What is the evidence that sound travels as a wa,,u vda, /cjhuve?

What is the evidence that sound is a form of en2x/yv f ybs6 4t6bgjjq7hx/6 cergy?

Children sometimes play with a homemade “telephone” by attachsrkt33i bu v6/ing a string to the bottoms of two paper cups. When the string is stretchs3buvt/ ir63 ked 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 frnz03 e37mrhz lequency or waveleng3zmnl 7ez0r3h th to change?

What evidence can you give tha(jkj av2t1rs*(j,gopg5f m /et the speed of sound in air does not depend significantly on f(( 1o/r2*et jgv apmjg5sj k,frequency?

The voice of a person who has invp/widf3gm- ws+t t7k:gk c4+haled helium sounds very high-pitched. Why?

How will the air temperature in a room aff r2q;;auz -)ob gfmb3qect the pitch of organ pipes?

Explain how a tube might be used as a filter to reduce the amplitude xl 8px-lnrka,0b e8f b v2j,/uof sounds in varioex 0,uxbj fnl kp,blra-v882/us frequency ranges. (An example is a car muffler.)

Why are the frets on a guitar (Fig. 12–30) spaced closer togetwt.z2akf:7kmtmguf +: ieczzg 7+kgm+8.pe7her as you move up the fingerboard toward++k+zgmft2zcm i. 8 gk7:.t7 e7:ewfukgm zpa the bridge?

A noisy truck approaches you from behind a building. Inh4r mi z0y93j j.,e x-gzljxa3itially you hear it but cannot see it. Whenji .ghyr zx 39jej 0zm,a43x-l 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 dh. 4 k+;l bef;mi/sblfue to “interference in space,” whereas beats can be said to be due to “interference k.hels mbi4l ;;+/ffbin time.” Explain.

In Fig. 12–16, if the frequency of the speakers were lowered, would thlb x.cwyc x83z/ h;rw1b;hez 9e points D and C (where destructive and cons91w zcbrlz/ebxh3 h;yx c .w;8tructive interference occur) move farther apart or closer together?

Traditional methods of protecting the hearing of peof pbtpeg e7277vy qr )de36j+ople who work 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. d7p)7ovprjt7y 2ef 3egb+6qe Instead, a device is used which detects the noise, inverts it electronically, then feeds it to the headphones in addition to the ambient noise. How could adding more noise reduce the sound levels reaching the ears?

Consider the two waves shown in Fig. 12–.il*qz5l/rjukrk q;:31. Each wave can be thought of as a superposition of two sound waves with slightly different frequencies, as in Fig. 12–18 lq uqr.z/lk:i*5 ;jkr. 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 zkj)usvh18 v/jhf u5qy27y/9hm n z7rthe same direction, with the same velocity? Explain.h/7h 7mukjsz1n)8yq rj5vv hu/ f2y9z

If a wind is blowing, will this alter th8 44 dq/5w6p(to5e 5pe hb bxff*y)o;xvibcnne frequency of the sound heard by a person at rest with respect to the s *(454b ;p eefhq5c5p yxndvtbof)6wbo8i /xnource? Is the wavelength or velocity changed?

Figure 12–32 shows various positions of a 7s6 xjtz k hz4av4rucwz:( 8t-child in motion on a swing. A monitor is blowing a whistle in front of the child on the ground. At which position, A through E, will the child hear the highest frequency for the sound of the whistle? Explain your ret 84t:h( u7zsavj -zkzcw6rx4asoning.

  A hiker determines the length of a lake by listening for the echom*r arm(tlye1 g) kj-t.e;l1s of her shout reflected by a cliff at the far end of the lake. She lmy t)lrj1r;-( mke.gtsa1 e*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 jusv5m jb1ts.mpm. lke3 5t 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 sesb. tmmm.3l155p e vkjawater is 1560 m/s (Table 12–1) and does not vary significantly with depth.    $ \times10^{ 3}$m

  (a) Calculate the wavelengths in air athw7p a l/9d-kr 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 s -04lo/zwe7:5 bf8 yn cibzojqchool of tuna on a foggy day. Without warning, an engine backfire occurs on another boat 1.0 km away (Fig. 12–33). Hlbczyoo70i /b-:zj8en4w qf5 ow much time elapses before the backfire is heard (a) by the fish,    s (b) by the fishermen?    s

