What is the evidence that sound travelxu 8eb1s vqvil2 2jd5ap(s7t*.tj b* zs as a wave?

What is the evidence that sound is a form of energs(/ 2+ iumxkkby?

Children sometimes play with a homemade “telex 14pe(cby t:cphone” 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 tra4e:ytbx( ccp1 vels from one cup to the other.

When a sound wave passes from air into water, do you expect the frequency o8;1taz izif q0r wavazfi1 z q;i80telength to change?

What evidence can you give that the speed of sound in air does not depend s 7swu-k3bdc +n9gj f6wignificantly on fre 37 gc96bsu dkwf-wn+jquency?

The voice of a person who has inhaled heliubye3rx.fu1x: d s(hu0m sounds very high-pitched. Why?

How will the air temperature in a room afjj8b ggd87sx(v 3367hq.mdrep e yz e/fect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundspy8*,d2 3,hlcu:ttvjkt;vr h in various frvc; pt3l2ktd:th uhv* 8,y, jrequency ranges. (An example is a car muffler.)

Why are the frets on a guit,n 2/ldb579b x mjknzwar (Fig. 12–30) spaced closer together as you move up the fingerboard xnmkz,wnj/d b295lb7 toward the bridge?

A noisy truck approaches you from be(;d1gw , r ib.asr/ulhhind 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-frequencyglr i/shdw1.,a(b;ru noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “interfih ;mkv .51 efg8fdo)rerence in space,” whereas beats can bevg;df1mk.8ef )5hori said to be due to “interference in time.” Explain.

In Fig. 12–16, if the frevt28/oo 3q -. vqlkaapquency of the speakers were lowered, would the points D and Ca/l o8q3aqv2.p okv-t (where destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peoplet6f zka:a5vz* wjt6f; 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 noise reduce the sound levels reacwzfk *v:aj6at;6t 5 fzhing the ears?

Consider the two waves shown in Fig. 12–31. Each wave caw-(hdqb;q5oc r4zm ycmtz 80kg ;w7s) n be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, sczwdmbz0 qog(twm)y;7 8 ck5hr4q ;- (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 m it:xz quw*33move in the same direction, with the same tqu:33i*xw mz velocity? Explain.

If a wind is blowing, will this alter p2v56gv)a) 0tfqm y + 0rumesothe frequency of the sound heard by a person at 5 vsq) 2tmr6v+omy )p0 ua0gferest with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in motion on a swia* xn h3uok3,w,hal yr.: 6kzing. 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 whistle?3:yhw*, k. ,auh3rzoki6ax nl Explain your reasoning.

  A hiker determines the length of a lake by listening for the echofr: n dqfwbru y/5.;( nxa2om7 of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 s a fo7.mdby:/ar x(f5n;u2 w qnrfter shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. o) jd imt9nf,t; sy(8lHe hears the echo of the sound reflected from the ocean floor yn;d9l mts)( ijfot,8directly 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 inh0yn ba9h0.tx 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 drifti/ f7jrs d2jmz4rhg.i (9)i 8qiy;blihng just above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 hz8(/ilb)q47idj;gysf j. r2 i9m r ihkm 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 todv yu 18*p2g a i.n*6tbclc1ydp of a cliff. The splash it makes when striking the water below is heard 3.5 s later. How high is the ccbdpvud gt1n6 1y a8c *i2*yl.liff?    m

