What is the evidence that sound ttyfw kww;. o+:ravels as a wave?

What is the evidence thx w1t wf/3r+mmat sound is a form of energy?

Children sometimes play with a homemade “telephone” by attaching a string r; ,yc cpk82lqhfhy0(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 q(8c l yrhfkh2p0,;cywave travels from one cup to the other.

When a sound wave passes from air into water, do you expect the freqwv- 3t3qsly.l uency or wavelengt3vqls l 3wy.t-h to change?

What evidence can you give that the speed of sound in air doe 4gqqqw*m *sq8s not depend significantlyqqqq4**m gws8 on frequency?

The voice of a person who has inhaled helium sounds very high-pitcsdomqxp/ i4g +f83 ,2 bovy;vthed. Why?

How will the air temperature in a room affect the pitch of organ pipes.bg z6k(2b qle?

Explain how a tube mighh9xh:zp.l/jbymg u2. 8c ; hdat be used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is a car mu/z lxhm 2d:ugyp j8bh;9h ..acffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as ( rj22toyh7suyou move up the fingerboarsjoyh72 (rtu2 d toward the bridge?

A noisy truck approaches you from behind a xfblt 93q n+99q0aks /0 mq4dlukexz 3building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighk 9f3/ea3t0umsq zkx+9 d0q4qb9xll nter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diffraction.]

Standing waves can be said to be due to “inx:l0v0 cqemz,terference in space,” whereas beats can be said to be due to “interfelzc , ex0qm0v:rence in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poind0qb55l3trfn -ewpx 8ffx2 o2ts D and C (where destructive and constructive interference occur) mfn0tq5- e 2l8 23ffw rb5doxpxove farther apart or closer together?

Traditional methods ofog8c2m* bjn, p protecting the hearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce nois8mob,gj2pc* ne 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. Each wave can be thought of as a sup6 e tt, k(07a/gdmouooerposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the wavda,607 kmto oot/(egues, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and ob(ml3ix6,mt waserver move in the same direction, with the same velociawlx( m 6m,t3ity? Explain.

If a wind is blowing, will this atgk0 e (g1mh(qlter the frequency of the sound heard by a person at rest with respmgth( ke0(q1 gect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a a /w etwbk60+ zg,lex9child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A throu 9tb0gk/ezlwea+,6x wgh 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 echo of her shou)l5plffj/rov0 e s)hgby5y3zg-4k ;ut reflected 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.)/r g0 3)yy-l5 ofk4;g5s pjhvbfulez $\approx$    $ \times10^{ 2}$m

  A sailor strikes the /bf hs,t6vxm .side 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 the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary si.vf bxh,6t/msgnificantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in ysx/eyios((ew qkn9u q mgz54va1g cc,)l 152air 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 tuzm)1ftnm mem (pz,fe u*7wuo-w/fk)6na on a foggy day. Without warning, an engine backfireoz) n7ew m-) m(fz kw*,e1u/ff6 mptmu occurs on another boat 1.0 km 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 splash it makes wbkn9)-2qtv0ypmvgfn: 9h- b when striking the water below is heard 3.5 s later. How high is the clif9qb- 0 tk2n-nw:vhgby9 f v)mpf?    m

  A person, with his ear to the ground, sees a h(f68ig/smqn8x:j j kh uge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they/ j:hsfqm(8g8i j6xk n 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 * 4yrahqys :8.o+z,rjw8daci one mile of distance by the “5-second rule” for estimating the distance fro zc*wi ,ohr: r8 4aysdaq.j8+ym 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;2q 3tee+ffjr 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 y1w+rmnp 4oe n -ynba4z(jnz003a of 2whose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers pr wg;fsieb3 7xgw;h3k8oduce a sound level of 95 dB when fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hint: Add intensities, nofie38 gwgh;7 w;ksb x3t dB’s.]    dB

