What is the evidence that th6le v(ds be fe(*e3(sound travels as a wave?

What is the evidence that sound is 4hyh:/s le*.2o kculphu ) k/ja form of energy?

Children sometimes play with a homemade “telephone” b;g 9lksa- bhs,3;cn(e0x)evbzo v ;lsy 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 sv;0;3 -()e 9xvnz,hk sgelslbc ;obawave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the2pfg psowergds) b-j mdlhm (.(wa6m 4y() v,( frequency or wavelength top(2evp4r -((wsdbgd.(lomfmhmj6wg ),a sy) change?

What evidence can you give that the speed of sound in ai5j )bjroym dn6d)cu)8 r does not depend significantly on freq)8mryu cj6d b5jn d)o)uency?

The voice of a person who ha bd7x-kde ) b/.*fjvkjs inhaled helium sounds very high-pitched. Why?

How will the air temperature6o-+ii ry umc 8c61tci in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filc37yz da1*g c; hv(ekzter to reduce the amplitude of sounds in varioe7cg1*zh(c dv3 yz;kaus frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced czjklsok* 5 ,47 6km 9b-i,ekn bzkz.jiloser together as you move up the finkkj7 ,bsk. mkzjl*z4 e9ki-nz5 bi6,ogerboard toward the bridge?

A noisy truck approaches you from behind a building. Initially yzcs57 ;dwhbi q*fr)(qou hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “b7qq)fd(rhbi5z*;s cw righter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to bu a;r cqn p (jun q41wn8ng8b)pqi0(a0e due to “interference in space,” whereas beats can be said to be dc880jw0)gn;1npuna nbu (4 iq qqpa(rue to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the points n lsgc2 yb i;od56u-r)y+47g a(rzsmkD and C (where destructive and constructive inte 64s7kzm +brygiuyon c)(2a-s; dlr5grference occur) move farther apart or closer together?

Traditional methods of protecti: :zhklrurmn ph,0z1+pc1q 8t ng the hearing 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 rz, zt:k:lpmu pnr0+81cqh h1technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–31. Each wave can beh55 bs :o+:wucxdn dh;5l9mvm thought of as a superposition of two sound waves with slightly different freq :5+: ;vudwd5h mlm59osnbxchuencies, 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 sourceuw6 uklem*j49 and observer move in the same direction, with the same velocity? 9 k*4e luuw6jmExplain.

If a wind is blowing, will this alter the frequency e:(4utj gjqk8 my 1,woof the sound heard by a person at rest with respect to the source? Is the wavelength or velocity changywm4utk1 g:j j oqe(8,ed?

Figure 12–32 shows various positions of a child in motion on a swing. A st rt9q8y (xq ,4gozg/monitor is blowing a t8q yo(4x,st9 rz/gqgwhistle 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? Explain your reasoning.

  A hiker determines the length of a lake by listening for ejl)milm; w4t4 ck 9a;the echo of her shout refme4icmt)4lw; l ak;9jlected by a cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. He hears the 6cydod:p/rxt/j m 4+jecho 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 1560 m/s (Table 12–1) and does not vary significantly with djcpdytm o /r4jx:d6 /+epth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 20ei ;kq4e23sne 3d ok5e $^{\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 :eo :q8ve+ q pywiy)sr5.ahh;a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much timeh iywq ;yea5) hr8se:+ :poq.v elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes wheour1 u: 0hmcebv;x qmg,29ujf h fo;.u*fj) x.n striking the water below is heard 3.5 s later. How high is qu; ro,hj g1ux mvx mu9*0hef2 cfo)jf.; .:ubthe cliff?    m

