What is the evidence tzsmxwwn9a15iazo4s2 y m,( o 2hat sound travels as a wave?

What is the evidence that sound is a uqw ag7+3gj hhc02uv9qk/ ,qm form of energy?

Children sometimes play with a homemade “tel /ytmk8-*g;x5zp wt glephone” by attaching a string to the bottoms of two paper cups. When thk/yxlwt8; *tmg zg 5-pe 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 cup to the other.

When a sound wave passes from air into water, do you expect the frequen y:1fcr l5fvgh8xv26lcy or wavelength to chly8g5vclhffr1xv :62 ange?

What evidence can you give that tf4a:op fo37g + r tr(ft1epdq02 *llyehe speed of sound in air does not depend significantly o (roe*p4l703 2fpfof1dg+yl aqtter:n frequency?

The voice of a person who has inhaled d+a a zw+ f8g8*orqsd2helium sounds very high-pitched. Why?

How will the air temperatu ui:pi3 :aejw7-vz kh1re in a room affect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude of g; mos;4/cddnk6gpu1 sounds in various fr cn/g41s6mgop;dd ;uk equency ranges. (An example is a car muffler.)

Why are the frets on a ggu njdb .d9mu93mm() xw)e/scuitar (Fig. 12–30) spaced closer together as you move up the fingerboards(.39bc9ued ) nxmjgwmmud )/ toward the bridge?

A noisy truck approaches you from behind a building. Initially you hearj41ry eai3;j p it but cannot see i ie y4;j13rpajt. 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 diffraction.]

Standing waves can be said to be due to “interference in space,” whereas bea nz0qi f kk+m:)wpoh4-ts can be said to be due to “interference in -k+ :q0wkh4 nopmf )iztime.” Explain.

In Fig. 12–16, if the freq ws60lx d+axn xt0:q/suency of the speakers were lowered, would the points D and C (where destructive and constructive interference occur) move farther apart or c:xsta/d wq+00 6 lxnsxloser together?

Traditional methods of protecting the hearing of people who work in areas wicc,/.e p+w vk4j2yzjq )u5 lo 9;oemgh:hit0hth very high noise levels have consisted mainly of efforts to block or reduce noise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which dek/.o 9j ztmgl ijep2 oyhv,c)e+u5ch;h:q4w0tects 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 caog.oz5e i+ nz98 wytc. h7q9svn be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18 .oq5ezyzovitsc8w. g h99+7n. 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 obseaklaih 4saxz.7s3:( h rver move in the same direction, ah3z( ass4la:k x .hi7with the same velocity? Explain.

If a wind is blowing, will this alter tqb0(jf3 /o oycyuku; .he frequency of the sound heard by a person at rest with respect to the source? Is the wavelby(0fjyou/o; . cu 3qkength or velocity changed?

Figure 12–32 shows various positions of a child in motion on vw+- :g*d9njzd v lamvjk :,z3a 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 for the sound of the whisd-zvl 9,w:k+jv*m:na d gz3 jvtle? Explain your reasoning.

  A hiker determines the length of a lake by liste91l( rd mrdbd4hvw mr iml76+ w6/xp+bning for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.0 +mv7m 6r4dr x 9(1mdb6ilw l/ bhwdrp+s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hv vd rebk5e8+ix, h*l.e 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 ie+* vb5,xievrh 8d. lkn seawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengt03oumw x,rb(v hs 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 abov ikt k25*wei3jd08akve a school of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time5di0j akt 23 wvk8*ike 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 1-yk -4fveq dgwhen striking the water below is v 1-f-e4kqdgyheard 3.5 s later. How high is the cliff?    m

  A person, with his ej7xj. 9/ trekhar to the ground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and.9ehr/7j txkj 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 ofdt im fd j0vtq:sl t8* y.vxa6hct5.5. distance by the “5-second rule” for estimating the distance from a lightning 8i: . 5a0vst6mttjhclf5.d*q.x ydvt strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pa ot3ux ( cz99yf)9kcfxin level of 120 dB?    W/$m^2$Compare it to that of a whisper at 20 dB.    $ \times10^{-10 }$W/$m^2$

