if the fr13fb;oiou cujun cco/y*g(7/equency of the speakers were lowered, would the points D and C (where destructiuoiuyo jo1(;ncc*gb/cu3 /f 7ve and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who work in areas with li*x+ z7+x k, w,ig(2pbwyb iavery 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 noise reducxiia7*kyg,pb w+ xi2blw +z,(e the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each /-k +bre 4f rrb dfs.kafy+75vwave can be thought of as a superposition of two s+frek+f.ryk7f-rsb b/a 4d v5 ound 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 ktvl; 2 j;2 1qpqwaiy*in the same direction, with the samqj1q altvi2; *w;k yp2e velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heardrj)l -a gqgkz;23ohj3 by a person at restj-zgoj r3;)h2 q3 glka with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swiz t86;jkj b*)pkxr4xw s:q7zmng. A monitor is blowing a whistle in front of the child on the gr p4rzzqsj*xk;b )67xj8tkm:wound. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of 40iuq*nbmw0- ;gpj hla lake by listening for the echo of her shout reflected by a pb -i0mq4j0;gu nw*lhcliff 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 njgdjk 9p v +/w/-:9xtwra,f lship just below the waterline. He hears the echo of the sop9t 9/wa-xld fjg wv r+:n/,jkund 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 wavelengtb2 ews0oi:naec+2u3 mhs in air at 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just abo8bq3s3y/hasze/wdh 2 c-qsj 5 ve a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the back sss /c83y3 2zawhj5/beq-hqdfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped frp7nmofb :9 t-jom the top of a cliff. The splash it makes when striking the water below is heard 3.5 -7o:btpjf9m ns later. How high is the cliff?    m

  A person, with his ear to the ground, sees a hugeos qd0x/ yaph-y(4:zf ndf r61 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 o4nxhfdrqpfz(a 1o6/ yy- sd: 0ccur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent erro )ohi8 ib:nlv2r made over one mile of distance by the “5-second rule” for estimating the distance from a lightning strike if the temperatur v:nhl)8i bio2e is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain levelcm2 f;: gx qcb0 +lnuwd:(7smm 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 qka,j9pmhw-on(k u :,is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level6fi. - esgt d7fph/lk)ad+)py of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, not a).)he/tpl+d-7dgkif6 f pysdB’s.]    dB

  A person standing a certain distance from an airplane with four equallylr1 q502ej8l wxr;q+1op kwv k noisy jet ekj 08rq ;ewkl 2l+q1p5wx1vorngines 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 engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, whky9hh(r33 a fiereas for a CD player it is 95 dB. What is the ratio of intensities of the sigf iyr3 k93a(hhnal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speakinv6h84wdvl n8d g9 x6pfg in normal conversation. Use Table 12–2. nd64pl6w9dvg vx h8 f8Assume 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 strikes an eardrum whose 0dz5sv-t0+*nb1kiromyq o+t area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifieqcctaf r 743k7r B is rated at 40 W. (a) Estimate7rck3cq 4t 7af the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 13d)a k9a y,:qoz0 dB when placed 2.8 m in front of a loudspeaker on the szq9yo ):,akdatage.
(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 d2w r 4o)8 ,zx1oi-0clsq++gaq ddabbxetect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose level q)ad2xq,b0scrzw+ogo8bx+d 14- lias differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by wpa6r e9q3 b-p0liu3 uhhat factor will the intensity increase? Il6 i-eu9 b3h0rqp3 puancrease 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 twice the fr3- so axx sctay)h-*9kequency of the other.9xsy- 3xhs-a ktoa)*c What is the ratio of their intensities?   

  What would be the soundyi,mn 0k575pzkkb-fn +aiz3 e level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecule z5mi nib 537aey+k,p f0kn-zks of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have suo m u6 ;x.1/abct,xywhat sound level to seem as loud as a 100-Hz tone that has a 50-dB somxou a.1yxc,;6tus/ bund level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ea.j9wwll22vm1 u g og+ar can detect when the sound level is 30 dB?1l2vmgu w9+ ja.g2o lw (See Fig. 12–6.)

  Your auditory system can accommo sbr62.t ro7sdfuu7d- date a huge range of sound levels. What is the ratio of highest to lowest intensi.ou dsf d rrt767-sbu2ty 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 :y4+8j nqk1jn l a 0spz1koska/ u(e,pfundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under snp8q, 4 1e/nskjoal 10kkj+au p:zy( what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental z4cflbytl )48and first three audible ov4 l)f zlyt8bc4ertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequesu+o 3-.tk1d f/co2b8d(cyx c+owb zkncy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep ct 8kfsbc-ozw/+x. d 3 k(ocdu1by+o2, 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 wi/j4taypsd x/o4fq 57 xth open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the lxxs/ptd /q j a44y5f7oengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its third harm97y 0ah di id,0/u qmhcj7be9aonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its orig/bhqd9i 9uyhiad7ma 0 07jc,einal length?   Hz