  A person, with his ear to the grr y/a g*2uouagu4gp+,ound, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact:4/ay2r g + uuaoggup,* 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 distance by the “5-second ,2n,i7g mt fz 4azma or;1b*bfpq/;sj rule” for oj,4*zrz/ f f2 bn7q;msg bp ia,am;1testimating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pal r hl9uudr7. 7mc d:o;-itb.vzd06rwin 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 int3w3f/ofmr .ha7: ntf censity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB b kk6z8kpgaq +1ov42u when fired simultaneously at a certain place, what will be the sound level if only one is explok8p qgka+k16vzu2 b 4oded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with /;fx5a4kbg tn four equally noisy jet engines is experiencing a sound level b gkatx/fnb ;45ordering 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 d*nd) tl5 wb )vsw9t,ciB, whereas for a CD player it is 95 dB. What is the ratio of intensities ob vlc9),5tnw *) wsdtif the signal and the background noise for each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in normal conversa3yf2p zkup6 s:s+i:l ztion. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the moi+fzuy36s::2 psp lkzuth. $\approx$    $ \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 ca+wql915c 0z tm;xvu an eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, whill./z xfh;ey tyw 758bpe 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 loudspeake.f 7bhtwely yp8/5zx; r 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 1h4d:gx ft+ekyisre.hh .2: 1u30 dB when placed 2.8 m in front of a loudspeaker on the stage:1k tr:+exdueygi2s fh h.4h..
(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 soundvf+/(ap efokhn l,.j nz5c8m) level of 2.0 dB. What is the ratio of the amplitudes of tf.)cznvl5km n/ej8ah,f+( powo 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 intensixh58*2qgbfx5clqo a ( ty increase? Increa8 qf5acx2hbo lqg*x (5se by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement 9os 6or4xnq l6amplitudes, but one has twice the frequency oflo69 q6osx4nr the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air tha,qjd3no(9l :yrsbhf 4x sb7i 7t corresponds to a displa joq b7 x4b,y9sihnfsdr7:(l3cement amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound levef v g.ilir28ku4y 0ga9lpw*,y l to seem as loud as a 100-Hz tone that has a 50-dB sound level? (2vrg 8lp.lka*i9,fu yg wy i40See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can/:v w 4fh1 ac/3ghftf:c3omz n detect when the sound level is 30 dB? (v3cg/1 3ofw hf/ n4mhat: fzc:See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. W,ect 7u0ty*iq9( nvx ghat is the ratio of highest t,u0 g eqx9ynt itc(*7vo lowest intensity 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. The lengg;gqd;; )iyb;8nkq hx(c :sqjth of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the q(dchky8;qs g ;:)igj;nxq;b string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and first three aur3bu bbb 44h (t:zrl x9b2i+vudible o x4tur2: lri9h( zu3b4bvb+bbvertones 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 frequency would you e+r+,5qvq 8 buo0u i3j) adxjrbxpect from blowing across the top of an empty soda bot5irrjq u dxb 0b8+) ua3,j+vqotle 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 pi e /q6;oxj,adsa/g 5jgpe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the ran egos d /a;a5,qgj/jx6ge of the lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequens3hiaj0 kmu8p*.hp b xs4vq3coi2w 88cy of 540 Hz as its third harmonic. What will be its fundamental frequency if it is f asmjc0su xwpik.hb8qi24 8*p3 38 ovhingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is m) a8byz: +nhf0.73 m long and is tuned to play E above middle C (33:fyma)+ b8 nzh0 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 emicoz;dgp w r95kgx990sf ;i (ikts middle C (262 Hz) when the temperature is 21 z;gcpiis w9;(kxk9g5o90r f d$^{\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 20 u8l 4wdo rfql2zi8 v-8$^{\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 shouj3 qzhvkk j+8mme r4 zii2w0:3ld the hole be that must be uncovered to play 3mqk i: m8+z0jk2 jv34e rwhziD 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 ,8 t+tcy o b1 45rkpsy3dmz7sx264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show tt3oz18bymrs ykp45,x +d s7c 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 lonotoq t9tg (k 0/(lf7azg is open at both ends. It resonates at two successive harmonick09(7l(qt z t gao/ftos 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 j5ewr3 g/6h+h /yalzo $^{\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 audible range for a vpt0pv45nlj12.14-m-long organ pipe at 254ljvn0 pp vt10 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is . mi1s3i a( qxox8sc6papproximately 2.5 cm long. It is open to the outside and is closed at the1.6oc8s3qa isp m ix(x other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryinem8 b qkor*p(gf1p 4)ng to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other string?8kf) bgm1q4(p* ope nr ±    Hz