  What is the sound level of a sound whose intensit w tejtoo43-q;.bz: ezy is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fizocj/eemm.)+ ul ,) fired simultaneously at a certain place, what will be the sound level if only one is exploded? [Hi)lmio,uc)fe.je+ mz/nt: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane ssi0(oce :8/ds/s v snwith four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would8e nsssc i0 //dovs:(s this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is 0yik4i edp5 q3e4ri7pa2 r6j gsaid to 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 background noise for each dev3jp5 r2ya e74dr kqigipe60i4ice? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a py9v,-vw7p ,pgz n 8hnlerson speaking in normal conversation. Use Table 12–2. Assume the sound spreads pw7yh,znvl p,-8 gn9vroughly 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 e9 yenlm7+jesun9yl0 - ardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while t)bgzy g24pmltj htg/)7b 7ak;he more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3. a; m247g zgb/l)7g)ybk httpj5 m from a loudspeaker connected in turn to each amp.$I_{250}$ =    dB $I_{40}$ =    dB (b) Will the expensive amp sound twice as loud as the cheaper one?

  At a rock concert, a dB meter registered 130 dB when :pa *0c,lfms +buua,mplaced 2.8 m in front of a +cbsmpl:u f,0aum* a, loudspeaker 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 differe3* slvih0 gzr(nce in sound level of 2.0 dB. What is the rathgis*r v l(3z0io of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound mo5ab g)x 1 gm6uhh+q2wave is tripled, (a) by what factor will the intensity increase? Increase by a fach um2xg oba+ qhmg)165tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacemec ;7lh1n hhhfr8;el) mnt amplitudes, but one has twice the frequem)h ;r8hhe7h;l ln1fcncy of the other. What is the ratio of their intensities?   

  What would be the sound lev j7, j3i()qiman9nk.b(oaas bel (in dB) of a sound wave in air that corresponds to a displacement amplitude of vibrating air molecules of 0.1i 3qsnomjbaba akn.7 i(,()j 93 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sounm g1x/ky hqmh5sc; 8i1d level to seem as loud as a 100-Hz tone that has a 50-dg;hci8 1s/h 1 x5qmmkyB sound level? (See Fig. 12–6.)    dB

What are the lowest and hige3 ae4txb03nc k;k(jbpm*9v yhest frequencies that an ear can detect when the sound level is 30 dB? (See Fig. 1ek* tej(c3k 4x 9;3anbbm0 pyv2–6.)

  Your auditory system can accommodate sjl2 q0rul*y/ nr*v:ba huge range of sound levels. What is the ratio of highest to lr2/:*jb lysq0*nu vlrowest intensity at
(a) 100 Hz,$ \times10^{ a }$ a =   
(b) 5000 Hz? $ \times10^{ a }$ a =   
(See Fig. 12–6.)

  The A string on a violin has a fundamental freqqes.1v k,m0 sjuency of 440 Hz. The length of the vibrating p0kj., mvs1s eqortion is 32 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 are the fundamea;x lv 04rsc wr q.mag36 um/0;fhh)ysntal and first three audible ov.)/s 0hma3x;gf6r 0 mla4cs yvwhu;qrertones if the pipe is
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency w6p)hsvk2o w n2ould you expect from blowing across the top of an empty soda bottle that is 18 cmv h)6ns2po 2wk deep, if you assumed it was a closed tube?    Hz (b) How would that change if it was one-third full of soda?   Hz

