What is the evidence that sound travels k2,xf3nh9 inn2 dvrblt,vx76 as a wave?

What is the evidence that sogb5t;nn lhq7 4und is a form of energy?

Children sometimes play with a homemade “telephone” by aizbqiezw zm xp /i:/ ,p.t 0/3lhm8ei;te 5m,ottaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks intoee.5 z/iql0 /mi zh;,:w 3mizmxtb8e,/p ipto one cup, the sound can be heard at the other cup (Fig. 12–29). Explain clearly how the sound wave travels from one cup to the other.

When a sound wave passes from air into water, d6zuwr q+)w,lf o you expect the frequency or wavele+q w6fluw)r,z ngth to change?

What evidence can you gz0;/umi 8*uyn x 1447fixd7evcgyw y uive that the speed of sound in air does not depend significantly oze084vfu7 47igi*uc nyyydm 1 /xx;u wn frequency?

The voice of a person who has inhaled helium soun2kb1h.1je l)k,qj wacds very high-pitched. Why?

How will the air temperzu*uu *;8xmw, 7r gclfature in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the hju5t u .*j(eramplitude of sounds in various frequency ranges. (An example is a car uehr*.j5j(u t muffler.)

Why are the frets on a guitar (Fig. 12–:t *s v(qw,ig1e6jgjf30) spaced closer together as you move up the i*t6 j , fej1vg:(gwqsfingerboard toward the bridge?

A noisy truck approacq qtve6ft ks-5so;.c-hes you from behind a building. Initially you hear it but cannot see it. When it emerges and you do see it, its sound is suddenly “brighter” — you hear more of the high-frequency noise. Explain. [Hint: See Section 11–15 on diff-t-scesq 56; ftq k.ovraction.]

Standing waves can be said to be due z3n lfr 1)ovuf 32gln fv -0b49kux1ruto “interference in space,” whereas beats can be said to be due to “in u olukux-3gf9r)1f nv1vrb n42zfl03terference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the poinq5l) oi.4 ftnt i3.ublts D and C (where destructive and constructive interfe) 4ion. iu.t3llf5qb trence occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wo * uu 3be *jbums:/+kph)dowg.2 mmsj7rk in areas with very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technolo : s 7mumbojuk. )/dme*jp +gsu3h2*wbgy, 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. Eac fpy a6l3ia;* ipsf06ds( /pkch wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18f* /pa6s 6a0fpkcdl3sypii ; (. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the2k6vt0f/ wlv z,wmlm-vet: 8a same direction, with the same velo:m -8, tw0l/ wevtzkl6v2amvfcity? Explain.

If a wind is blowing, will this alter the frequency of t/urs yiu3r z(;he sound heard by a person at rest with respect toyr/zrius;u 3 ( the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positionsc 4oo*kq+l -po of a child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency 4clqok *oo-p+ for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lakjfkr/ px,d5h+6 t( fwve by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears thxvr, 5fw6 dph/t+(jkfe echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship jy jm/(q3cn2sqztnu/w3*cf ,nust 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 thmzntu/*/q33nj( y ,cwfqc n s2is point? Assume the speed of sound in seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air atsajq;5k /+uwds 1mr vdmi7 -b/ 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 l.ecizgpn 9q; 95s( (2v zrjhijust above a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33).g zpi5j(z.9c2e 9 r(hilvq;n s 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 tf9qpx0b 9xm*:b oygzqwbw g-9, 4wb)cliff. The splash it makes when striking the wat90gb- )m,xfqg:o* 9bt9wwxz bybqpw4 er below is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the grc 8fi-q51 mgu9x9duppound, sees a huge stone strike the concrete pavement. A moment later t cq gm5d18uf 9x9-pupiwo sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the impact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of dista n+;yae n.ncc8nce by the “5-second rule” for estimating the distance from a lightnyna8cnne ;c+.ing strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the*7 v7 uiofvnb4z;fqf0bh qx2/vror6+ ovp. -k 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 u1 q ,yq0;o-kep7cjvpwhose intensity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB whexss6s egh pu3+n7i,j9n fired simultaneously at a certain place, whasp g6 ns9jh3u+si 7x,et will be the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance frhl tg)nn6 b,fuui.802,gd s ohom an airplane with four equally noisy jet engines is experiencing a souotngn 8 b2shgl u0h,), i6.dufnd 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 sim/c9 c+bnc0c egnal-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 background noise fo/ecbmc+cn c90 r each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking-i(2geus4r gg in normal conversation. Use Table 12–2. Assume the sound spreads roue-guig4(s g r2ghly uniformly over a sphere centered on the mouth. $\approx$    $ \times10^{ -6}$W(Round to the nearest integer)
(b) How many people would it take to produce a total sound output of 100 W of ordinary conversation? [Hint: Add intensities, not dB’s.]$\approx$    $ \times10^{7}$people

