What is the evidence ta/j 7m os9bel6hat sound travels as a wave?

What is the evidence that sound is a form of eny:n: prl iuc.3ergy?

Children sometimes play with a homemade “tec0 uxw- t8igz8lephone” 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 travels from one cz g8xct8u0w-i up to the other.

When a sound wave passes from air into water,;xltlj6d k 1yxm4jo+, do you expect the frequency or wavelenx4;j, jodl6ylxm+ 1t kgth to change?

What evidence can you give that the speed of sound in air does not dependmtyrdj.ddak;rj 0: ,: signifr rkdam:jtyj .:d0 d,;icantly on frequency?

The voice of a person who has inhaled helium sz;y9gr1vhtx1qxo - u (ounds very high-pitched. Why?

How will the air temperature in a room affect the pitch o ,.yevt -sw 3c;yzn q7i8j-j,e : jpwxauu5lh+f organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of soundsrbyskt e:xfo c8zs0 a+:2mbi488.xy a in various frequen :ai2fo xsby+s 4:y8ekz.rb8ct 0x8macy ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–.lr k-.1 qzsqv30) spaced closer together as you move up the fingerboard toward ther..vz 1sqlq-k bridge?

A noisy truck approaches you from behind a bu4 o 0zorboyy/p 9 tmh7 qj)if;cw0ps-8ilding. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11 i- 7o9prtbs om0jp/hwy4z)fo8qy ;c0–15 on diffraction.]

Standing waves can be saidheztq8xhe +wy7ct7 9*z 8fe6p to be due to “interference in space,” whereas beats can be said to becz 8e7ph wyx*z feqht78+9te6 due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered,twt1pv0:yy; a9h-4n -4yuz bol 3rvje would the points D and C (where destructive and constr;4n:z-v br e4otjy l 1tv -03w9hyaypuuctive interference occur) move farther apart or closer together?

Traditional methods of prot6 68ac-pduvnxecting the hearing of people who work in areas with very high noise levels have consistecu-8x vanpd66d 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 reaching the ears?

Consider the two waves shown in Fig. 12–31. E-f* iw1ax,.2rtzx yh4ekl7/uzex9el ach wave can be thought of as a superposition of two sound waves a1-7,lf94h*ee xytr2x we lkxu/ziz. 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 th9n1)i bx vnw/:os2vtx e source and observer move in the same direction, with the same velocity? E2:o tsx w1 nv9invx/b)xplain.

If a wind is blowing, will this alter thetst2+ th5tzq5m.2qgc frequency of the sound heard by a person at rest with respect to the source? Is the wavelength or velocity 2z.ts5t +2t 5hgqqtmcchanged?

Figure 12–32 shows varihm5,s 4qw *x1iveo m2vous positions of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At wq 5m4*emsv owhxi2, 1vhich 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 the e6 0z5yr1+krzxmfvdg +cho of her shout reflecdgrm +zz5k0r f+1x 6yvted 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 sidu d:cp.pj hw74e of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is th:p pc4uj.dw7 he 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 wavele9pituhr n4o -es6)r5*m/g apv ngths 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 above a school of tuna on a foggy day. Wi 9mbluxd :bsqmt2 e1,.thout warning, an engine backfire occurs on another boat 1.0 kt2m. 1be :qsbm9,xuldm away (Fig. 12–33). How much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splas ejwq slh*i+gm;7 1w7bh it makes when striking thei7*; 1eg+bwm wqhls 7j water below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike j+gb :vjlnp 6(the concrete pavement. A moment later two sounds are hear +vjp6:g(j nbld 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 occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second ily0 mc) )+8mkpc3pom rule” for estimatingm )cop08p mlyic3m+)k 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 pain level of 120 dB? 1p1sled8e w4nvo v7e3   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 i+4-jyqii:n- bey:crl ntensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a soundvy mwkw , xr.6/5amha( level of 95 dB when fired simultaneously at a certain place, what w5,6ymavxr( w akw.h /mill be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equally noi9 fi5fjvg nb+ls.(c d(sy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not i(s5l(n9v+dcj f gf.bdB’s.]    dB