  A stone is dropped from 8btah0t2cc a) the top of a cliff. The splash it makes when striking the water below is heard 3ta2ac0)c b8ht .5 s later. How high is the cliff?    m

  A person, with his ear to the ground, sees0y xv0 dkdo c:7(anysd(/l;oa a huge stone strike the concrete pavement.y y ((adxs0:d7od v0ka nclo/; 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 of distanx4he9mv9gd zm)t g3b 3ce by the “5-second rule” for estimating the distance from a lightning strike if the temperature is xg)3v e34bdtmhm g 9z9(a) 30 $^{\circ} $ C, $\approx$    % (b) 10 $^{\circ} $ C$\approx$    %.

  What is the intensity of a sound at g(oq3hnss ;x prao cel:*la0/l9+lv+ 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 c5ftes-- 6tqlis $2 \times10^{ -6}W/m^2$?    dB

  If two firecrackers produce a sound level of 95 dB when fired simultaneously ataet6-tczt* (;l9a zjzzcj r 4: a certain place, what will be the sound level if only one is exploded? [Hint: Add j :-;t *z6l4tr9tzacaj c (ezzintensities, not dB’s.]    dB

  A person standing a certain distance from an airplane wit))yimpqworl- e9 5 xc,h four equally noisy jet engines is experiencing a sound level bordering on pain, 120 dB. What sound level c )eplr,q)5-yiowx9mwould this person experience if the captain shut down all but one engine? [Hint: Add intensities, not dB’s.]    dB

  A cassette player is said to have a signal-to-noise ratio of q4ntl. .xa h*j +.m gn6amydts5 p;f)f58 dB, whereas for a CD player it is 95 dB. What is the ratio of intensities of the signal and the background noise for. .5+ p)qt. f6fnmya4sxnd lhtam *gj; each device? 58 dB =    $ \times10^{ 5}$ dB =    $ \times10^{9 }$

  (a) Estimate the power output of sound frxe 4)96s xggx 3eqsxfl:fa0d)om a person speaking in normal conversation. Use Table 12–2. Assume the sound spreads roughly uniformly overef0 xf 3e) g)x6qaxd:lssx9 g4 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 e geqw 98xal 0ln4jb)p)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 1 fgirc*a+;i wis rated at 250 W, while the more modest amplifier B is rated at 40 W. (a) Estimate the sound level in decibels you would expect at a point 3.5 m from a loudspeaker connected in turn to each amp.a +ifc gr*;wi1$I_{250}$ =    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/ky(bczs2* l p 2.8 m in front of a loudspeaker on the stage. b(*csz2l k/yp
(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 difft*++y npaihnm:3em +q erence in sound level of 2.0 dB. What is the ratio ynn:++mq 3am he*pt+iof the amplitudes of two sounds whose levels differ by this amount? [Hint: See Section 11–9.]$\approx$   

  If the amplitude of a sound wave is tripled, (a) by what factor will the inteim )f d65 *zlf.r2fmr/10yv tkf.k ogjnsity0/rfj l)y.r1if6k5td.m*okz2v fgf m increase? Increase by a factor of    (b) By how many dB will the sound level increase?    dB

  Two sound waves have equal displacement amplitudes, but one has twnh::86f n: wq irtzcqt4t. 4rtice the frequency of the other. What is the ratio of their intensit zrrntn4:ittq h.w:qt84f:6cies?   

  What would be the sound l8 sg)jnn+ jy))5dxaa*efi+clha t( 9tevel (in dB) of a sound wave in air that corresponds to a displacement amplituaj)ft)8ja +n)setgia d *9+ (lhn5yxcde of vibrating air molecules of 0.13 mm at 300 Hz?    dB

  A 6000-Hz tone must have what sound level to s*o3ok1y abdk3jfg1l *mek0 j+ eem as loud as a 100-Hz tone that has a 50-dB sound level? (See Fig. 120o1kodbya*e13gm+k* f3 jlk j–6.)    dB

What are the lowest and highest frequ-gd9ua.u(xp w encies that an ear can detect when the sound level is 30 dB? (See Fig. 12–pduwg9-( axu.6.)