  A 50-dB sound wave strikes an eardrum whose ,yfqek3/x0n3jrmiey6:. f vf7owt5 carea 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 q03d n fq8qae9 k55lzbxk3pq3the more modest amplifier B is rate 385 keqp 9kal0dzn33xf5q qqbd at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter regist ,fxe/;oalt y*ered 130 dB when placed 2.8 m in front of a loudspeaker on the stage. ae,l/tf; oy*x
(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 sounf63l)ga5cn f o*dv ow:1foxd-d level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels o xnafvc w* 5odf-olf16d3g :)differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is triplevi./ +e rbc3zhd, (a) by what factor will the intensit.ebziv/ 3rh +cy increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement azk8yna0k n8 3r:ntbj,mplitudes, but one has twice the frequency of the other. What is the ratio of their ink8z03knb ntn r,ja y:8tensities?   

  What would be the sou-n2 2gjk 8emyxnd level (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air 2gy8-njmek 2xmolecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 15l/1 zxbtf wv+,ycp(k 00-Hz tone that has a 50-dB sound level? (See Fig./(ky5c+vtp z 1 ,wfxlb 12–6.)    dB

What are the lowest and highest frequencies that an ear can detectq *un2d6a5f9x jzwu;4tjo+ al when the sound level fq*j nj 245zuo6xwa d9tua;l+ is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodate a huge range of sound levels. What is the ro2s05 w6qp wxcatio of highest to lowest intensity p506ww cox 2qsat
(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 leot 6 dgi2e,(1bu 6sj1 knw8sakngth of the vibrating portion is 32 cm, and it has a mass of 0.3 k1ie 6,oswd8s(g6ajnb u21kt5 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental+9-wt (dx tw (ai4pjcj and first three audible ove9ptjcw(w -j4a+x(dti rtones 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 frequencbwcn)ho7dr43 ara8e :y would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if you assumed it wacar e8rb:3ho n)7a w4ds 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 w)io2o2f 4fderith open-tube pipes spanning the range of human hearing (20 Hzdiro o f42e)f2 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 Hz as its third harmonic. What wiocx*b,c9n s; hll be its b, xn;o* chcs9fundamental 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 abovucggh/6obcb*j0ig -; ;y bt/ge middle C (36 b;h - gb0y*;ti/g/cbcujgog 30 Hz).
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an8c -c j1ejy2a3k5aydko k3 -ne open organ pipe that emits middle C (262 Hz) when the temperatury-kjky1cc-ea a2k5d3jen8 o3 e 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 20 vk2r)v e+ c0iovlp0+e$^{\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 hhk (2nlb molmj;r6/:x ole be thatj hon;x/m (6 ml2r:klb must be uncovered to play D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 264 e8 gxgrm+;5jt7v hv-cHz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Seg j-xm 8t;rh+g75cvvhow 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 openqy.dfbm .4 ,x1a.-yyq jyhbq( at both ends. It resonates at two successive harmonics of frequencies 275 Hz and 330 Hz. q(bhyy jq, a-. xy1bfym d.q4.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 a)vokq44jj w67y pt 2y$^{\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 a 3tq 2dh*kah-xudible range for a 2.14-m-long organ pi dxhk*a 23q-htpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approx-j gi3(gze6e jak,f )bimately 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 relationship of your answer to the informa -kjfe(6je bgig,)3 zation in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0t.)4vr p05-r5: i 3zywcwkf f-xlcppi s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frequency is the other stri5wz 5 0r3kwrix tc:fvp)f c-pilp.-4yng? ±    Hz

