What is the evidence that sound travels as a wa 7+noe, :w 4v7-qqh:fjn,blt v ,gzmhxve?

What is the evidence that sound is a form or1ys, ,rwx5ukf6- sh1r qr 2ai:yoc) mf energy?

Children sometimes play wilr45a -f*o f)qro)q:fnl)kr pth a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretched and a child speaks into onerk:lfrlr )af4q- o f))*p q5no 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 watuetck z6:vr lrd5i 166 wy.)uxer, do you expect the frequency or wavrc65etykwdl)uv6 1rx.u:6i z elength to change?

What evidence can you / g4*mpwjt omvm)9go9give that the speed of sound in air does not depend significantly on frequeng 9pj/wt*o94 omm)vmgcy?

The voice of a person who hn 2e *kar/s*)blen 7it g;)zhaas inhaled helium sounds very high-pitched. Why?

How will the air temperature in a room affect the pitch of organ pipeu2.65ybjys.7e9sngif a2k aa bt 6bi/s?

Explain how a tube might be used as a filter to +- ii+7ckf baoc+uq.k reduce the amplitude of sounds in various frequency u iai c+-fkc7k.q+bo+ ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer together as you move up bli 4qz2j-xx; the fingerboard toward xli- zqb4xj;2 the bridge?

A noisy truck approaches you from behind a building. Initially you hear it vod/w l /r pt05fzhv)4;qbk q6but cannot see it. When it emerges and you do see it, its v;0koq rpwdz/6h)tfqbl 5v/4sound 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 k4ju:v 0ox4;w bbxvo-efohy) ) imr+ /to “interference in space,” whereas beats can be said to be v0 yukw omhxbv)4;/j-+)r oxf oei4 b:due to “interference in time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would the pointssjoja :,: b 8sktz)-lv D and C (where destructive and constructive inter zj:svoabl k,sj -8t):ference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of people who wo6e 0,fg9: iun/vv ubgwrk in areas with 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 deebvn i:f w9ugg,u /v60vice 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 suub2,- z)vv fk)lxuppshn9r0 kx4+6n skch9e ;perposition of two sound waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are tzv ukph f0nknl492x)ve c9,s;- bu )r6shx p+khe two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and nv eq j,-106o djmj15dxyhct1observer move in the same direction, with the saoy16nqhjx5 - 1edt0jc m vdj,1me velocity? Explain.

If a wind is blowing, will this alter the frequency of the sound heard bs bk 5bwz:62bay a person at resbba bzw26k 5:st with respect to the source? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a child in342x6 j ,lohxn4weo bu 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 for the sound of the whistle? Explain your reasoning. u xxnwehl,bj446 oo23

  A hiker determines the length of a lake by listening for the echo of gmivzg*m2lxg(y 77v (her shout reflected by a cliff at the far e g 72mgvi(v *myz(7xglnd of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the side of his ship just below the waterline. Hep4o7/ tvrm:if 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 t/7 v im4port:fhe 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 a zpbp)o .. z.9ceix4eat 20 $^{\circ} $ C for sounds in the maximum range of human hearing, 20 Hz to 20,000 Hz. $\lambda_{20Hz}$ =    m $\lambda_{20kHz}$ =    $ \times10^{-2 }$ m(b) What is the wavelength of a 10-MHz ultrasonic wave?    $ \times10^{ -5}$m