  A person standing a certain distance from an airplane with f b:wquets, :1un5v(fqour equally noisy jet engine,q1sweu(5fnt vu:: qb s is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a srfx y-lqq 7d.,( abh4rignal-to-noise ratio of 58 dB, whereas for a CD player it is 95 dB. What is thrh- b d7q.yq,a4 l(fxre ratio of intensities 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 n+d : i(b7nemjperson speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on:(n7ji be+dm n 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 strd3 w1 69pm/i9neva rrtikes 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 rnmk5tki, xv -c)m, edn( vh f4ood,3p:ated 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 louotv:np de( ,d-ih,5xm )k3of,cknm4v dspeaker 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 ok;v xue2fg83 mno )r+pf a loudspeaker;e2 8g+nk m fv)oup3xr 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 diffe .g3bw.w wlmpk1d,uf -rence in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels flw-,wuw 13. gd.bm pkdiffer by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) bumsliz4b)x7h/;x s r 3y what factor will the intensi) x3 m7ru4bisx;/hslzty increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemenm0hpouhq3;.kxkn3e d j 4;sv5f) k6,tjxc8dxt amplitudes, but one has twice the frequency of the other8hevtd 4x)x3h ;n.pk6c3 5sd;ko jqux,f k0 jm. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sojbv8 8pmqg ,n221yo bhund wave in air that corresponds to a displacement ammbhp1qg8y28j2 ,bo vnplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whatj5/8m w ndpjnl; n,z, h*uwtj6 sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? (S6j j;,njntl*dz pw 58/uhnmw,ee Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect when zsgzx 9 t 2wueoq1-s:f v)5*ibthe sound level*)zxe1 5wfsgt-9o:i vuzq2b s is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a hulaqp a8v9+2g4(1uo xi fshdh4ge range of sound levels. What is the ratio of highest to lowes4a9 fl shgq1xiho2+da8(4vupt 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 fundament;t4jj*j4cekypu kg .6al frequency of 440 Hz. The length of the vibrating portion is 32 *c4. y u4kjjte;6jgpk cm, and it has a mass of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What areb-02qhbgd+ kg/d8q*7wku clj the fundamental and first three audible overtones if the pipd hck0qk*q78bgw/u +g2 db-lje 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 woa+no ag+qm8/ ow-s -bqcaxg85uld you expect from blowing across the top of an empty soda bottle that is 18 cm deep, + s+bcg oax8 q8mqa/wn-a-g5 oif you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the rangf+ mm4;sfmh9 ee of human hearing (20 Hz to 20 kHz), what would be the range of the lengths of pip 9;4 msfhfmm+ees required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as its t y rq 7bt+g607l-(diwgm**f qsljdcg ,hird harmonic. What will be itsgb7*(f6 mid+g r*j qwtqll7-dy,c gs 0 fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E above middz(c/fu-z be/unxksr/e v) 59lle C (330 Hz). cnubezs)uf-9/( r /kv/ xzle5
(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 opzb.x xb 71wt( a*m reb:q4gaa9en organ pipe that emits middle C (262 Hz) when the temperatu erb q9.:z4xx b1bamga7* t(ware 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 awt9- kjyj5s4) evww-gt 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 the hole be t7 psgq iu+ai1lhuew-e:n)o - 8hat must be uncovered to play D above middle C at 29i eo78ne)1- w+ lushuq i-a:pg4 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 Hnmxe4 i.6 6.p wzvb8zbcy;(xez, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a closedme6z4zx.6(yx i ec;wb. vnbp8 pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at tw:uja cv/1l75 k0v1wxy7n gj pro successive harmonics of frequenciwv nu7gajk0/lrv y: 11cpj7x5es 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 .;8pkl i(5 fbcno +qik$^{\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 rcnc:*rwe fn s/+rt(h- ange for a 2.14-m-long organ pin* (r-e+ twhc /cs:rnfpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm +8ev8bxfk8qvz h-soy14,v cvlong. It is open to the outside and is closed at the other end by thev 8 kvh,z1f-vyo8 v8ecxbq4s+ 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 oneq/d;s gqaho8h-7hjg8o ( l -re beat every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stringd/eql- ; ajo (g8- rqhohh78sg? ±    Hz