  What is the beat freque5 //ghrp v /9gc8ouzrn4frcq. ncy 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 a2 jt*n kl*e:janother (brand X) operates at an unknown frequency. If neither whistle can be heat2 ljnea kj**:rd 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 la9./ eba*or utq.zs44 beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tunin/saqt b zlu.*94.oae rg fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings arie g+gi(4i sl--tdp g+e tuned to the same frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will be the beat frequency hg-sdlp4g( e+t -ig+ iieard 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 playipw),i goz j7qws6,ka*4ha -v middle C (262 Hz), but one is at pa4 o,7v k whzia)q s,iwj6-*g5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, andvmnup)e) y*m0 C. Fork B has a frequency of 441 Hz; when A and B areuy ep* )m0mn)v 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 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 perso-n6:v4mv 6hs1zx yxtqn stands 3.00 m from one speaker and 3.50 m fmq 64-vv1ts:z6 y xhxnrom 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 mv.a2f/ s u9flo1ag:x59us xisupposed to be vibrating at 132 Hz, but a piano tuner hears 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 otf u1aa.99lxvu: sx/ f2ois5mgher ?   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 wtjb z6hgv,84uls i8l )avelengths 2.64 m and 2.76 m in air. How many beats per second will be heard? (Assume lsz,l)v 8jg86bthi u4 T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when 9 nq;3uf 7(lhke/ xhpkat rest. What fre(nekfh;3 k pqh97u/xlquency 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 frequencytocwg 2d /3pv) do you detect if a fire engine whose siren emits at 1550 Hz moves at a speed o odv3 pg)2/tcwf 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz sourcercj fg*0oa+j, ,zhpp 9 is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frep 9rjc +,opgjhz a*,0fquencies 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 s)uv37d qsj/ nxame single frequency horn. When one is at rest and the other is moving toward the first at 15 m/s t7ns/v qx j3)duhe driver at rest hears a beat frequency of 5.5 Hz. What is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sounyth.f1an eb o;7y1u3m d waves at 50.0 kHz and receives them returned from an object moving directly away from it at 25 m/s What is the received 3 ;.ufymo7bt1yhn ea1sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/sq wg;co.5y ); g*kcfbdxb74*frbtv3ef9hjl4 As it flies, the bat emits an ultrasonicel3jdfb; .qvx45gwohr *bfc c4g*79b) tf; ky 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 tuba was played on a :/90 ,qm +phivn ghcaamoving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was heard if the 9 naq /,hai:h0 c+vgpmtrain car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow speeds. Suppo jm5 d1zo hwjf1q---chse 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 oc -qzd5jw 1f1h-hmj-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 ultrasonic waves of freqayds -6ieh *;01pmfqe uency $2.25 \times10^{ 6}$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 veln:blwoij d6*+.2 saig ocity is 12 m/s from the north, what frequency will observers hear who are located, at res*bi2l o. n 6wds+aj:git,
(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 movic 3wzo5zz fg5:y*fnq 9ng on land if its speed at 20 $^{\circ} $C is Mach 0.33?    m/s
(b) A high-flying jet cruising at 3000 km/h displays a Mach number of 3.2 on a screen. What is the speed of sound at that altitude?    m/s