  If you were to build a pipe organ with open-tube pipes spanning the range of n5enbp. st3 .bhuman hearing (20 Hz to 20 kHz), what would be the range of the lengthsbns.tbn. 53pe 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 willfk9o 89jmv/ea be its fundamental frequency if it f 98mk/oavj9eis 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 midd -.ka,faw hbc17gcuz5 le C (330 H-hg .wf7cu1,kbaac5 z z).
(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 o +ib:puj;djkl/ -wu h g95hub7pen organ pipe that emits middle C (262 Hz) when th/:h9u ku;-pbu7wijlh5 j dgb +e 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 atya6 ylb3x/ 2at 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 hoao g-1fs pa7;duf3g4zle be that must be uncovered to play D above middle C at 294 H g7ffopsz;au4a d g1-3z?    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,q;ka8co 2 s9hmbt*oznj)el(jg+ ; wk2 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show why this is an open or a cl;eh*ctnb2()sl +oqmzjwaog jkk9 ;2 8osed 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 resonps) 7gl-m sl 2kzstp(xx) k-3e7-o newh 3cx6dates at two successive)(exsl-pxc mtwe h776d-lx3 gos23zk nks )p- harmonics of frequencies 275 Hz and 330 Hz. What is
(a) the fundamental frequency,    Hz
(b) the speed of sound in the gas in the tube?$\approx$    $ \times10^{2 }$ m/s

  A pipe in air at 20 wqrji9x2b08-ht3b,;l w dkqy $^{\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 presexr4hk5+ ( pp 7h*+oogoar pk+snt within the audible range for a 2.14-m-long organ pis4o+ox op+ap h kh*k7g( 5rp+rpe at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approximately 2.5 cm long. It is open to the outsi+bm+ohpv 1a d-6 kq*ytde 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 information in the g-vq m+y6oh dp+ bt1a*kraph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beafa0sauv w* wc55 wi4(itphh w8fyp*: :t every 2.0 s when trying to adjust two strings, one of which is sounding 440 Hz. How far off in frefswpif* thu(hy84aa*wvpw:c55 w0 :i quency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) al(6w2l mlx + wjewd(6mnd $C^＃$ (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) opfw;d5m y;lmhtxp;.6q erates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs whe q.dphtf w;yml ;m65;xn they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 xj1wb g r;n6e)beats/s when sounded with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuning fork. What isn1; 6jrwbx)g e the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensiy1+afc0ya vo1j k0 cqrm8/qy -on in one string fr +y/cmj0a10v1yo8 -qa kcq yis 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 heard if two identical flutes ea0kfvbo+q/ o9sch try to play middle C (262 Hz), but one is at 5.0°C and the other ato/s+k v9 qb0fo 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning6ct1cns7mn3 ph -wd/ k:zjhz zjt q),1 forks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a beat frequency of 3 Hz is heard. When B and C are sounded together, the beat frequency is 4 Hz. What are the possible frequencies of A and C? What beat frequencies are possible when A and C are sq3 jn n:pwzh cjh6tz1kc/zs m1,dt7)-ounded together?$f_A$ =    Hz or    Hz
$f_C$ =    Hz or    Hz
|$f_A$-$f_C$|    Hz or    Hz