  A person, with his ear to 5*mgd xaa(dd4 the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and theyx5a *4gdad(dm 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 i 7s;8 r+9l8xlvoqumn one mile of distance by the “5-second rule” for estimating the distance from a lightnin; x7umqr+9 8n llvo8isg strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound ) 60dt8n/ge.5(ej dj6ibqgzz ;xv dxfat 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 intb* 5kuv/d)j eudti8z0 ensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 d efbje4+)xhiwnic8p t24 ,8ue w82 apvB when fired simultaneously at a certain place, what will be the sound level if only one is 8 fpp 8,w2jiv ei4nec4 ae2+xbt8h)wuexploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four eq at-7qw1jqe3 pca9c *nually noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experienqj 3 9-weaq7ca1n pc*tce if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a s7 p.) xcy013 xhuf-tbm cbo-bsignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intens3b7b1h) bocm-fs-u xp.y0txc ities of 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 cpev l5:bn:6cij50k k bonversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere0:cbje kv p65k:binl5 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 eardruw0asv* mh*vn(hx h9a0b 8ei,xm whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest m +16a4be+cmbhhwx6x:z szn7 amplifier B is rated at 40 W. (a) Estimate the sound level in deme: b z cmb4 7x+61zhhwnasx6+cibels 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 130 dB when placed 2.8 m in front o4, w(l kz(lyj5qw.wavf a loudspeaker on the sw(y(l,wa54zw .kjlq vtage.
(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 m2mx 9 r8nzb )f6q+erzevdh4( difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose 6m4brf)z2 nhex8v(9em rzd+ q levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is trmhosio (3 :a6 ,)+a 1pdhyddcripled, (a) by what factor will the intensity c spr (h,ido:had16 3d)+ayom increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twice the freqn3 dz 4jtm 4svjie;kz+3zf:yazl 32 8puency of the other. What is the ratikiyz234djfn : a svj3t;pze zl384z+ mo of their intensities?   

  What would be the sound level (in dB) of a sound wave in a5(qnw c7 iy7j02s 5 jswsgdp,;( :e:auow rrnair that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mm at 3 5a0rs(u(7ww d 2js7o5rni qjsncg: a;,ywep:00 Hz?    dB

  A 6000-Hz tone must have what sound l85j ,6k6i rsvxq(yh s rvb1oa;evel to seem as loud as a 100-Hz tone that has a 5018jxky5v o6 as6b,rs;h rq(iv-dB sound level? (See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when the85imej b04lp x sound level is 30 dB? (See Fig.m5el8ji x p40b 12–6.)

  Your auditory system can accommodate a huge range of sound levels. Whati:69lfand - jtsn)s)awhr5g2 is the ratio of highest r :s6-gw d5njha)n9a ) tfsli2to 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 m2gd 3r i:-ljnlength of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tensiodigm:rnlj- 23 n must the string be placed?    N

  An organ pipe is 112 cri a3k*.pafz / dzl3w341.ftt lp5jk92 qyhvnm long. What are the fundamental and first three audible overtonez.332a4zl93qpd 5yl.kij * /rwnf tthpa1 kfvs 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 expect from blowing acro( sc(x6opbtxc563 imtss the top of an empty soda bottle that is 18 cm deep,tbs ci6(3 ct( 6pxm5xo 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 30 hotax9 ga1hdth6 x*organ with open-tube pipes spanning the range of human hearing (2h*3a0h 6hd1 tat9 gxxo0 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 has a frequency of 540 H6 i m konwynhi4n:.-5uz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of wkuy-o:i65.nn in m h4its original length?   Hz

  An unfingered guitar string is 0.73 m long an(svx3*9xkwy x d is tuned to play E above middle C (330 Hz)(x y *9kwxsv3x.
(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 emitq1pq8w:br; mn np9je7s6*ix as middle C (262 Hz) when the temperatq;w 6sre mja9n1i:*px8n b7pq ure 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 +,j miz8*mkqes d9)u p20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flud8l065zq htr xte in Example 12–10 should the hole be that must be uncovered to play D above middle C0 qz5 tl8h6xdr at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 440 Hztt6uybr,4l 9/y ufl 9i;w esbx)zaj ,9, and 616 Hz, but not at any other frequencies in between. (a) Show why lyay6 9 fr9,u;ti e4sz wb)lut9xbj/,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 ,fx-xy3 ke raj/su ,t-long is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hze-ufjs-3 ,xta r,k/xy. 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 gz, k*-mz/z lu$^{\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 2.14-m-long orgvr (.lq+mw/tjh5d t2c an pipe2(j5+tl/ v c mtwhqdr. at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is appro bey0lxwyzft8eh2:5 qd+d/- bximately 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 the rqf8h/ b:e2y-+ewb lx0zytdd5 elationship 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 trying jyg(3wk0n1 qtto adjust two strings, one of which is sounding 440 Hz. How far off in frequen0jwgtq3(y1kn cy is the other string? ±    Hz

