What is the evidence that sound travels a,ub (ksh d m6vghcd,1)s a wave?

What is the evidence that sound is a fji3pj- :49q0jvts+p ;x apagt orm of energy?

Children sometimes plast+(s(znid591. gkqg l a;hyv y with a homemade “telephone” by attaching a string to the bottoms of two paper cups. When the string is stretcs;dtals zv (.5 gi9hk1gnqy+( hed 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 yoa1rog1 (wv kvi/ )4wktu expect the frequency or wavelengtvw/1 k14tgwkv r(i)a oh to change?

What evidence can you give that the speed of sound in airokjtpd9 qxos-t vtu *3*+u2fpul :r// does not depend significantl/tdfs+utpk:rqv3 ot u*o9j2lp*xu/- y on frequency?

The voice of a person who has inhaled helium sounds very high-pitcvt3 z 5sm+usz:hed. Why?

How will the air temperature in a room affe3qhvu; l-- rfr0ui nn(ct the pitch of organ pipes?

Explain how a tube might be 6-qncqd i-fi* used as a filter to reduce the amplitude of sounds in various frequency ranges. (An example is aq-cn-fd6 iqi * car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togethef,gz*ql6)n q xr as you move up the fingerboard towardnf*g,l q6x) qz the bridge?

A noisy truck approaches you from behind ej/5bosejt 5 20 ewmh8nydp0.a building. Initially you hear it but cannotwedy.2ne/505pjt o m0 8ehjbs 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 diffraction.]

Standing waves can be said to be due to “interference in space,” whereas *8ok,y q2u26g8tom vh1 bgb wrbeats can be said to krgg8 1,8b6vt w2mohb*q2u oybe due to “interference in time.” Explain.

In Fig. 12–16, if the frequencei9)f6eaka s k9bs,a/y of the speakers were lowered, would the points D and C (whibs/aek,esa9 ka)6f 9ere destructive and constructive interference occur) move farther apart or closer together?

Traditional methods of protecting the g*( y*pyby*dphearing of people who work in areas with very high noise levels have consisted mainly of efforts to block or reduce n*gy(yb *p ypd*oise levels. With a relatively new technology, headphones are worn that do not block the ambient noise. Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12ndu- ,84oqt qt–31. Each wave can be thought of as a superposition of two sou n8t-uqq4t,odnd waves with slightly different frequencies, as in Fig. 12–18. In which of the waves, (a) or (b), are the two component frequencies farther apart? Explain.
(12-31)
(12-18)

Is there a Doppler shift if the source and observer move in the same direz vww2*2:q0;fe tr5ifnz+nuu ction, with the same velociwv w ufre nfzi zqn+5tu;0:22*ty? Explain.

If a wind is blowing, w da4zzd5vsb9qca()g apb, *iajnu/*/ill this alter the frequency of the sound heard by a person at rest with respect to the source? Is the wavelebaz b)g/q* ,5jzdu v/p9da4iac*ans (ngth or velocity changed?

Figure 12–32 shows variouoe*1iyd6m.5hegtzr 8i 5y io1 s positions 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 heaiy1* 51g rt oe.mho5dzei68i yr the highest frequency for the sound of the whistle? Explain your reasoning.

  A hiker determines the length of a lake by lq m yvnoc00y8*xn8s6y istening for the echo of her shout reflected by a qo sx80cyy80 mny*nv6 cliff at the far end of the lake. She hears the echo 2.0 s after shouting. Estimate the length of the lake. $\approx$    $ \times10^{ 2}$m

  A sailor strikes the si2 +1bxmi i /gwdxox:ehk8kr:*de of his ship just below the waterline. He hears the echo of the sound reflected from the ocean floor directly below 2.5 s later. How deep is the ocean at this point? Assume the speed of sound in seawater is 1560 m/s (Table 12–xw1:brh iei d:2g/xm8kok *+x1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air at 8 sylpe gkhgc-y::jlawye e3 6, a:8h820 $^{\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 foggy9 nr(h e5;e,6 khec3xy/ :jek;z pbgly day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). How much time elapses before the backfireelnxhe ;c,y/g5k9zj 3ke hy;:rp6b (e is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from the top of a cliff. The splash fw hg)k0,- dg.ssngctq;:6v u it makes when striking the water below is heard 3.5 s later. How hig-hgq. 0wut:cnsv)k6d,f; gsgh is the cliff?    m