  Your auditory system can accommodate a hugezu8 pu 7 k*nqia(nu/ +jz8n5 :fuh(j9f-bgvnb range of sound levels. What is the rat a9-knh8n(guf ji7p/nb 5jz +u * f(nbq8u:vzuio 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 Hz. The length of t. ok92sn q8fl3il5hiozwm4q0* 7nwu bhe vibrating portion is 32 cm, and it has a maf hz.o7kio9 wlui2n8l5*m4sb03qw qn ss of 0.35 g. Under what tension must the string be placed?    N

  An organ pipe is 112 cm long. What are the fundamental and4qo f7cw9.f1hg5hc7 3,rk zn3lfvt dh first three audible overtones if the pipe is z hc9rhh3f 5.w4d3tg locqv7,17kffn
(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 blowing across ;w7u:hmv.jc8or 1 b q;vstrm6 the top of an empty soda bottle that is 18 m:owr v 1mutjh;6qs.8r; 7cbvcm 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 buildz7 sbrh5lek);3hiw 7gotewj+.c- dx . a pipe organ with open-tube pipes spanning the range of human hearing (20 Hz to 20 kHz), what would be the range of the l7s+g webo;.5k hw xr )7eh.cl3 tjz-idengths of pipes required? $L_{20 Hz}$ =    m $L_{20 kHz}$ =    $ \times10^{ -3}$m

  A tight guitar string has a frequency of 540 Hz as itsi,c 8 w0cn1rdr third harmonic. What will be itsir dcrwnc0, 18 fundamental frequency if it is fingered at a length of only 60% of its original length?   Hz

  An unfingered guitar string is 0.73 m long and is tuned to play E e+ p7f)gtvc. babove middle C (330 Hz). gcb .e)f7pvt+
(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 midddm bvsse o+3 /kwk 8i899ohd71hz 0il bn82vwcle C (262 Hz) when the tbn2disv81scbe+wdv h9woo89 miz0 lk8kh73 /emperature 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 2 h(qju2 z ,zubg8bo1;zg+h6fk0 $^{\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 yw thh9f9k g5 d*e1x l2sae;;whole be that must be uncovered to plays gwlwt2e 5 91efk*x;d;yhah9 D above middle C at 294 Hz?    m

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

  A particular organ pipe can resonate at 26 2mfulxd+m1eb kq ci(a8 /ww,:4 Hz, 440 Hz, and 616 Hz, but not at any other frequencies in betwe/,e8d m ikm:1wq2fw a(uxcbl +en. (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 9 x+p;gn*m7igh dz6 nb7 ruoa0is open at both ends. It resonates at two successive harmonics of frequencies 275 Hz anda7dhig xnzg6 nrup*+709omb; 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 v/osks7jzi1ippc +0d- :rf*b$^{\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 pres .h;rvozty47x ent within the audible range for a 2.14-m-long organ pipet7;xhroy. 4zv at 20 $^{\circ} $ C
(a) if it is open,   
(b) if it is closed?   

  The human ear canal is approxjdhv, 531fz(6mhbsp 5sm1 m i8 r3iihcimately 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 standingi 31m5bisc,zm fh6hh(m i1jr p5 ds38v waves in the ear canal. What is the relationship of your answer to the information in the graph of Fig. 12–6? $f_1$ =    Hz $f_3$ =    Hz $f_5$ =    Hz

  A piano tuner hears one beat every 2.0 s when tryinkqvtwt8 ambh9w qkho6x 0./, (g to adjust two strings, one of which is sounding 440 Hz. How far off in fhq k.o(bk/98t 60av,m hwqx twrequency is the other string? ±    Hz

  What is the beat frequency if middled6qe;a90 ikp.e9 msuj 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 23oh:a60sl suf4.5 kHz, while 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 occurs when they are played simultaneously, estimate the operating frequency60sf hsu4al :o of brand X.    kHz

  A guitar string produces 4 beats/s when sounded with a 350-Hz tuning fork and 9 0.c u w+awwue8beats/s when sounded with cw80ewwuua .+ a 355-Hz tuning fork. What is the vibrational frequency of the string? Explain your reasoning.    Hz