  An airplane travels at Mach 2.3 where the speed of sound is 310 m/s (a) What3,ou6bako9sa 5.eqtqxj5n (u is the angle the shock wave makes with the dir9ouokaqu6 a35j (bnq s,. tex5ection 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 whe6ja.zu61 vn ubwj*b f8 0xfg4tre the speed of sound is only about 35 m/su fgtwvx01b6u *4fabj6z8.j n
(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 the shock wave ugc2vh3e5z/y/a tk( jangleketv/3 y (/h2jugc a5z it 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 i stiz*.8b e/kah m,(u j+8jlm$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overas ou wy ( e1,-t4f/uteg0sk)yhead and see a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a agw1t-)4 / ,yfsusyeto e(k0 uhorizontal 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 sem,wsn pee8,j g vz+ k7grqa-.;nds 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. 7nmgjzqwk, -g.+pe 8va,;serIf 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 the1g78oq*/mruyg9xyjh re in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony. g3.yl1t(vpmwimmkxn 19b d9(It consists of many plastic pipes of var(l wmnm9d1b3y tgix9 p1.kvm(ious 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 threshold of 7cqko)j.ue0re g))vk human hearing (0 7erj)vko)g )q.ku c0e dB). What will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB.-p*rthrccof1yri 1s3*l b s+ sound are heard simultb1lpit+h sf3y rrs.r*o1 -c*caneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 13e9s5b en q4fx05 dB. What is the acoustic power output (W) f5 9nbesqxe34of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output a s5jn1un.esycn:o88f t 1000 Hz. The power output drops by 5sj .c1 u 8:nsonf8eyn10 dB at 15 kHz. What is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wpfv+ r 03ho5dsear 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 ead3s05rhp+ v ofr has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications syste/v;qmyhgrk074v 7zxhms, 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 tu.(x)q/ ljxnjaz h 5zq1ned 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 longaiey:x6iagknvn m5tf9 3 ),p ; between fixed points with a fundamental frequency of )xmf3:ii9k 6yae5vgnn ;t,ap 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 vibrationj sh*7xj/; uif above a vertical open tube filled with water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency x;i /h7s jfuj*of the tuning fork?   Hz

  A 75-cm-long guitar string of mass n izc tm/3u )vy.6fvf,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 produce resonance (in its fundamental mode) nf6tzv .)v,m/yfc3 u iwith the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was 1 okzxe8u f84fobserved to resonate 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 ranh)is;u6 *qnso ge coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m far *;io6 sqhun)sther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. O n3vx /q0by/jh(v2 rn1 :ivuqbne train is stationary. The conductor on the stationary train hears au2jbvhn/y /3:1nqbir0 v xq(v 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving train?   m/s

  The frequency of a steam train whistle as it approaches you is 538 H7 b qeikmox5jvg -/w,v**ksg 5z. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (assume constant velocityv-5*so* 5/j7vxemqiw ,gkb kg )?    m/s

  At a race track, you can estimate the speed of cars just by listening to the di k;j 1g;mfe-k)/gw/g ycy2q4ie+q pyvfference in pitch of the engine noigp)mq/ eqkyv - ki;;wg1/4+2fy egjc yse between approaching and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, pd/k4e r2v t9kgroduce a beat frequency of 11 Hz. The shorter one is 2.40 m lekt/4gd 2 k9vrong. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad car as it moves p+n1m 6euwxrc5ast a stationary observer at 10 m/s as shown in Fig. 12–37. If the speakers have identical sound frequencies of 212 Hzn e1r+mcw xu56, 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 normallybm )3yd qami99 about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and remiaqm99 yb) d3flected 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 whil bo ny h./m;2bpyp+ ;dudy93eee the moth is flying toward the bat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat afte+.y/p 3 b m yhypdb;oeeud;n92r that wave reflects off the moth?    kHz

  A bat emits a series of higgmd) u1j +gya(h frequency 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 one chirp returns before the next ch)dyg j 1g+mua(irp is emitted?    m

The “alpenhorn” (Fig. 12–38eajkv yrf:nb, ei4,hna 39l 9w; dr13(rz6 thy) was 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 ,ky4rfe9zl rdn 3 3;:ybe6jr(inv9ata1, h hw 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 presen-rj-ma e*q *goce of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in thisgo-*e*ma r-qj room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves d.vlg61 g feifx y2ifpv1//: aa 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 r 21/elv.1 v/fad f gfi6pg:xiyod 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 he8awh (04 mhi tu-oyg8varing for the human ear at a frequency of about 1000 i8m(hhu-04awo8 tvy gHz 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 h/f 4yo5w4 p*kz:ru5bhz*:*a pmkyy yyears the sonic boom 1.5 min after the plane passes directly overhead. What akyo 4z/yzy5b*uym::h5* wk4fyrp *pis the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 15 m;ssc5kz n(ssyj97 *f$^{\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