  A person, with his ear to the x xf69 3+fk ik- bq;auohw(8ydground, sees a huge stone strike the concrete pavement. A moment later two sounds are heard from the impact: one travels in the air and the other in the concrete, and they are 1.1 s apart. How far away did the i i3(-yxukbwa;6x k o+ffq8dh9 mpact occur? See Table 12–1.$\approx$    $ \times10^{2 }$m

  Calculate the percent error made over one mile of distance by the “5-second r2 mrf,pmm 6c+mu +z:0ir;c*ugyd9yqz ule” for esti+ dy zgmqciz;uc*290mmpf6: y+mr, urmating the distance from a lightning strike if the temperature is (a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sourw7s9bcw 83djj :z,y/yc 1g-irp h5ound at the 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 whose intensity is q:( u4xrx)i /up3wj8:/;uk yar ezg tj$2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 nx, g - j-:fvis3s.rtkdB when fired simultaneously at a certain place, what will b.sjnsg,rx3tk-i - fv:e the sound level if only one is exploded? [Hint: Add intensities, not dB’s.]    dB

  A person standing a certain distance from an airplane with four equallyofb6,u; i8zb6qyo) nx ho0l7e noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level would this person experie66bxeol)ho uf,;qy n8i70 boznce if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of 58 dBx5x e32)a i aijgwfu,7, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for eachgiux,awf) 5ei32 7jxa device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound from a person speaking in .pu 8e;glf) y* w8 gvfzgtd9,nnormal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly over a sphere centered on the mouth.d )zf8guf e,g;g*y pvnt.9w8 l $\approx$    $ \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 btdl5z9/is+/l k9poe eardrum whose area is $5 \times10^{ -5} m^2$ (a) How much energy is absorbed by the eardrum per second?    $ \times10^{-12}$W (b) At this rate, how long would it take your eardrum to receive a total energy of 1.0 J?   $ \times10^{ 3}$yr

  Expensive amplifier A is rated at 250 W, while tht 0: bha**.sbrk+vw pte more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibel.+:b t0k*trb*wahvs ps 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 when placed 2.8 m in frol4 lf;9 .ha0u p16vgelq hzh7int of a loudspeak.z0ig 9vf1pa4;hqllhl7uh e 6er on the stage.
(a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?$\approx$    $ \times10^{2 }$W(“Round to one decimal place)
(b) How far away would the sound level be a somewhat reasonable 90 dB?   $ \times10^{2}$m

  Human beings can typically detect a difference in 8:i ny .uv1knrevs,1ssound level of 2.0 dB. What is the ratio of the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 1.: y,ks81inuresnv1v1–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor wqj oqlh+. ,d9anzt(,sill the intensity increase? Increaseq9,j (,tzqd. oh+n lsa by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equad:hs92yi)i q tl displacement amplitudes, but one has twice the frequency of the other:hs di2t yiq)9. What is the ratio of their intensities?   

  What would be the sound level (in dB) of a sound wave in air that corresponds ca f;2axno a2 5s,g5kqto a displaceme 5 2a,x ck;2ngofaq5asnt amplitude of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have whatcg(7 m yk6)knzdz).gw sound level to seem as loud as a 100-Hz tone that has a 50-dB sound level? )6n(cgz7g y dk.mkwz)(See Fig. 12–6.)    dB

What are the lowest and highest frequencies that an ear can detect s;bz/ v8sb + anhd/j)dwhen the sound level is 30 dB? (Se/n+8sd ;b av/ j)sdhbze Fig. 12–6.)

  Your auditory system can accommodate a huge range of)zmzyf )p3tz88ib;vy9p z be/ sound levels. What is the r y i) zmfpz/p8v ;83etbbyzz9)atio of highest to lowest 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 frequency of 440 Hzmh: c+4 opw(ysuoa, ,w. The length of the vibwcu oowap,hs y(+ m:,4rating portion 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 fundamental and firstdlowl8ldsz; 8l/; -yh three audible overtones if the pipe id 8loy-lh;d;ll/ w8 szs
(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 frequeq5zt ,8obthq1ncy would you expect from blowing across the top of an empty soda bottle that is 18 cm deep, if,qhqtb 5 8ot1z 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 hugyh34 y26bsww man hearing (20 Hz to 20 kHz), what would be the range of t gbw4h63 2swyyhe lengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a ujc 0h8fl l-v9frequency of 540 Hz as its third harmonic. What will be its fundamental frequency if it is fingered at a length of only 60% of its original lengc 8juh9vll0 f-th?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E abb c+ebfdbyo n0,5b 1.)sj+ ljaove middle C (330 Hz).b5)cbdo+sjyl a, b.0j+fb1 n e
(a) How far from the end of this string must the finger be placed to play A above middle C (440 Hz)?$\approx$    m
(b) What is the wavelength on the string of this 440-Hz wave? $\approx$    m
(c) What are the frequency and wavelength of the sound wave produced in air at 20°C by this fingered string?    Hz    m