  A cassette player is said toz e n +g7mg(eoemrf*ca d7eks- 3)d5r; have a signal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the r-grdek5sm+)a cg nmz; 773d*(eefoe 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 wd ubizg:u 5rco 6).a.conversation. Use Table 12–2. Assume tha.5 bz r6iuo :)ugwc.de 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 d6f )i1gcqq6m4al3 e;mjx oe, 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 rate:* hm84i(qej. lh8rewo 3p uhmd at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker(h 8.e83u oh hr4*mqmpjwle :i 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 ysr lza s --)b(e7vei-registered 130 dB when placed 2.8 m in front of a loudspeakee s7zy-la b(ivs- )-rer on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in sound level of 2.0bbcj1q0 0oqmh t 1vtv16+3nef dB. What is the ratio of the amplitudes of two sounds whjcov1 1qq3t0h+nm61ev0btbf ose 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 intensigj vyd 1)d)t0aty increase? Inv0y )t)1d jgdacrease by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have eqkr * -6doo1pgwual displacement amplitudes, but one has twice the frequency of the other. What is the ratio of their -1krd6po g*wointensities?   

  What would be the sound level (in dB) of a soujqy0()4ptz p k lv(y5cnd wave in air that corresponds to a displacement amplitude of vibrating air moleculesk4vjyyl cq(0p tp5( )z of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have.q n.v4eq p89b) hmc xgv.*luy what sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig.lxu.qc*eyp9b)h4 .nv qg vm.8 12–6.)    dB

What are the lowest and highest f6 .eyex*fhgi/ui lf8 2requencies that an ear can detect when the sound leve gex82y6.efl u*hf/i il is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of :rxn5ah f ;7kesound levels. What is the ratio of highest to low;rh k5 7:fnxeaest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin hash;b(/u0 +wo ;r0gzmdh/hn fnt a fundamental frequency of 440 Hz. The length of the vibrating portion is 32 cm, and it has a mass of 0.35 g. Under what tension must the string;rn 0b+n;mhh ( of/t0gzdw/u h be placed?    N