  An ocean fishing boat is drifting just above a school of tuna on a foggy day. W khmwiz5a r8698w vk,,u/osmqithout warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfire is heard (a) by u9 w5 ik,,rvm6o8qkhs8amz / wthe fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash it makes when strikka cn37w k:a)k- 7bxtring the water b3cxt ka7kr a7k-):nbwelow is heard 3.5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees a huge stone strike the concrete pa7 fwkti0 ez8h/vement. te/8k0iwh7fz A moment later two 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 8. un1ii(1tcr a rx,ex/qx/d jof distance by the “5-second rule” for estimating the distance from a lightning strike if the temperature is (a) 30 1x81txdr a(iu/c, .nr/ejq i x$^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at the pain level of 120 dB?;c,sq(ljkgyfm:gr fn 4 o* y(5    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 intewh01 -qdesm 93k3kv zbnsity is $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneouslqa77 si,q)luaadd.j:n. ou 2ty at a certain place, what will be the sound level if niouqdsq7:u2.a aa,.ldtj ) 7 only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain ;2j .;tvnqlx zdistance from an airplane with four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB v;qt;x2l.z nj’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dB, s*t /g.kj o.hcwhereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for each device? 58 dB =th .j/* cg.oks    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speah+uy ts9y x 3q28q kjwam12q4z,lqi-bking in normal conversation. Use Table 12–2. Assume the sound spreads roughlh1ax4q uw38yq2si ylq-b2mq,+ tj9 kzy 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 who3n amq*n 2vi/9apjiev)g4m 3mse area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while the more modest amplifier B i v/3ymutv+o+, 4*x 8aoyzlljiumx+)f s rated at 40 W. mu+ yjzo*/uaxyi ofm)+x4l 8+lt3v ,v(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 registered 130 dB whes;lq i5+peu: jn placed 2.8 m in front of a loudspeaker o;+iejl s q5p:un 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 typicm7,0mlj , ,nmrj of9aoally detect a difference in sound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amoumm a,7jmfrn,j09 oo,lnt? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by whatp,sse.:fk c1 h8l*bwndz+e 0 s factor will the intensity increase? Increase by a facess1f+scn0 z*wedh, 8bp .k:l tor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amqburg x0ug h9q 22ozz7o *2a(gplitudes, but one has twice the frequency of ougz07gx2b2 g9 u 2qzoq(har*the other. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in am9m8g u: 4rtclir that corresponds to a displacement amplitude of vibrating air molecules of 0.13 mu:m 9mgc t8rl4m at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to seem as loud as a 1z/t oxb+a:cb6 00-Hz tone that has a 50-dB sound level? (+bcz :6/bxtao See Fig. 12–6.)    dB

What are the lowest and highestcycz78jiqdk.4 0,m re frequencies that an ear can detect when the sound levele m rj4c.8k0czd7q yi, is 30 dB? (See Fig. 12–6.)

  Your auditory system can accommodatx t8qlh (k-sx4t+ wv0he a huge range of sound levels. What is the ratio of highest to lowest 8h0q-+x(t w 4t svklxhintensity 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 frequencye9wlo ou q krx59h.55h of 440 Hz. The length of the vibrating portion is 3x5le9 o hwq.ukhr95 o52 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 fundamental and first three aud0 y3h)rasmi6sible overtones if the pipe is a0rysmi s)h63
(a) closed at one end, $f_{1}$ =    Hz $f_{3}$ =    Hz $f_{5}$ =    Hz $f_{7}$ =    Hz
(b) open at both ends?$f_{1}$ =    Hz $f_{2}$ =    Hz $f_{3}$ =    Hz $f_{4}$ =    Hz

  (a) What resonant frequency would you expect from blowi- qsebd5,p rd-ctcn35jp). cong across the top of an empty soda bottle that is 18 cm deep, if yo -c-t o3b.cpnq5csjd,rp)d 5e u 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 buildmcjk8m xur( +:7 hoj.r a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 2h:jm .j7ck8o( m+u rrx0 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 abm8 .e p5z 3i tc+rsa6n2wrz*os its third harmonic. What will be its fundamental frequ .z mnrwo 6ir*8stcpza32+be5ency 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 tof m- wx2fhqmi sgr1l;*-8xvf mp-/q0p play E above middle C (330p 0 m2ghwfqp sq1;mrfvl *m/- -x-if8x 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 an open organ y-r2z /jr*b7nt x+/olbk . zdbpipe that emits middle C (262 Hz) when the temperature r* k27z/.t+-b yborln j /bdzxis 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 kt)u*pj l/f45 pdw 2xbvafn87$^{\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 12–1i5xr;zh4s xgsib5gg1s a+60d0 should the hole be that must be uncovered to p5 s54 d0g;+sgirisx bx1 ag6zhlay 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 resonata8wy .y(r6jfq0w6vv ) /:renp s7wy kje at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies inyp/wv6:( j r ne8y.)vjwfrqs7 k y0aw6 between. (a) Show why this is an open or a closed pipe. ----待选择----closedopen  (b) What is the fundamental frequency of this pipe?   Hz