  An unfingered guitar string is 0.73 m long and )tpg+ 4qm,du+*zlb, o dzd.2pbe+x ccis tuned to play E above middle C (2ub* pzd+)qc4.+,gdclp ,toxz bd em+330 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 aom+*q qn awv ./aag6 xhaq/l;8n open organ pipe that emits middle C (262 Hz) when toam/;l 6.8ga*hvnxwq /a+q a qhe temperature is 21 $^{\circ} $ C.    m
(b) What are the wavelength and frequency of the fundamental standing wave in the tube?    Hz    m
(c) What are $\lambda$ and $f$in the traveling sound wave produced in the outside air?    Hz    m

  An organ is in tune at 209trwz 8 duon2g8kxk); $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Edo cu06y5qp b7xample 12–10 should the hole be that must be uncovered to play D above midy05uqdo67pb c dle 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 4 h2 wn i/+0fkir32nij dd (s9cpi6brq264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in bet kjd ic rn2 6bii0fqn4 92/phsw3(+ridween. (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 res l5q,u oyh2m5lh ue2;-iihmcxc/ j0w+ onates at two succecqi,2 m /lw5eojh2u;c h-0 +u5mi lhyxssive 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 (y;*p ,n)ofp yhrpsvcb 1h26 p$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audizn:r ;xc eoq2luh+6(bble range for a 2.14-m-long organ piuqb+r 6:h(xe ;lo nc2zpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal ifj 4xd6jn yr))ulj (8tket 2*os 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) of the standing waves in the ear canal. What is t ltx2* )4rj6uoje)k (j ftn8dyhe relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2+bjr d 6sf)tx,5ikkkuc0 0g2pavzt:b,v 4-xj .0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string? v2jkikx+)s0,4k p6b:a5,rtg -d0uftcjx vzb ±    Hz

  What is the beat frequency if middle C (262 wo)sb t;zz0 j(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 anothe6* k1vycjezj2r (brand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simuk6yjv j *ezc12ltaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s whta-cg-ny, r qk( d;1yven sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hg-vq-n ;y ,ydack( tr1z tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 -i y j/htr4hr-Hz. The tension in one string is then -jt-rh/ ir 4hydecreased 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 identical flutes each try to play middlnna- ;:nm5b zpesb1s 3/9frkh e C (262 Hz), but one isz9np- f3;ns:rnkma bhb/5 1se at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B hai zec/ n2xs7n2s 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 frequencisxe7z/i n2 2cnes are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person stands 3.00 m frob /c.ihi 5b g7a/ce5;8zvqrno) oiu /rm one speaker and 3.50 mcvioa 5h)/u irb cn5.b/; o7re /gq8zi 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 supposed to be vibrating at 132 8 ho,zu67knxr/bqktlp2g)z h n0k 4 r.Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If one is vibrating at.p2, kzzn4xob ) 7khlq0 8rrh/gknu6t 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in. u,px97(zx z4unjg8 5htkp yn air. How many beats per second will be heard? (Assume T = t9.,zx54 nz ghpkux p8jnuy(720 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain f0 l(6mimotlb* ire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a* m0t6bom(l li speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if a fire engine whose sx 7pg0 kxsk.4kymt wc7r x,/n+iren emits at 1550 Hwck /r 4pm +kyxknxg0.,s7 7txz 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 movxv /s39l*s8by9 mt wmiing toward you at 15 m/s versus you moving toward it at 15 m/s wbvxt 899 3*ilsmm/ys Are the two frequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped /r:0 jhqw dpljm)y6;efgj+ )nwith the same single frequency horn. When one is at rest and the other is moving toward th; mrj+e0q6p:gl nhj ))djf/wye first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrr1;dz+ct o6 pes vc;v)asonic sound waves at 50.0 kHz and receives them returned from an object movin)evs c;o1 6d;+vtrp czg directly away from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ul acc,:gbr4e 8y s5gqo3trasoy c:4esrg83gc, qa5o bnic sound wave with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original D;j nwq3 pc/-wloppler experiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed ofn cwqj;3-w lp/ 10 m/s ?   Hz