  What is the beat frequency if middle C (262 Hznee5h5zm gzy+i 0s.*6uzcsr 0) 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) od652 qcy8 hwieperates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of fre 58ywiehq6d2 cquency 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 atqnhkl2);qf/ix 9 ,g350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency )2 qai klh,/nx tq9fg;of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same fre6(p jmvbn0frk/chlya 6 6e25iquency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency hearilr66eyp0a( h f2knv c5/b6mjd when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be a:w0o.v93+y3 dooyoqv wm) ltheard if two identical flutes each try to play middle C (262 Hz), but one is at +o)w olvmy 3 3:yovdqat.90wo5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning for )imc xgd+yfxjke .p+p,q:9x1ks, A, B, and 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 a egdpk y+1x.jfm:px)xqci, +9 re the possible frequencies of A and C? What beat frequencies are possible when A and C are sounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1.80 m apart. A person spt3tgw+: vin:ng0,yi tands 3.00 m from one speaker and 3.50 m from thepw t,ygigv:n 3n+ ti0: 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 Hz, but a piano tuner hxk: ka)w6 oev.- nwqs,ears three beats every 2.0 s when they are played together. (a) Ifkx.w6 o san-w:e)vq,k 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 waveljjn 7g2*tr9, esuxck byx25 e-engths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T =j 7tr n,9x *csuyxgjk2ee2b 5- 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a ceau-jkg: y i7t1rtain fire engine’s siren is 1550 Hz when at rest. What frequency do you detect if you move with a: i-k1ut aj7yg speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequ7-u f, w,lhspl ka2c:mp ze:t(+8ehfoency do you detect if a fire engine whose siren emits at 1550 Hz moves at a speeow m+z:8 stpe2e,:hff 7cl-khu(a lp,d of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequv,tyn8q:d99 3 gs rcicency if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are they closiq8s y:9tr gcd,3 nvc9e? $f'_{source\,movine}$    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 frequency horn. 5bd4 p/ffai icpkt qt 6t3)o22When 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 emittf6k t3aq 4iicd2)5f /p2to pb? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives themsx;8 r c1s0nrt returned from an object moving directly away from it at 25 m/s What is r8 tns10 ;xsrcthe received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s fy4nn6ssba:ey7xl .aj hx.;8 As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kbsl;fehn8y xa7.jsxy :. a4n6Hz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler exper77 ;x:/jkwmh/*jxx)ih blgnv iments, a tuba was played on a moving flat train car at a;l/h7g xxk jvw/ni7m) :bhjx* 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 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-nnnpngf54s; g/ 5. prm;x gu x4-ti3nhflow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is tapx i4;-s 4nxrut5fgn3nnnh mg 5;/.pgken 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 ultras,ovd -8hl m 0ab./yk dynv5a;idu*jiq)g*-s conic waves of frequency $2.25 \times10^{ 6}$Hz is used to monitor the heartbeat of a fetus. A (maximum) beat frequency of 500 Hz is observed. Assuming that the speed of sound in tissue is $1.54 \times10^{3 }$ m/s calculate the maximum velocity of the surface of the beating heart.    m/s

  A factory whistle emits sound of frequency 570 Hz. When th lj lue5u f,edtja25:9e wind velocity is 12 m/s from theee jut,j2al :5u9df 5l north, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed a,vb:g3i +a f:hccz7g as9aso:t 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a)vwo2 n0e-31otr7h9x tj:hpuq What is the angle the vhpwton 971-ruxht 3o2 eqj0: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 (ix+ sd s 4fawj5a)oi-a planet where the speed of sound is on(4a+d-xiw)a5j os fs ily 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. Determi)z. e vdkhql2oo++h +rne the shock wave angle i)oh+ 2. h+ore +kqzlvdt 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 .t e :b)clch4)q4m cvp$/theta$ 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 /kcs 1oy/z58 ,clnc7it/e g) ogj vin(1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonioyeizc(1 /n, 8n5gcgkl j7v/)i/o tcsc boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz t 9wyjstf8;nz 5yv on9*4sw :b ;,yhffsound pulses downward from the bottom of the boat, and then detects echoes. If the maxims:fy8 vywhf9b9s ,o 5tfz y n*tw;4n;jum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are thc:z6 j8p ieyv4ere in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consists ot))- mpih+ otsf many plastic pipes of various lengthm) )+pt i-oshts, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound cle54 snb0qi+f rose to the threshold of human hearing (0 dBb5rfinq0 e4 +s). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound3u5 sio-hf;wu*;f i ui and an 87-dB sound are heard simultaf ihui u;s*-iuf3o;5 wneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. Wha;..i e4pcgvtq,6 gywwt is the acoustic power output (W) of the speaker, assuming it radiates equally in alw vtwg4p6gyi.;. ,q ecl directions?    W