  A uniform narrow tube 1.80 m long is open at both ends. It resonates at tc 6cii/l34ffjwe- 7 rj2kqrs/wo successive harmonics of frequencies 275 Hz and 3-r7f6iq2e/3ckjs i 4f/jwcl r30 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 zto(d ug3cjt z h,z38;$^{\circ} $ C is to be designed to produce two successive harmonics at 240 Hz and 280 Hz. How long must the pipe be, and is it open or closed?  ----待选择----closedopen  f =    m

  How many overtones are present within the audible range for a pm fr2m2 h*3rx5+w bi xum1-sl2.14-m-long organ pipe at 2-2mrw2prx5lmxs*h u13 mf+ ib0 $^{\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 outside fd.; )bvpwt-hv- ei7 63kneynand is closed at the other end by the eardrum. Estimate the frequencies (in the audible range) of the standing waves in the earn t. enb-)yph;vk vdf 6-37ewi canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjubw;lm 8q. c4gtst two strings, one of which is soundi ct8;bl4.qmw gng 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency i bf6)rvj -rmt1p8kt 5bvux6 8cf middle C (262 Hz) and $C^＃$ (277 Hz) are played together?    Hz What if each is played two octaves lower (each frequency reduced by a factor of 4)? $\approx$    Hz

  A certain dog whistle operates at 23.5 kHz, while another (;f+uy6alou s/8qk w)ebrand X) operates at an unknown frequency. If neither whistle can be heard by humans when played separately, but a shrill whine of frequency 5000 Hz occurs w)k/sfeq 8u;w yol6au+hen 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 tunin l7zbza.bup34g fork and 9 beats/s when sounded with a 355-Hz tuning fork. What is the vi .7 bl4zup3zabbrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The ten gevicju3 q:2zg*95 zxcvw4u 3sion in one str3g4jqi9ucu xv 53cve2*gwz: zing is then decreased by 2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if x( isv8r7j fc)jk+6lr two identical flutes each try to play middle C (262 Hz), but one is at 5.0°C and th)jk lrj +sr7 ixc8v(6fe other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning 4 9lo::m*apwfi .9a +atzmt. a5uuqkzforks, A, B, and C. Fork B has a frequency of 441 Hz; when A and B are sounded together, a b:l :a+a4 tt9m5a9u .*.pwaokfiuzq zmeat 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/x2o1fikl).qh 8 z0qlzvma8v6 qui0t n stands 3.00 m from one speaker and 3.50 m from the othei1fl h2 /ul0)v0q tkzqm6zo88.iax vqr.
(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 awhz;vo2y)1m/0g) swz3yv dmvm1r. ca t 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played together. (a) If ongmm/ v oysvc w)11aywd)hr. 2vz ;m0z3e 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 6 gcuhra st,-+umj62l9z(zzbbxk 9 0cand 2.76 m in air. How many beats per second will be heard? (Assumgm(+xbj6r u h-2 zs6uktl,cz0z99a bc e T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant freqow-y+xrh*4i (pev (dd uency of a certain fire engine’s siren is 1550 Hz when at rest. What frequency do you dethpr( voix(d yewd*4+-ect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detectvxhljwg 9)x20 if a fire engine whose siren emits at 1550 Hz 09 v)gh2xwjlx moves at a speed of 32 m/s
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in frequency if a 2000-Hz source is moving toward 4zjg1clx lb.5f2nk+7gg t,h d you at 15 m/s versus you moving toward it at 15 m/s Are the two lh1ck2 n7lggb5+fd ,t zjg.4xfrequencies exactly the same? Are they close? $f'_{source\,movine}$    Hz
$f'_{observe\,movine}$    Hz
(b) Repeat the calculation for 150 m/s and then again
$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz
(c) for 300 m/s What can you conclude about the asymmetry of the Doppler formulas?$f'_{source\,movine}$    $ \times10^{ 3}$Hz
$f'_{observer\,movine}$    $ \times10^{ 3}$Hz