  Two loudspeakers are 1k(lk e5l oy*9x xd+zc6.80 m apart. A person stands 3.00 m from one speaker and 3.50 m from the othe*e9l o(x 6 lcyzdx5kk+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 pia9+-tgnb ob 0ccg1s:m vno tuner hears three beats every 2.0 s when they are played together. (c:0gb -gmt 9ovs+1 cnba) 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. How many beaww+8q/dud 5i uts per second will be heard? (Assume T8d 5/uwu+diq w = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s siren is 1550 Hz when at7jg/;nt uw4 ay rest. What frequency do you detect if you move with a s w4g7aj;ut/ ynpeed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency dobga v-4yn 97lm .jyi*r you detect if a fire engine whose siren emits at 1550 Hz moves at a sprjaym9y-v i n*7l4bg .eed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source i4hz e;5hdxxp/ s moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the same? Are thepe;h4hdx5x/z y 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 toh *7sxu:qz(3+2jxn vrx -wo ohe 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 tx-*h:sx u3zonrjoqovx2(w7 + he frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 ks7rj3do hl.p ey7xo/4Hz and receives them returned from an object moving directly away from it at 25 m/s3 7dx.o4sp 7 oehy/rlj What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a sd 0jteu 5ah.9lpeed of 5 m/s As it flies, the bat emits an ultrasonic sound wave with freq9 t50le.aujh duency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experd-)yvs h .v3rdiments, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same tone while at rest in the railway station. What beat frequency was he 3vdsv-r ).hdyard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to m e trtr4c+t-9 19d+,e pdzhhtaeasure blood-flow speeds. Suppose the device emits sound at 3.5 MHz, and the speed of sound in human tissue is taken to be 1540 m/s What is the expected beat frequency if blood is flowing+r 9ph1t,dedht9t4rtaz e c-+ in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultrasonic waves o:flqzqp -a; 64jco+zge6sd 8v f 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 7jq (: kw mue, wg-0r4 zshlpm,ug;mx1of frequency 570 Hz. When the wind velocity is 12 m/s from the north,l4 u7 gkm(mw jzpxgs,;eh mq1r- 0w:u, 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 ifcdfws6u0 f: ;sb m-1e zgy)+ru 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) Whagzi79cv 8*di)ghafp 7t is the angle the shock )77*dichgpag8 vf9 izwave 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 entersh9wd,ic qd) c(f(/lqo2h7nhzu4q6yr the thin atmosphere of a planet where the speed of sound is only about 35 6(q yqq9 hdh4,icl2 cwudz7(frhn)o/ 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. Determine3r9pnu s5t5py e+wc9l kkzvw s3 ;-x 1jajh0w8 the shock wave angle ith1wc3rx 9 -0 a+lsne5szj pkwp;3uwjt9 5vy8k 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 oij 1f8 *jm6r* eta/uf$/theta$ 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 kmime 0q3d +ci(m above the ground flying faster than the speed of sound. By the timeqim3ce i0 (m+d you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fig. 12–34. Determine
(a) the angle of the shock cone, $\theta$    $^{\circ} $
(b) the speed of the plane (the Mach number). Assume the speed of sound is 330 m/s   

  A fish finder uses a sonar device that sends 20,000-Hz sound pulses dkuw:srezr000v *dm+je;f u ;bownward from the bottom of the boat, and then detects ech00jumrefws;:0 r bz;vkdu* e+oes. If the maximum depth for which it is designed to work is 200 m, what is the minimum time between pulses (in fresh water)?    s

  Approximately how many octaves are there in the human audible 8u2ayjy6i(2i -ebf hh range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a tl , 910lu 7mzubdss/xt6sm 0idisplay called a sewer pipe symphony. It consists of many plastic pipes of various lengths9/t6 7u0,mlxbitsdms01 u zls , 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 thresholdr,x8rejs;.x,usx ma )c.xw;z of human hearing (0 dB). What will be the sound level of 1000 such meazu .xw)x;s mrxcr 8, s.x;,josquitoes?    dB

  What is the resultant sound lev,wrm7 vy3 ep:+ xzphp7el when an 82-dB sound and an 87-dB sound are heard sim3hppe ,x pw +:v7z7yrmultaneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, iia6.pn d -ssy yz2e 2cwz62gg(s 105 dB. What is the acoustic power output (W) of the speaker, assuming it radiates equally in al yd2 s gi2z6 6ywngp(sze-.2cal directions?    W