  (a) Determine the length of an open organ pipe that emits middbs*cf6a ) xzegz1z2(/i/ ya6la4r :l w,oq dqmle C (262 Hz) when the qaxe rf41zqz6/ z blwdla :)o*s,amy 2gc/i(6temperature 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,+8 j )q.3ldt wohmfto $^{\circ} $ C. By what percent will the frequency be off at 5.0 $^{\circ} $ C?    %

  How far from the mouthpiece of 0, 6 3zj 4alhv:jgkysgthe flute in Example 12–10 should the hole be that must z,4 :gs3kvlyah0 g6jj 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/hxct,ddn k;d;a*+nje d *rz ( can resonate at 264 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in between. (a) Show whycj;dad et+(hd xdrn, *n/ *zk; 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 a5 ub5b ijx*f2ip cy9z5t two successive harmonics of frequencies 27x95*ii upz bcj 5f5by25 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 e5uv3 . 8eoqm+wv) +(ss uh ammc/kj.4i b8iiw$^{\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 witg6(jo9oea q k)hin the audible range for a 2.14-m-long organ pipe at 9( g)6jkeoaq o20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is v9r:im- j8j8s)eig)6wsai yr approximately 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. Wh)jw8sag-yies v mr9:i6ijr8)at is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when trying to adjust two stringmqd00 sumqr3 5ipy;w)mo4 dt2s, one of which is ) m 2yi0;5sdqp340ruqmwo t mdsounding 440 Hz. How far off in frequency is the other string? ±    Hz

  What is the beat frequency if middle C (262 Hz) a(m8 ly2 ison 3-1xxkkfnd $C^＃$ (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, buj:e * (k6 /+xcbzz+vxc e:f 7ced4fqwhile another (brand 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 occ6zxq(cz:jx 74cu/bf*fdeev:k+ ceb+ urs when they are played simultaneously, estimate the operating frequency of brand X.    kHz

  A guitar string produces 4 beats/s when soundedxe5m( amb0m*n with a 350-Hz tuning fork and 9 beats/s when sounded with a 355-Hz tuni(*mx 0mb5 nmaeng fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same7r+; ij0m7fstiyyg.uz9j re 2 frequency, 294 Hz. The tension in one string is then decreased by 2.0%. What will i0 i.j f77t jsgre+r 2yy;zmu9be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to play middle C (6ngii p z30b4b262 Hz)gp0n6zib b4 i3, but one is at 5.0°C and the other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuning forks, A, B, and C0m( d g),n 7xscshjxhs6 p7-pn9 pebb-. 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 possib7s,-6cm9)jhbgne(snhp 07dpx-b ps xle 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 *nnq86tbac.vh0u n3no; 0znd h(q; lw m apart. A person stands 3.00 m from one speaker and 3.50 m from8v *du(0nnc .nat0wq bh; ;nqo36 zhln the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibrating at 132 Hz, but a piano tunerr87gwb1s5t f fd6 e xyb864plw yfgv4: hears three beats every 2.0 s when they are played together. (a) If one is vibrating at 132 Hz, what6y644x:fwtg8dfy sb rgf85v1p l7bw e 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 aiq mrgh 2,hij-n0mcd gj 0tz6g+t,8hng6n :)zir. How many beats per second will be heag-ngi g60dr6tz8)jh 2gimqhnh t,:mj,n 0zc +rd? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency of a certain fire engine’s f-k.sfge.nl wg u2-j4 siren is 1550 Hz when at rest. What frequency e f-.kl2 .wgusf4g j-ndo you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What frequency do you detect if yf--dbi;; ta5kh x l+ga fire engine whose siren emits at 1550 Hz moves at a speed of 32 m/s fty;a-+xhgk5; lbid -
(a) toward you,    Hz
(b) away from you?   Hz