  What is the beat frequency if middle C kcpi1ax 50ck qyt 1*f1(262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (brand X) operates am),k 18hce9kxl4l/)l ne evrxt an unknown frequency. If neither whistle can ben 9cvle e4el)k1lk)rx/, m8xh heard by humans 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 sounded with a 350-Hz tuniqi/usih41.bwc 9 y c,vng fork and 9 beats/s when sounded with a 355-Hz tuning fork. Wu ybch4w1v ,qi9s.ic /hat is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to td:+ coxbcvw10 he same frequency, 294 Hz. The tension in one string is 0xdb+:wco1vcthen 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 heard if two identical flutes each try to plad-2+hd1 )atnxh k ey2wy middle C (262 Hz), but one is at 1)awt+e-h dhdnyx22k5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C. Fork B has a frequency of 441 Hz; t,9d)pu*hj/eb w16wz l bng+ bwhen 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 frequenciew9+6g ,bbl/j putd*)bn1zh wes 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 persr(*wpbi:mbd o/5r9 n0v j:sbbon stands 3.00 m from one speaker and 3.50 n/(:brj0 :wv*rsm 9o5idpbbbm from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tuner heasn2 .b1oupm;ars three beats every 2.0 s when they are plap1.un ms2bao; yed 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 wavelnlvsa8b0 s 8y7engths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume T = 20 vy 8lan8b ss07$^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1wpx fv+.m) yk3od8dr) d lblj:nz*, 8y550 Hz when at rest. What frequency do you detect if you monwdr d y3xv8ol, y)pj8*dk.lz):f+ bm ve 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 detectfsc+81 rd quu- if a fire engine whose siren emits at 1550 +uu1c 8rdq sf-Hz moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in oy ),8 yv)gsvcfrequency if a 2000-Hz source is moving toward you at 15 m/s sy,vyoc8) )vg versus you 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 zlq6h q 4 ip)u43ww.ddwith the same single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T =.dq wldq6w 4)uh34zp i 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50km fleqj(:c.:sg e95s.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the (ejfl:g9k q:m ce5s.sreceived sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s As it flies, the bat emits an ulb8qkq zbv ovn53vt78f1 e0hj 5trasonic sound wv ekbh851bvj53 n70fzqtqv o8ave 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 tuba was played on a moving flat; ;o: ufmtx/u*nhce l) train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if f/; ot)em: ;lxun* chuthe train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-pvy-u; ,/cqgjade et3 7kdh-/flow speeds. Suppose the dtd;ke qpad7u -hjc /3g/ev -,yevice 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 sound source?   Hz

  The Doppler effect using ultrasourv4mo6 bv f60nic 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 the wind velocx0l 3hut :bwr5ity is 12 m/s from the norbxw5l 30 :rthuth, 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 2s06s 6yush pe8-8ntlt 0 $^{\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 sous0idm 8+ hk8ccnd is 310 m/s (a) What is the angle the shock wave makes with dck8h8 sc0m+ithe 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 plan2 vrk7a-0pvxqjhi.p61opqq a*z s7r -et where the speed of sound is only abo0rvqk i67qr z* a -pp-opq2j7v.axsh 1ut 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. Determine th9ce8h *ql4ey he shock wave angle it produchy4l9c8h qee*es
(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 qs or,a-x;e :t$/theta$ 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) pxnag rd**p.4k8v: jv(t.pq siwcp0 above the ground flying faster than the speed of sound. By the time you hear the sonic boom,4 *p:0.g xvwr *sn8.qpaipd jtcpk )(v 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 pulses downwaxjd)rm wy30h)mtg 9-ard from the bottom of the boat, and then detects echoes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fres)wdx9m)jm-r 30t yhga h water)?    s