  An organ pipe is 112 cm1wr(u t27ftikg 7+7j d( ynabw long. What are the fundamental and first three audible overtones kdt( 21nui(watf b7 r7yj+wg7if 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 freqdb; mv5mu0sx; uency would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if ys0x5duv;; b mmou 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 edj 4 ovnzes.b4 lkc,4a/-(fi 7livk2 organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the zs44.di 7e(kkb-i ejvvfl4 an/ol2c , 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 Hz as its third harmo:5 ev ca k10bgkh+h7/yls 0jrh-gyx7jnic. What will be its fundamental frequency ifke7/5j0 k0a vyhr1b-xlcsjh7hg :gy+ it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar sh0z:h vlx)rj8;,x r 4qvpq7x ntring is 0.73 m long and is tuned to play E above middle C (330 Hz).n7 jx ;lzxvprq0x 8vr:)4, qhh
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits mji84h +tpu: d :snyr*knv5j+c iddle C (262 Hz) when: knh + uj 84y+ivdn*pj:5tsrc the 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 ate+h2 u,rcq5 ha( jy3cr 20 $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of the flute in Example 12–10 should v naf7(-q7)aivh xog ;the hole be that must be uncovered to play D abo)n qi(;fahvv-g77x oa ve middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 Hz, 3k( rcarfqp ee6qp*9;440 Hz, and 616 Hz, but not at any otqk(e;*pq6p r fe9rac3 her frequencies in between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open au4x+bp/sua qil)/ o5c t both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. What+ 4/)qpuixoac s /lbu5 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 z*rh1 0yqp:vgbsj; 2s$^{\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 di c78nldd40 ta 2.14-m-long organ pipe dncl4d8 7i0 tdat 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is apprq* . a rp,)gbxoshm43roximately 2.5 cm long. It is open to the outside and is closed at the other end by the eardrum. Estimaa)r, rxo4bg3s.mph*q te 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 trying to adjust two stringxparc,tgl7g5,q9-ntf/ukr dd3( u8f s, one of which is sounding 440 Hz. How far off f9rrx 83kgqt/5u7 (f lpcndguat,- ,d in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) al-e 3 8uqc8gi(pa0etbnd $C^＃$ (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) operates ri;*)s 0bjr ipat 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 simultaneously, estimate the operating fjr0 s piib;r*)requency of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork x ds b(v .xyo:2ceaw :*pgo0:sand 9 beats/s when sounded with a 355-Hz tuning fork. Whdx*:b:.gcp:ov e (aox20wy ssat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to aus z0cdii, 3 4n.u.zlthe same frequency, 294 Hz. The tension in one stz sa 3 4l.,0uziudcn.iring is then decreased 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 heawy d2*c7y:zi crd if two identical flutes each try to play middle C (262 Hz),:z 2ydc* cyw7i 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 k. metqui)npxyq15 fprn9(- , B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are p(k-rn 9ix5p,)fnmq 1 qtye u.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. a8+5uyqg)ss vA person stands 3.00 m from one speaker and 3.50 m from the othevgya u)s8q5s+r.
(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 heae3qgpz: jn 5i2pn*3o tm fna2/rs three beats every 2.0 s when they arep 3nman3:2 gpen/i jf25 *qotz 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 air. Hotdr::sx p4ej+w many beats per second will be heard? (Assume T =d r+e4pj :t:sx 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s*w svzc wp1w9ld.+ h oprnf1-+ (hruc, siren is 1550 Hz when at res+.pn- zp1(l* c wf vcw,rro+hs1wdhu9 t. What frequency 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 detec40aq li uv.oc9t if a fire engine whose sireno .lvua 9i0q4c emits at 1550 Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequ -b1unbb 49qvlency if a 2000-Hz source is moving toward you at 15 m/s versus n-9 1 qbulbb4vyou moving toward it at 15 m/s 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 with the same single frequgrev 31taoz5 t gl*,d)ency horn. When one is at rest and the other is moving toward the first at 15 m/s the dt1vto5d z3, )rge* glariver 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 ultrasonic sound waves at 50.0 kHz and receives them reoi02 tu5aiclu:3lbf ,turned from an object moving directly away from it at 25 m/s What is the receif50 uil uc:al,i32b toved sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, thyur:)y/ zkh 5wc maiw4r j)6)ze bat emits an ultram)j4c/ryyu6i: z)k)r5hzw awsonic 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 Doppler experiments, a tunm7vdx 62a6g nba 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 i676dann2gmv xn 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 meeuxm r6mo3n -)asure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the n6-e3) mru xomspeed 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 sound source?   Hz

  The Doppler effect using ultraso 6jblviz*k 4h+uaf;g 6qzv1(mnic 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 uew4bgk0 ;fd+ frequency 570 Hz. When the wind velocity is 12 m/s f fdk0eg4;+ uwbrom the 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 at urs 2 jx:y)wx220 $^{\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 M:e a(j*(tmut 0 huc9tbach 2.3 where the speed of sound is 310 m/s (a) What is the angle the shock wavt(ut*0m:uejb9h(t a c e makes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet where thet;o5gyt vag)r: )eejs /2cl q7 speed of sound is only ab)ov e;2rs c:tejl/7a )gqtyg5out 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 strikduow c1wor- /(es the ocean. Determine the shock wave angle it pr-(ru/wdwco 1o oduces
(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 9*c zi2wvcc ww- ao;k;hjr 1p)$/theta$ 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 vzw+jh* 6 3 zve:+tzuyr0ndq91.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boo6q +znhe*ujyd3 wvrz+90t z:vm, 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 m1*cz72-p ihb(njr p3q-l jxz20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maximum depth for which ij3j7- zpr nhm12xz *i-( clqbpt 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:1nxij2fnq:p;zv h:5n xxq u2 human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called d jz d,dh(o99; xc9rjua sewer pipe symphony. It consists of many plastic pipes of various lengths, wd;dx,c zo(dhjj9 9 u9rhich 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 persgbpp.j du5it1 x22ci1on makes a sound close to the threshold of human hearint5 d .xjp2ci2 1bp1ugig (0 dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and eg c;o9ph3dt9l wc 36nan 87-dB sound are heard simpch ;t3leo9n3dwc 69gultaneously?    dB