  A stereo amplifier is ratelh f1x)wtrwt4,o*ca2 o7j bj9d at 150 W output at 1000 Hz. The power output drops by 10 dB at 15 kHz. What is the power output in w 24t9bfchrtw, x wojl)oaj 7*1atts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective de ij72cw2osb6fvices 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 radius6cw j o2fsbi27 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 communicbtmd kvlh(,s*z6*pe7 ;gotu*hpz+ k 4ations systems, the gain, $\beta$ in decibels is defined as
$\beta$ = 10log($\frac{P_{out}}{P_{in}}$)
where $P_{in}$ is the power input to the system and $P_{out}$ is the power output. A particular stereo amplifier puts out 100 W of power for an input of 1 mW. What is its gain in dB?   dB

  Each string on a violin is tuned to a fhp n5w5naqu;pxe 436lrequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm long between fixed points with a fundamental fp js v513gg4hjrequency of 440 Hz and a mass per unit length ofj4j sghv5gp13 $6.1 \times10^{-4 }$ 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 vibrationcy:w7l )eb4 k )nc2kwbn8x hi1 above a vertical open tube filled with water (Fig. 12–8:4c xwb hiew27)1clk n ynbk)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 of the tuning fork?   Hz

  A 75-cm-long guitar strilxo) r+ l;8l9i vv)hwqng of mass 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) with the third 8;q9hv wvlo)+ll)r xiharmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observegw5w o ,s/xyqbei2p ;+d 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 range coming from two souru qzp1):6 rwme:o- .qltcgr4y ces. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves aboc:e- :4qrl otg 6 pm).zu1rwyqut 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 tao c mt1 fp*ie4b2,f1uj/j- jnrain is stationary. The conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the speed of the moving tr-f/ bt iaufc1o* n1p ejjm4,2jain?   m/s

  The frequency of a steam train whistle as i f,5iktj;qnhvov +*d84u (vfit approaches you is 538 Hz. After it passes you, its frequency is measurv4i8jovh k ;+ui(vnt,f f d5*qed as 486 Hz. How fast was the train moving (assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening to the dif+m g26 hwma5ftference in pitch of the engine noise between approaching 6+mtw fgma 2h5and 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, produce a bea lzxwjb 29y8p8t frequency of 11 Hz. The shorter one is 2.40 m long. How long is the ol 8yx8 92wjbpzther?    m

Two loudspeakers are at opposite ends of a railroad car as i-3l2zu dfzfa6 t moves past a stationary observer at 10 m/s as shown in Fig. 12–37. If the 6zzauf3l2f d -speakers have identical sound frequencies of 212 Hz, what is the beat frequency heard by the observer when (a) he listens from the position A, in front of the car, (b) he is between the speakers, at B, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is normally about 0.32 m/s what beat +(m62/4 hrdq-ey szfdk slo0gfrequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected fr(0lq/6y4gdszm2 +kf -res od hom 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 toward the b:0adjgr 9 f5;uc+7mtpsx ;jtvat at speed 5 m/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wav;tjspc ; mg:t f5a7rujv0d x+9e detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high mdfphe l4y94l:x 2 evme6ojjv ,;( a9bfrequency 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 chirp is emeoe(ab94lfxv,mjd924 lp; : ej6h mvy itted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from n dhj(cdzs9eplp.d/88 or6 : uone Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to cdozdl r 6:/hs8d.j9(pucpen8reate deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening ccl2 m0qg 7*tiian be compromised by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the imi l02qt*gc 7standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slender a-zxic n +nbae,86 b(nrtx6xympl6dje n1 7s54luminuz l ant6bp1,sy 64b+m n7x-x 8dni5ren6je(xcm rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little practice, the rod can be made to “sing,” or emit a clear, loud, ringing sound. 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.;cjvu3:zh jyfzdx .im+ dqf)wqo 58, of about 10wyvfz.) z.mq 3qic,:u+hdo8xjdf j 5 ;00 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 5+87c 2m+n+s m dnc . mhvspckcck(-atMach 2.0. An observer on the ground hears the sonic boom 1.5 min after the plane passes directlyknacd+p+5.schck- nm 7( ctcs +8mmv2 overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat ixg * 4*khzyl5kgr-x9a s 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