  (a) Compare the shift in freque:nh b 7i+ l9/;qxnxgbnncy if a 2000-Hz source is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactq/x:i+nxbhg b l9 nn7;ly 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. When onxq3e swe;z5zq,j4el3 e 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. What3,jeqzx;e q3w s5 e4zl is the frequency the horns emit? Assume T = 20 $^{\circ} $C    Hz

  A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives tmyzq91a3 ab yjrks;k8m0 9q*57 bzhwihem returned from an object moving directly away fro jmb8sma5 *iz y;y3 9q9hq0kkwa71 rbzm 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 As it flies, h3r9a/j) /2up a iaokfthe bat emits an ultrap/aifa )/kor3u 2 ajh9sonic 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 experimentap*ttq 3 ddibxb6it6 1) :te6ss, a tuba was played on a moving flat train car at a frequency of 75 Hz, and a second identical tuba played the same to)ap tsd*:ib6i d b6e6t3xt1tqne while at rest in the railway station. What beat frequency was heard if the train car approached the station at a speed of 10 m/s ?   Hz

  A Doppler flow meter uses ultu7b, a1i cn;e*vg: fdsrasound waves to measure 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 ibncf;1ue:, d av*gs7 flowing in large leg arteries at 2 cm/s directly away from the sound source?   Hz

  The Doppler effect using ultraso 0yqx4oz/ 4ioefl0k+s nic 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 sou,(t5au)dmo)idf nka -nd of frequency 570 Hz. When the wind velocity is 12 m/s from the noida)o k( 5t u-,and)mfrth, what frequency will observers hear who are located, at rest,
(a) due north,   Hz
(b) due south,   Hz
(c) due east,    Hz
(d) due west, of the whistle? What frequency is heard by a cyclist heading    Hz
(e) north    Hz
(f) west, toward the whistle at 15 m/s?   Hz
Assume T = 20 $^{\circ} $C

  How fast is an object moving on land if its speed at0xo -4 ilpxb0j 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 i0oz ,;le 46akg( k,ut9fsxfx 8kkiq(sound is 310 m/s (a) What is the angle the shock wave makes w4t qa 8,6 xgukk xk;i0,z(fofk(li9esith 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 whe)num- 1n5exb hre the speed of sound is only about h51mnn)e-bx u35 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. +/pvjaj54h+ai) sank20dc v uDetermine the shock wave angle it prod0v )v5+u ps4jadjkan +hai/c2uces
(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 ha3r;0tvf:p1 osy, jenz*sfce1 2 d8v$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead andv.s3:0(107 v(rw my vefcbf ydiv l3zz see a plane exactly 1.5 km above the ground flying faster than the speed3 lc(i( zfwvym s de30fvyzr1 b.v:0v7 of sound. By the time 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 sotcar1 .jg kqj2(00npjnar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and then detects echoes. If the maxr1jn .q2(pj00tgjcakimum 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 w7a4r0 t*z)e dowri plc :;(aloctaves are there in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has*b : k0nnd(4i3imzrs: dqp4u v a display called a sewer pipe symphony. It consists of many plastic pipes of var srn:(*ivkni4q4pb 3dd0 mzu :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 thresholdhmzop93xra6 .: h uh7h of human hearing (0 dB). What will be the sound level of 1000 such mosquitoxoa7rzh up .h 9h:6m3hes?    dB

  What is the resultant sound level when an 82-dB sound and ajavbf6+*ez xe b3 jw6qme)27tn 87-dB sound are heard simultaneousjza m6t x27e)ev6w bjqf*be3+ ly?    dB

  The sound level 12.0 m from a louds6seq 01+ n0 k+k m pk(k)qlz(3wj9xlecyhl8cbpeaker, placed in the open, is 105 dB. What is the acoustic poksn9l(h 6qzy380k1xk )c0++bq(m jec l k lwepwer output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at 1000 Hzulwjbl 4 a04q 0+o2rcn. The power output drops by 10 dB at 15 kHz. What is the power output in l0a2j4o n04cwlbru+qwatts at 15 kHz?    dB