  A Doppler flow meter ;ktu kri qo. 0/j/y)mkuses 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 blood is flowing in large ;)/jmy io k trk/u0kq.leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves yq5tme,) sg6 *orrahmbgw204 of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When the wind velock3ke0*+u zyizity is 12 m/s from the north, what frequency will observers hear who*+ yzkkieu z03 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 ll4gyci6(z((va je . goand 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 acd:p a;4s c* p(rt0c0v1gwy txt Mach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wave makes with the direction of th4 ryca c0g(0 c*1tdp;:xs vtwpe 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 atmosphva, xv 1*,;ggbt3j 1bhwp 8qszere of a planet where the speed of sound is only about 351*bxathv8qg; w, vbs1zp gj ,3 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 strikesg5x 87h()i yrh)x+/hky aos ap the ocean. Determine the shock wave angle it pro87+ (hoxa5a)gp /skrh) hi yxyduces
(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 nv x4p*c uwkq h-m)15x$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 kmkksv4g4qbq 94 above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horisb49kq4vqkg 4zontal 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 sonar8jgs .)q jekk5i 9xun irqq-by3 ac4;: device that sends 20,000-Hz sound pulses downward from the bottom of the boanj;kcik:sr.e8b9 3- i)uqqq gy5 4axjt, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how man k5(6uwmkdpb 0 d; r*p-jty/upy octaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a displlwz.: eux ,+cafu3k:n ay called a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open on b. ,ceuznklu::+aw fx3oth 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 mmv(wt6i* evjgn- 2tl:akes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?ml :jwn*t-tg(v26vi e    dB

  What is the resultant sound level when an 82axa ezvv15:*(2 s,ox xr( y/vwp qn8yp-dB sound and an 87-dB sound are heard simultanevp xpy*2yr/ q,w(x158n sx(eaz:v ao vously?    dB

  The sound level 12.0zhis477emsj-igf 3rvb, r - h+ m from a loudspeaker, placed in the open, is 105 dB. What is th- i 3r-sszgef,4hvbr7 jim+ 7he acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. Th- 5 fjaovj:a0k65 mcske power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?fo:akkc5v0s6 5-mj ja    dB

  Workers around jet aircraft typically wear pr7f7la,o)pfcgu 7p/hnyk 2 p: potective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 12ckp:7po)hf u7a7 l/p ngfyp,40 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, the gain, (bdb if v.v8x kx0c(d0$\beta$ 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 violimss (zv 5oi.m)ss e41fn is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin ) jysxk4lwq ;h,7t +- h+g,g tzwywc0mis 32 cm long between fixed points with a fundamental frequency of 440 Hz and a mass w4xw )hh,+m lcqy zy;tgjtgwk7,+ 0s-per unit length of $6.1 \times10^{-4 }$ kg/m
(a) What are the wave speed and tension in the string?    $ \times10^{2 }$ m/s    N
(b) What is the length of the tube of a simple wind instrument (say, an organ pipe) closed at one end whose fundamental is also 440 Hz if the speed of sound is in air?    m
(c) What is the frequency of the first overtone of each instrument?   Hz    Hz

  A tuning fork is set into vibration above a vertical open tube fill ydlig 7)c/z:hed 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 resonate with the tuning fork when the 7)hyzdg: il/c 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 as-6s;pb k fj4t tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to producefpj6 k4-bt ;ss resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one,*vo:lr,d rm:e xi-td 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 comr)ol2kdth iz;j3 9:k;u /j-er-ik iqcing from two sources. The sound is loudest at points /i jr2ht z-kjlk3; ;d 9:-eiciqruo)kequidistant 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 sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The 7l 8;n vaz0aasconductor on the stationary train hears a 3.0-Hz beat frequency when the othe 7a s8zna;val0r train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches qrqwk r52 (7l8(s ,lyq.lz/ynn-fq gfyou is 538 Hz. After it passes you, its freqf8zqyl l(y-.5 gkrq,w(nr2l q /sn7 qfuency is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimatd5/h apbvt1y4- z/kcx e the speed of cars just by listening to the difference in pitch of the engine noise bety/a1- /b4ctvpxd k5hzween approaching and receding 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,o(dfzrlh o: 89 sounding together, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is the(8orlzh d 9:fo other?    m

Two loudspeakers are at opposite ends of a railroad carmj/)l ov (9zz0 wa)juk as it moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies o au0koj)v zzj(m9 )w/lf 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*uf odwzd2 6k30ne0t d flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected wodt36d0ez d2 * 0knuffrom 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 mxu 7g2x7uk 7mmoth at speed 6.5 m/s while the moth is flying toward the bat at speed 5 m/s The bm xukx7277 gmuat 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 sound p:iq c2gkcm.o1c2g la. ulses 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 detected by the bat mgc. c.aog2 :qk 1i2lcso that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was7z d df72ifsj6 once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long 72js7z6d ffid 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 lap, mz*pcn1 .qistening can be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure p *qap1zn .,mcnodes. 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, cal.gdw8e:lr39. ( xbofi i -fsghled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a li - eiwl8f:fdxo(3.h9igsrb. gttle 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 eab* m57 ho/qfqw+w:qvwr at a frequency of about 1000 Hz if/q7 *qvwwb+ow5m:q hs $I_0$ = $1 \times10^{12 } W / m^2$ 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 hearz9yfscx447y (fd-ah qs the sonic boom 1.5 min after c fy7q-4za( fy9s dh4xthe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 /h6hrr9i2m9y d nm0+t el-hwc $^{\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