  Approximately how many octaves are there in the human au:gab s fvzc38uek 7*9 qt ,;kw/x8drxudible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. It consd f42 oudlrgot-421u w-fg3 jpists of many pgolpg wdr2 -u124dj43u- fftolastic pipes 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 person makes a sound close to the thresd p//p rsath8:s(;i9 ;gkbiadhold of human hearing (0 dBa/hg; ikip:9(bdt; s s/dr8ap). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB s*fw7 fpfw2k7w ound and an 87-dB sound are heard simultaneou 7 f7wfkw*wf2psly?    dB

  The sound level 12.0 m from a loudspe3e0dfa 2( fnscaker, placed in the open, is 105 dB. What is the acoustic power output (( 0scfd 2fena3W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops ;r9ffpgh.he4v0.ku zt3g fz-by 10 dB at 15 kHz. What is the power output in watts at 15 kHz? ;-gpfk9 fzrg43.eh 0v z.uthf   dB

  Workers around jet aircraft typically wear aopwk +lx-)s+ 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 woulp)ksxa -w+o+ld be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systedajl.90 9havc ms, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a frequency v /mmw t )ft06kdos1w61$\frac{1}{2}$ 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 ho 0 ;x1 k6l28o 4fthfvp2pdpe-3lpprlong between fixed points with a fundamental frequency of-16 3 8to0d rle;pf2hv oppf p24kxhpl 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 abovjod(cg.+z mfp 3ru1o) e a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As irm dfo3p(cou).z j g1+t 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 ojyc0(sqj:3 ref mass 2.10 g is near a tube that is open at one end and also 75 cm long. How much tension s erycq0js:(j 3hould 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 resonatepzvqr 55r9;lj0iuhy4 yg p8g0 as 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 pure tone in the 500–1000-Hz range coming from two sourfmx--ic*8aub p 90dawces. The sounfi-*9u0pw -dcaa bx8m d 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 source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is statikogsse8j3z; g2 yl5d8onary. The conductor on the stationary train hears a 3.0-Hz beat frequency when theggksyd 8l5jo2se 38z; 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. A uut-3o4 ag z8-ryb)w *n;pih4ojqs8qfter it passes you, its frequen-i3hqb88on-g4;oqj s)uyw*r4 azpu t cy is measured as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the sp2pfpdocv6 8e8+ku zq nx2p.;v eed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway;2p8dqz8vf vp +xe uo6.nkpc2 . How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a b 3r 7+tfs/aecieat frequency of 11 Hz. The shorter one is 2.40 m long. How long is tetr/7ca+ s3 fihe other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves t3 teoe+4 ke.vpast a stationary observer 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 pott+e.v 3k4eoe sition 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 ab;mbco9a0 hz8uwn:z.exi.z (5bm+ ktorta is normally about 0.32 m/s what beat frequency would you expetibu nb 8c z9zme(wx ;0bma .+5hzk:o.ct 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 while the moth is 4-afx,bxrl rg71 yr2 eflying 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 thelf2y4b rx- x 1reag,7r bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approaw0fp2e p8*ukrches a moth. The pulses are approximately 70.0 ms apart, and each is a r pek*up820wfbout 3.0 ms long. How far away 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 once used to send signals from oneo+5 fbw 6 y,lfugr-f7/zeux8d5(qlav 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 resonatingfux5l- , 7ydbaefql/r8f +56zuv(o g w. 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 compromwcdb7h(4y ;on ised by the presence of standing waves, which can cause acoustic “d7w 4don(ch ;ybead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, zs); )jrc vpa+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 rj );c+sva)p zmade 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 o mgypi+y.agacb)ly p/ (052gdf ab gy2lgyp +a)p 5 a0mgd./cbyi(out 1000 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 thetlh4 5lvly.;ohn/gts/ c jh yg*(2: xi sonic boom 1.5 min after the plane passes directly overhead.xy 5gil/ hytj 2cgh hslt;(4/on:*v l. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboab-/rffd t(a*s t 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