  What is the beat frequencyni *e3ohg;9bi ek v1v/ if middle 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 (bra(vu:jjn x;s+(kghnm4z dnw 6/nd X) operates at an unknown frequency. If neither whistle can be heard by hu;+h vmz(nd 6/wjs:4g kn(jnuxmans when played separately, but a shrill whine of frequency 5000 Hz occurs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundedl8- (okbme9p*us - erq with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vibrational frequency of the strik us oer8-me(bpq- *l9ng? Explain your reasoning.    Hz

  Two violin strings a r:/pm4ct0e pmre tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat 0pc:me/ mrtp4frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes eahl2*lj r y52ia; ud0ru -uk0euch try to play middle C (2622 j;5ur-uar2 yh dlu0eluk*i0 Hz), but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a fr ,pwc m7),dczqijmp7;equency 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 frequenciesc)ji ,qm7w;c7z mp,p d 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 from one speahyq y vcet720/ker and 3.50 m from the othervy72hcyt0 / qe.
(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 fedw-xv:z 9x- to be vibrating at 132 Hz, but a piano tuner hearfe vx --wzd9:xs three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what must be the frequency of the 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 airz4p f; sr;kp+q. How many beats per second will be heard?+rp4z;q;s kpf (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fir f (cu z)jx +hnydh,tvbz:w8)1e engine’s siren is 1550 Hz when at rest. What frequency1,f ujcyz hb(xz: )8)wvndht+ 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 you detecbdtre4q0 u 89rt if a fire engine whose siren emits at 1550 Hz moveeu4q9b08 rt drs at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency a6u 3:ebelk0yif 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 exay0u6e leb :3kactly 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 singl)g4l*-tnelf it)b*6 icfa5 jwe 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 lec)ij nitl * 5fa)*t4fb-wg65.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives the9 anu3cph8g k)wzr/ .um returned frop3 .uaunk8wc z) 9/rhgm 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 a speed o1 eblbh359:ureyxaaiz9 6d:vf 5 m/s As it flies, the bat emits an ultrasonic sound wave with frequency 30.0 kHz. What frequency does the bat hear in ebaa: 9u dxbv6yh31iz5er 9:l the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler expe m b4v,z12 fz w56aym b/yzwg9h6zys/oriments, 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 hearw9/y 5oyzz1,s6/mm6zwa vybbg4 z2f hd 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-flow s6jz)v3nz1a+q;fd ounsl* ; dn peeds. 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 leg arteries at 2 cm/s directly away from the zn+s6ladn;fqd;n3 z*1u j) ovsound source?   Hz

  The Doppler effect using ultrasonic waves of frequenpn/)b a *e3jkicy $2.25 \times10^{ 6}$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 freqa6ng z f+n5gy:uency 570 Hz. When the wind velocity is 12 m/s from the north, whanyg5nfg 6:+zat 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 at 2f le+5fc18y3zn/m2 wd apj/j x0 $^{\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) Wha2lg0egmt ;+h5wj1 vwyt is the angle the shock wave makes with the dvh12t0j;5ew +gmg l wyirection 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 at5 uz8hg61y;ynwivz r t-8h1gmmosphere of a planet where the speed of sound is only about 35twg zgy18 n18iuh 5vh-z6y;rm 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 strikexcwd08 -g wjy0s the ocean. Determine the shock wave angle iy 0gc8dx w0jw-t 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 kl2j-no2 y :oqo nbec65 ns2;q$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and see a plane exactly 1.5 km fzrwt qgbe/+l8(30is above the ground flying faster tha +3tw0sbrli8qgf(/ ze n the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pu3iyaxfw8x 8a1 u6 n +a0;7urst1mmmfcerx 0/ylses downward from the bottom of the boat, and then detects ecn 8xa 8 seu+;frm6xa/arw0fi yt m0x3yu7 11mchoes. 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 many octaves are there in the human a -vxk5. ustp;uudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display c9fqfn ,+r3h imalled a sewer pipe symphony. It consists of many plastic pipes 3if, mfhrqn+9 of various lengths, which are open on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a peop-v:xz (p+ ncrson makes a sound close to the threshold of human hearing (0 dB). What will be the sound level of 1000 such mosquitoes? (v-o n p:z+xpc   dB