  A stereo amplifier is rated at 150 W outpu/ pcl./cjf qzddtj1 v))ee,p9u*+gbut at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the ppe,gvj uc*cqz1bddlf9)+ t/e /j.up )ower output in watts at 15 kHz?    dB

  Workers around jet aircraft typicall e-gpft j/-s3iy wear protective devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would begjie sf-pt /-3 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, t2zdkf83,uk uozyd 79 $\beta$ 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 ,6cp 9iw po,jnd3 t2f4xwm u p.v2:zbhfrequency 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 fixed points with a frr-.eg j:z .r ,5c.rsd8iua2a jb)af dundamental frequency of 440 Hz and a mass per unit len,ja:sa2.r ir . bdfu.c5ra8e)rd-zgj gth 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 vect+ d b87 lygkb2ztt0g)5d. oibration above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. A )tdb.btk5c de0z2tgo ylg7+8s it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube that o8c 9tmj3jfoy7m1j+xis open at one end and also 75 cm long. How much tension should be in the string if it is to 1 fmjj+ 9o8c3ymt7jxoproduce 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 loop ukbpse ,4d-m ,($\frac{1}{2}\lambda$) 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 tont lp)x g(s)ak:5aopj/e in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one sou)/s:g5 p) atlajxpk (orce than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. The conductor on t-bwu 7 d61kn kqu3as.0ixs0rvdj:cn : he s d3-vkax kqji0nw0ur: d6.n s1: 7cusbtationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approach8c i28l (agu h5:z+layi) fc-dvt1vnpes you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (asshll n fy:i+5t dv up)2cicaaz8 -vg1(8ume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dymdfv;j ( /-bsifference 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 straightaway. How fast is it going? ( yjfdbvm-s /;   m/s

  Two open organ pipes, sounding together, p prxy)l7f(136 vivfy 1 wvfxh(roduce a beat frequency of 11 Hz. The shorter one is 2.40 m long. Howv(il1 xr )fyff6wy( pv h1vx37 long is the other?    m

Two loudspeakers are at opposite end8y)* kr0cmup xg u*)dkwj98v us of a railroad car as it moves past a stationary ob*mju 8wg u9k )pyk)8x d0urvc*server at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beat4z+qbnsy/7 ph frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from thep /7sn+4qhb zy 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 mfry)ruk p3): noth at speed 6.5 m/s while the moth is 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 after that wave reflects off thu y:fpkr3 n))re moth?    kHz

  A bat emits a series of high k*eyrk1mql; flbg)w/*0rvh3frequency sound pulses as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away can the moth be detected by the bat so tef / 0 khq*rbwg)3l1 mrlv;y*khat the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was once use:)t l5pm v6/oaoa+rntd 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 ( t+5/atnvaol:o) pmr6 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 cani ruh w )a* i82-r:)w/rdgdgjt*afs.n 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 j)r*rsr/f d ih i gt*2u8wa:.aw- n)gdin this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstrati3y 6/vmsjx bj 3hes8yasiy3 lv/5j 7d2on, called “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 little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound.v3ja6yyms x8/esyj 7/s3j bl5hd 2vi3 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 humanxqlwan )8+wb9 yj z9lko fx+ ykif,m)8039lyi ear at a frequency of about 1000 Hz ywiw) xn a83l) jzfqmolxi909y+bf+,l 9ykk8is $I_0$ = $1 \times10^{12 } W / m^2$ 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 6zpp7n1 o1qqpthe sonic boom 1.5 min after the plane pa7p11p6zpqon qsses directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 10nk( c8e4s9b n8wogxmic,s(t 5 $^{\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