  The sound level 12.0 m from a loudspeaker,x6+hqa1mi (x* 7 0fd oc(z7yq1pg/ pkzz1pxyq placed in the open, is 105 dB. What iso0pqxz qh(m+fppq7g d zxy(a1z7 *c16/ik1y x the 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.u t- i2kzcy.va +w-w pr7hwj9*-gavrna4:3lp The power output drops by 10 dB at 15 kHz. What is the power ov puwkw- -g7yr 2tw4ra v3l+cz:j.-p9n a aih*utput in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protb6iy hb.ny+l)-hj4 fsective 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 be the power intercepted by an unprotected ear at a distance of 30 m from a j)j6-bys4. +hinbyl hfet airplane engine?    W

  In audio and communications systems, the1opgjls h3g 6l *;jc(m gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fre -ciev,1 pwy:wt73svjquency 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 4o cbv -w+fer8t0stu ,long between fixed points with a fundamental frequency of 440 Hz and a mass per unit lengt4w,vs8+ be- tufo t0rch 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 with wa +w24(dqi jxquter (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 distance from the tubwdqq(+u24i j xe 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 tvwbf l;p sr ypin dkgsqwv:a5g922)+7 f7-a6nhat is open at one end and also 75ka2fyn9gvqdls2) p7a5:gs 6n;vib+ 7f rw-wp cm long. How much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate as one full jd psmkl3 )*fvb l3-q7loop ($\frac{1}{2}\lambda$) when a small earthquake shook the ground vertically at 4.0 Hz. The highway department put a support at the center of the overpass, anchoring it to the ground as shown in Fig. 12–36. What resonant frequency would you now expect for the overpass? Earthquakes rarely do significant shaking above 5 or 6 Hz. Did the modifications do any good?

  A person hears a pure tone in the 500–1000-Hz range coming from two sources.tpfj3v cp8w:5 The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds tha c8twjp3 f5v:pt 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. Th13sz nxr/*9p k9rrls 7g(atli e conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approachg trlr ( i/s7*9pk1zlax 3sn9res. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches ga-y /k )zff(0vi/5tzee9pw.ui plp /you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fa f tzaywze/5g kui)p/ .fpv0e-pl(i9/st was the train moving (assume constant velocity)?    m/s

  At a race track, you cancp.e 4++irrqm estimate the speed of cars just by listening to the difference in pitch of the engine noise b+c m.re r+4piqetween 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, sounding together, prort*-enqf gz:qb8c8s :duce a beat frequency of 11 Hz. The shorter onf:g8*zcet rq-8snbq :e is 2.40 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it mo) nhsttnoh 75n5k7g ,bge7/fj wkix).ves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers h7 b7hiwk5en5nft)7 ,x/. gj)toskng 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 aboutrua q,tvddg)z ,(r+f *h3kz,b (jf2jt 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along thhr3 gv,d(uktt+bad2z)j zj*r ,,q f(f e flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is flying trm*-o6ftsj: atk8 bz4 oward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency j8tksf* m6a4:orzb- t of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequenepzn799 *fq0s2mns.b lzsd / gcy 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 that the echo from on/nnp m2.9zsss lgb 9feq*0 zd7e chirp returns before the next chirp is emitted?    m

The “alpenhorn” (Fig. 12–38) was*opq53r(; ysicqi j *u once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must bq;por(jcsq*5 3*yui ie 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 bsw6:;x bzrw-ovult 8 cqx(j8) y 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. Calcula-br;cz:x8 t(ojluwq 6 )xw 8svte the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,f+k3ypb fec1mq6c n:o5w o 7f6” 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 “singwc6p51 :n3bkfc oof6y mqf+ e7,” 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 frequencyg;v/ u*dk)v xg of about 1000 x )gg kduv/;v*Hz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the ground hears ix bz*f c8ne/ 25/boh0.xmkqmthe sonic boom 1.5 min after the plane passes directkm8n0bchm/ z5qfeio .*x /2 xbly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboatur-,3 hk0,d2ffl dkz ; nxw3he is 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