  What is the resultant sound level when an 82-vg(+ )r,yoyj-6ms pcodB sound and an 87-dB sound are heard -+gy6j (m,yov)oc ps rsimultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed c,a.;; yujajfin the open, is 105 dB. What is the acoustic power output (W) of the speaker, ass; a .f,yajj;ucuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output pdcls0ns,n tu0)c*qx 6)r1drat 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in watts at 15 kHz?td dcsu,6*0rn)c)qrn psl1 x0    dB

  Workers around jet aircraft typically wear protective deviclh6y/s85 supb es over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from 85us/6lpy bsh a jet airplane engine?    W

  In audio and communica t4aaje1 xbd p-;3rwk;tions systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violinwca ufjcr: -) 2v;zpw:a c1h6 ki 7lspp(bb;i- 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 is 32 cm long befko 4( (o8mpqhtween fixed points with a fundamental frequency of(o 84k(ohfmqp 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 vibration above a vertical open tube filled with2bt l1-ku,rw* 3eb bft-;x iqs 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 dw, e2-stb-x liq1ku* 3rtf;bbistance 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 :e6:6yunq( r+rogrk g 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension should be in the string if it is to pqg 6re::r6(ongurk +yroduce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as 9:km ;+;3gd9h0cmlnc ncbmb v one full loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure0f5uhrox a( - kpa.ja7ks/ gcv.u.,cf tone 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 move. vca0.ru xc7 o /(k 5ask.fu-g,jfahps 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.csg(xix -kn h.-m)c+w The conductor on the stationary train hears a 3.0-Hz bea +.hkgcw x(n--x) imsct 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 approaches you is 538 Hz. +tpv,.atn nd zce -g(9After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (asta-g.zd,p 9c evtn+ (nsume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to t j7scg5 :cwky9lf 1nc10r s,nk 6ugj9phe 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 thejc ,01lfyc19jpn59rkukgg n7cs 6 : sw straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a beat freq,x7 yn-z7ts okuency of 11 Hz. The shorter one is 2.40 m long. How long is the other?onk ,ts -z77xy    m

Two loudspeakers are at opposite ends of a railroad car as it moves p o1okbh11fx7c k y2rs4wkm y(;ast a stationary observer at 10 m/s as shown in Fig. 12–37. Ikoxw;mfrys72h4 1kb o 1c(1ykf 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 normal :hfujfkw,1;r.wz yf/ ly about 0.32 m/s what beat frequency w f j z,hrffwk./y;1:wuould you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s whic1p3oq:oh -zm le 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 detecte:ozp 1oq3h c-md by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses ;p80upk snai,4;vsx ,kmgh( b as it approaches a moth. The pulses are approximately 70.0 ms apart, and each is about 3.0 ms long. How far away kxs;n(p;4p am i8 k sug,v0bh,can the moth be detected by the bat so that the echo from one chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was w7-jo2x wbj68v kj2g monce used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, gj7bvj 2jm o6- 8xw2kwlong horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be compromised by the presence of stad9k b jpvp ybv (f.4930kp/dov4gh)gtnding waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.vo)ykpp3th4b/( g j4.fp 0vd dk99 bgv0 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 od vn)c5ld*c:, called “singing rods,” involves a long, slender aluminum co :5d ncld*)vrod 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. For a 90-cm-long rod,
(a) what is the fundamental frequency of the sound?    $ \times10^{ 3}$ Hz
(b) What is its wavelength in the rod,    m
(c) what is the traveling wavelength in air at 20 $^{\circ} $ C?    m

  The intensity at the threshold of hearing for the human ear at a frequency of abe11frhh tpo 2b/bd:hg10 mqt3out 1000 Ho hh0g3dt2 :1 fm/1hetrq bbp1z 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 observhn iyr qn boz,5*r8o24er on the ground hears the sonic boom 1.5 min after the plane passes directly overheado , nnzrr4 2ih8*o5ybq. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is eho 6tw6342lg*j xqgq 15 $^{\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