  Two violin strings are tuned to the same frequency, 294 Hz. The tensionn pxpw-.m 40r)h;ebew in one string is then decreased by .hreemxn40;p- )b p ww2.0%. What will be the beat frequency heard when the two strings are played together? [Hint: Recall Eq. 11–13.]    Hz

  How many beats will be heard if two identical flutes each try to pq5ftn;v fobwo -)x/6zlay middle C (262 Hz), but one is at 5.0°C and tht z-fn o)o5fbxq6w/v;e other at 25.0 $^{\circ} $ C?    beats/sec

  You have three tuninzac9owjr 3)ho.85g uggd)if: g 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 arec.uga )ohwf8izgj g: 39r5o) d 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 person stands 3.00 m from one speoytnx . jc8 5;zn9iii3aker and 3.50 t3i5.xcinyoij 9 z8;n m from the other.
(a) What is the lowest frequency at which destructive interference will occur at this point? f =    Hz
(b) Calculate two other frequencies that also result in destructive interference at this point (give the next two highest). Let T = 20 $^{\circ} $C $\approx$    Hz $\approx$    Hz

  Two piano strings are supposed to be vibratpo.b41v d2ic et, yd9ding at 132 Hz, but a piano tuner hears three beats every 2.0 s when they are played togd ivc.p1 24ode ,d9ytbether. (a) If one is vibrating at 132 Hz, what must be the frequency of the other ?   Hz    Hz
(b) By how much (in percent) must the tension be increased or decreased to bring them in tune?   % increase    %decrease

  A source emits sound of wavelengths 2.64 m and 2.76 m in airm3.xbp,1lg8ft q eule /79llc. How many beats per second wiexbgl c8ltq7p ,/ll3.u 9fm e1ll be heard? (Assume T = 20 $^{\circ} $C)$\approx$    Hz(round to one decimal place)

  The predominant frequency )-. 8oqow ofobcsnuwj/u* (u7of a certain fire engine’s siren is 1550 Hz when at rest. What fr o /nu.fbwcou7js o *-uo(wq8)equency do you detect if you move with a speed of 30 m/s
(a) toward the fire engine,    Hz
(b) away from it?   Hz

  You are standing still. What fsm8/ m a* 3pju3mekpz(xr b.r.requency do you detect if a fire engine whose siren emits at 1550 Hz mov3.epzm jxa*bp/ 83mmr(s kr.ues 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 s wiv/6* 7vvv jr3g-nhqource is moving toward you at 15 m/s versus you moving toward it at 15 m/s Are the two frequencies exactly the samev3v 7n-iqg/vh* j6rwv? 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 freq1i o qssy+6*syuency horn. When one is at rest and the other is moving toward the first at 15 m/s the driver at rest hssiq o1+*y s6years 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 kHz2* 1nz 8isfukk and receives them returned from an object moving directly awaks 2if18kzun *y from it at 25 m/s What is the received sound frequency?    $ \times10^{ 4}$ Hz

  A bat flies toward a3; osuqsuc; /w wall at a speed of 5 m/s As it flies, the bat emits an ultrasonic sound wave;su su3q/ w;oc with frequency 30.0 kHz. What frequency does the bat hear in the reflected wave?    $ \times10^{4}$ Hz

  In one of the original Doppler experiments, a tuba was played on a moving flat tryl:y e *+pv5orain car at a frequency of 75 Hz, and a second identical 5 *l+yvoyp :retuba 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 10 m/s ?   Hz

  A Doppler flow meter uses ultrasound waves to measure blood-flow sp9 x(6xix; av3oc f:mlbeeds. 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 in large leg arteries at 2 cm/s directly away from the souc x b(a:6xxim vfl39;ond source?   Hz