  Two automobiles are equipped with the same single frequency horn. Whea q;a4jb.6 byyu68jm un one is at rest and the other is moving toward qya.;a6b8j4 6buyjumthe 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 = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHnua /5 +ecnt(uz and receives them returned from an object moving directly away f/ua5et+( c nnurom it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a wall at a speed of 5 m/s A+vt*utr x91p ktnsn5+s it flies, the bat emits an ultrasonic sound wave wit*n9++pn15sxrt tt u kvh 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 tw,cvu,1t z,p lrain 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 train car approached the station at a speed of 10pulw ,z v,tc,1 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood+oslvr/s2+hu+u :rrx -flow speeds. Suppose the device emits sound at 3.5 MHz, and / ++lor r+svh2:sxuruthe 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 ulyx+4.5 l -k62cjx * jemrwiznttrasonic 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. Wh djzwiri ;j+9g0v (fonwt5l5wm ,:m( sen the wind velocity is 12 m/s from the north, what fj9iiwwwzl(+(t5g0ov:d f rm ;,5njsmrequency 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 mj5t fe-rdtx z *04zjm-oving 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 smy+ to7wpze 98ound is 310 m/s (a) What is the angle the shock wave mak7+tm8w o9zp eyes with the direction of the airplane’s motion?    $^{\circ} $
(b) If the plane is flying at a height of 7100 m, how long after it is directly overhead will a person on the ground hear the shock wave? $\approx$    s (Round to the nearest integer)

  A space probe enters the thin atmosphere of a planet wbh1 7ix.( hujihere the speed of sound is only a1 (ixujhi b.7hbout 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/sx: p ot)u54pwe7ncd3v strikes the ocean. Determine the shock wave angle it produces3754nepx p:cowdt v)u
(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)5m vki/ hitc1/v yc:$/theta$ 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)akn* +(x x7e*plng0wtypdbkx+:na / km above the ground flying faster than the speed of sound. By the time you hear the sonic boom, the plane has traveled a horizontal distance of 2.0 km. See Fin*b*a+ypln pxe:wag kd7)k(x/ tx+ n0 g. 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 top 0gcz11q )e42reiw hhat sends 20,000-Hz sound pulses downward 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 betweqe o1 r1epc)z4w0g2ihen pulses (in fresh water)?    s

  Approximately how many octaves are ther,j;3 kmfesqe z t8uo;8e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display called a sewer pipe symphony.gqyd ks:i23x: It consists of many plastic pipes of varx23:sy : diqkgious 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 makd zu)2gcks+)c es a sound close to the threshold of human hearing (0 dB). Wsc)2c +zk)g duhat will be the sound level of 1000 such mosquitoes?    dB

  What is the resultant sound level when wb)+v2juot/onb ++av an 82-dB sound and an 87-dB sound are heard simultaneously t)b2jabo uv+/ +ovnw+?    dB