  Workers around jet aircraft typically wear protectivjeisa) 3t2un vi u6i6d:8 8ruhe devices over their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, and that the average human ear has an effective radius of 2.0 cm. What would be the power intercepted by an unprotect8 8iuu3r:h e tj 6ais2ui)dv6ned ear at a distance of 30 m from a jet airplane engine?    W

  In audio and communications systems, tsx*aoay qz:k qo2+y *)he 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 frequer i+)a9e0pseri+d 6 hincy 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 322 6m(aj3 jwgz(*yuk+h* ruloi cm long between fixed points with a fundamental frequenc uy*g+6rh zi jua2* j3(owk(mly 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 set into vibration above a verticv2b*k5vzf6ffbdb :jj3u6lk vnfr z +r4-*+ibal 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 abover:bbi36ff6+*zfnujk- fv d v5k*r4vz+ b2jlb the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is near a tube thatnz/lmykl6irf .s;0z*o8g 9y z is open at one end ayny06ols9 f;zk.g z8rmlz / *ind 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 harmonic in the tube?    $ \times10^{ 2}$ N

A highway overpass was observed to resonat 7 8+vf9i0/vqt7qajq fcc g/odiust /+ 5mltw2e 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 ranq9ts-, ydg1r yp n+rnmh2d:u4ge coming from two sources. The sound is lod12m+,nu: g rrhysdq-ny t 49pudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that the sound level is minimal at a point 0.34 m farther from one source than the other. What is the frequency of the sound?   Hz

  Two trains emit 424-Hz whistles. One train is stationary. zkdtg) +t5k /6 kk : db.vtyam+3.veweThe conductor on the stationary train hears a 3.0-Hz beat frequency when the other train approaches. What is the spzvgd: .w5/a beek63tt+).m+ kdtkykv eed of the moving train?   m/s

  The frequency of a steam train whistle as it appro a ar3r7cv he7* rlj*1n)18.*mzpubtt5tbehv aches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moanb*v8 *veaz7htu3l prttr )r5m.ejhc 1b*17ving (assume constant velocity)?    m/s

  At a race track, you can estov0w9 .e9owgryl yilh36t; 6y imate the speed of cars just by listening to the difference in pitch of the engine noise between approaching an; wy6 o olvtr.hiyyl3w6e99g0d 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 beat frequency of 11 ib6 elzufl/a6 p0pq;.Hz. The shorter one is 2.fuzalbe q;6 p6l./ip040 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad0 wqq6-t.jxqi2 pft s9ym-*g: xt fs/m car as it moves past a stationarmgq62yi0x tmf/qs q-f-x:stw. * 9tpjy 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, and (c) he hears the speakers after they have passed him, at C?

  If the velocity of blood flow in the aorta is norm1-v;li 3zpi84r gv biially about 0.32 m/s what beat frequency would you expect if 5.50-MHz ultribi 4vpg -1ilrizv3;8asound waves were directed along the flow and reflected from the red blood cells? Assume that the waves travel with a speed of $1.54 \times10^{3 }$ m/s   $ \times10^{3 }$Hz

  A bat flies toward a moth at speed 6.5 m/s while the moth is glpw(m,1u2lz flying toward the bat at speed 5 ml ,2 mgu(wlz1p/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 approaches a moth. Th: +xvc.+rmlq ne pulses v qlr:x.+ mc+nare 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 emitted?    m

The “alpenhorn” (Fig. 12–38) wpf7;z)ru e3f;;p n*cm tajq3was once used to send signals from one Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to create deep sounds. When played as a musical instrument, the alpenhorn must be blown in such a way that only one of the overtones is resonating.ef cqt fu;wp7 ;z)j3*ap3mnr; 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 compromise3qhh)7f7 6czkgf .sau1xem*j d by the presence of standing waves, which can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a safjg16fe7x.*h u)hmk cqz7 3living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, slei9nyh+ evj uq8ij/l- (nder aluminum rod held in the hand near the rod’s midpoint. Tinji8e/lvyq+ju(9 - hhe 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 ar 1;agmmp 5b0ez33dgk frequency of about 1000 Hz gprme1dm3 ; k3gzab5 0is $I_0$ = $1 \times10^{12 } W / m^2$ 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 thex4 nq-k (nhu9svmth- / ground hears the sonic boom 1.5 min after the plane passes directly overhead. What is the plane’s altih n(ks mh-tv-4qn/ xu9tude?    $ \times10^{4 }$ m

  The wake of a speedboat a:o 0ose,z (clis 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