  The Doppler effect using /zzve1 aee h8v/8v+ z(pibqy 7 j,rf)iultrasonic 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. Whe +f6s d0q bfgawqi bi;(d-5yx.n the wind velocity is 12 m/s fra-5dx; bff0qwd6igb+y. qi( som the north, 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 spe0xq/o m,a /mwscvq)b .ed 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 z q49k27yr s,uf.lbeyiy8x rq-j-b 5pthe speed of sound is 310 m/s (a) What is the angle the shock wave makes with 5, 4j-qb.er82q7 pubyzyf xl9k rsyi-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 plj+kqbam;mv, m 613gpg anet where the speed of sound is ;,gmv36+m1agpqmkbj only about 35 m/s
(a) What is the probe’s Mach number if its initial speed is 15000 km/h$\approx$    (Round to the nearest integer)
(b) What is the angle of the shock wave relative to the direction of motion?    $^{\circ} $

  A meteorite traveling 8500 m/s strikes the ocean. Determine the shox yed0xx//m9qmen6d2vm1yw2 ck wave angle it prodxm/d 2 1n ym0wyd/veqe6xxm 29uces
(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 ;)q-a(o)xprzxj9i hs$/theta$ a sonic boom makes with the path of a supersonic object is given by Eq. 12–5.

  You look directly overhead and u n,7 hp-wmc/*ufv3 szsee a plane exactly 1.5 km above the ground flying faster than the speed of sound. By the time you hearnw3s, c*/ uzu7fm- hvp 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 downward 3lrl ok0;s r-jfrom 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 betlk-j0lr3sr ; oween pulses (in fresh water)?    s

  Approximately how many octaves are therc4nf4 qslq) h.e in the human audible range? $\approx$    octaves (Round to the nearest integer)

  A science museum has a display callbd6wwi;q9;ru wg ;z /oed a sewer pipe symphony. It consists of many plastic pipes of various lengths, which are open ;uord6gi/9wwbwq ;z ; on both ends.
(a) If the pipes have lengths of 3.0 m, 2.5 m, 2.0 m, 1.5 m and 1.0 m, what frequencies will be heard by a visitor’s ear placed near the ends of the pipes?
$f_{3.0}$ =    Hz
$f_{2.5}$ =    Hz
$f_{2.0}$ =    Hz
$f_{1.5}$ $\approx$    Hz (Round to the nearest integer)
$f_{1.0}$ $\approx$    Hz (Round to the nearest integer)
(b) Why does this display work better on a noisy day than on a quiet day?

  A single mosquito 5.0 m from a person makes a sound close to the threshold 4jrg. mfm16t62dtqe nof human hearing (0 dB). What will be the sound level of 1000 such mosquitoes?.tt md16n64jf emgrq 2    dB

  What is the resultant sound level when an 82-dB sound and an 87-dB souney bjne71 g16bd are heard simulta 71 e6ybb1gjneneously?    dB

  The sound level 12.0 m from a loudspeaker, placed in bpnbro/* xgj(n 6 /6k4vc u*hcthe open, is 105 dB. What isn4urgc h nxbop(/ *bcjv* k/66 the acoustic power output (W) of the speaker, assuming it radiates equally in all directions?    W

  A stereo amplifier is rated at 150 W output at b6s(7w6ixholl;mi2l 3c 9 xhy1000 Hz. The power output drops by 10 dB at 15 kHz. Wh92 xhs 36clx(7 owmiliy;hl b6at is the power output in watts at 15 kHz?    dB

  Workers around jet aircraft typically wear protective devices over ,:oowc+pmgx d 9al1s+ their ears. Assume that the sound level of a jet airplane engine, at a distance of 30 m, is 140 dB, an m+o,p+sx w:lgaoc1d 9d 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 systems, the gain,u1w6 +s7b wpy+b k/kkb5 mcw+ gdlla5, $\beta$ 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 violoii . r*uq+*jyin is tuned to a frequency 1$\frac{1}{2}$ times that of its neighbor. The four equal-length strings are to be placed under the same tension; what must be the mass per unit length of each string relative to that of the lowest string?
$f_{A}$ =    $\mu_{A}$
$f_{B}$ =    $\mu_{A}$
$f_{C}$ =    $\mu_{A}$