  The sound level 12.0 m from a loudspeaker, placed in the open, is 105 dB. e3ur 7ozkg46d2i:f+cqiydg6 What is the acoustic power output (W) of the speaker, assuming it ra i6+:dy qf3ci 4ggrozk6ued72diates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hz. The power output drops bog.eol :ou)+t um wulg40;m 4ky 10 dB at 15 kHz. What is the power outputm;4w.l+u g ) g utk0meuolo4o: in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over their ears.me h5dr 08w qn+s5 brl(p.*zdu Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 5es( wzp8r5dn*0u+bl h. dmrq140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotected ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systemwn )0x 9 3apzt80n dyu0lv2vzms, 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 fre7 m 4oghzghuh:38a;wlquency 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 fundamenta hh.evhjdhe)v7 v-f eu97 e+;zl freudezf.h j ;+ev7-h eeh)v97 vhquency of 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 set7ny3s hkfk9 lf;r (i-)5mj *z* zbbtzt into vibration 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 distfk9t7 ;hrzzyf *jnk bi(-s*5l b3m )ztance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube t6vh)ffpk dm*ro2spv c6(cx0bw : g6 z4hat is open at one end and also 75 cm long. gbkfs o c)6x40h6p vv:*2zm p(d 6wcfrHow much tension should be in the string if it is to produce resonance (in its fundamental mode) with the third harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonate 3k-/0xsuoc 0 alf4sk,arti z7as 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 od-p.phc .j-5g-yoxs 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 farther from one source than the other. ps5.y-codx- o hpj-g.What is the frequency of the sound?   Hz

  Two trains emit 424-Hp*9 td2 3dorltz whistles. One train is stationary. The conductor on the stati3td dp9tlr *2oonary train hears a 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 whis ) 4,lz+/c)bqkpe9fam mpif 1ktle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train movingfepmqz9if+la)1 , bkc4/p)m k (assume constant velocity)?    m/s

  At a race track, you c,jw+1 p rc,*rykpja2o an estimate the speed of cars just by listening to the difference in pitch of the engine noise between approaching and receding cars. Suppose the sound of a ceao*2yc pjr,jk+r1 pw ,rtain 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 tocj2cl k.ldtqx;di,04s n 6t4jgether, produce a beat frequency of 11 Hz. The shorter one is 2.40 m long. How long is thidjl2;l6x04,t c.jd4n cqks te other?    m

Two loudspeakers are at opposaeo,1*f+s tjidbat, 3 ( u2vrqite ends of a railroad car as it moves past 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 position A, in front of the car, (b) he is between the speakers, at B, ands u 2(vtte jq1diaboar3,*+,f (c) he hears the speakers after they have passed him, at C?

  If the velocity of blo 9.5q / otm8s j8ma2xkrz-udhrod flow in the aorta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultrasound waves were directed along the flow and reflected from the red blood cells? Assume that the waves tr.mt88/u j 5-r9rzx oqkh2 dmasavel 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; y3 o 9wx(uvvyhvux3 +jzac o-y2o7r) flying toward the bat at speed 5 mayovju; xrcyo+ u)v-3 z7 v2yx3hw9 (o/s The bat emits a sound wave of 51.35 kHz. What is the frequency of the wave detected by the bat after that wave reflects off the moth?    kHz

  A bat emits a series of high frequency sound pulses as it approd6t .6rsp1ls4 eegx8g aches a moth. The pulses are approximately 70.0t1g6.8s4pxg dle r6s e 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 emitted?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one.3(fv ov lkto. Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep skt o.fvlo v3.(ounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating. The most popular alpenhorn is about 3.4 m long, and it is called the F sharp (or G flat) horn. What is the fundamental frequency of this horn, and which overtone is close to F sharp? (See Table 12–3.) Model as an open tube.

  Room acoustics for stereo listening can be c(6lg v0cnj **0vqctb* 9 dhow,qu7 xvi7j9lppompromised 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 fundamev0wb70,*qlcjtv9g p9vqch 6( oxdlj**ni u7pntal frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, lvme; rs 10eliq4b89ocalled “singing rods,” involves a long, slender aluminum rod held in the hand near the rod’s midpoint. The rod is stroked with the other hand. With a little ps94 e0ml;vqi8r 1lboe ractice, 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 fog *6 dwv sl6r2.lxihd6r the human ear at a frequency of abldvx2i6*6s6 whrg ld.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 2e ntzph -0e;mqp:de;:.0. An observer on the ground hears the sonic boom 1.5 min after t m0:pd; e-zepq tnh;:ehe plane passes directly overhead. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboat is 67kapb8 )2hhvk w/3ya9uqmu c15 $^{\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