  The A string of a violin is 32 cm longrbbb7;xqic+ k *( twm p+/piiy ,0o1bp between fixed points with a fundamental frequency of 440 Hz and a ma++bo bc/ b0iip(p7*y;xw 1kpriq t ,mbss 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 vertical open tube filled with)ud:9 fn +kgni water (Fig. 12–35). The water level is allowed to drop slowly. As it does so, the air in the tube above the water level is heard to resonate with the tuning fork when the distance from the tube opening to the water level is 0.125 m and again at 0.395 m. What is the frdg +fi) :nnk9uequency of the tuning fork?   Hz

  A 75-cm-long guitar string of mass 2.10 g is : khck1vdsxeux; xe0/uo3* a7e;*czonear a tube that is open at one end and also 75 cm long. How much tension should be i7e:0k 1c ese3u*uzx;/ xc aovhd;o*kxn 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 observed6khys5wyc px e26w b9 kre,y92 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 tonj1 1iyyqm8nn* e in the 500–1000-Hz range coming from two sources. The sound is loudest at points equidistant from the two sources. To determine exactly what the frequency is, the person moves about and finds that nyi jnm1q1y 8*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 wh4*.pijlddxo p* e(d/n -e.ol2h5 xwblistles. One train is stationary. The conductor on the stationary thd2(pdl.owi- *ol e.5 *d lepbn/x4x jrain 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;zu,qix (vipvy c w0. 1:vls3gtle as it approaches you is 538 Hz. After it passes you, its frequency is measured as 486 Hz. How fast was the train moving (s1vxup c;,zgi.qwvy3i: l( v 0assume constant velocity)?    m/s

  At a race track, you can estimate the speed of cars just by listening71 wh4vse4f wo to the difference in pitch of the engine noise between approac 4fs we1v4h7owhing and receding cars. Suppose the sound of a certain car drops by a full octave (frequency halved) as it goes by on the straightaway. How fast is it going?    m/s

  Two open organ pipes, sounding together, produce a 1eg lgm;6v)-pcqqt 5 wbeat frequency of 11 Hz. The shorter one is 2.4-)c g5 qptgm6l 1qwv;e0 m long. How long is the other?    m

Two loudspeakers are at opposite ends of a railroad ca9css)+ c,w:csp qq6p rr 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 be)s ,qsp9cw:6cc pq+sr tween 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 aozrm nzg;j dn; 2hq(k1+rta is normally about 0.32 m/s what beat frequency would you expect if 5.50-MHz +rnz d(gkm12 j nh;;zqultrasound 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.- h kh)rci;q7m5 m/s while the moth is flying toward the bat at speed 5 m/s The bat emits a -mki; q)7rhc hsound 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 ia9 vc ot6n*fnflsf -.7t 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 emittedf ol nn9s*a6f7-ft. cv?    m

The “alpenhorn” (Fig. 12–38) was once used to send signals from one;pv9tzl kt:( v Alpine village to another. Since lower frequency sounds are less susceptible to intensity loss, long horns were used to cz(t9kv ;tp:lv reate 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 listen(juk on/g+/bz jw/rs :ing can be compromised by the presence of standing waves, zbgo+ru(n/jw:k/j/ swhich can cause acoustic “dead spots” at the locations of the pressure nodes. Consider a living room 5.0 m long, 4.0 m wide, and 2.8 m high. Calculate the fundamental frequencies for the standing waves in this room.
Length : f =   Hz
Width : f =   Hz
Height : f =   Hz

  A dramatic demonstration, called “singing rods,” involves a long, sl:utolu0j (ut8 ender aluminum rod held l:o ut(8 jtuu0in 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 *d y,z jg./w 5mnvmzf**h5dj jthe human ear at a frequency of about 1000 Hn y5 */ jj5mh.d,*zd j*wmvfgzz is $I_0$ = $1 \times10^{12 } W / m^2$ for which $\beta$ the sound level, is 0 dB. The threshold of pain at the same frequency is about 120 dB, or $I$ = $1 W / m^2$ corresponding to an increase of intensity by a factor of $10^{12}$ By what factor does the displacement amplitude, A, vary? 10$^{a}$ a =   

  A plane is traveling at Mach 2.0. An observer on the gr*/ dy(la s c66kpy2ov+n5f ixeound hears the sonic boom 1.5 min after the plane passes directly overhead( /dn5y ixlpa ov *e2k+fs6cy6. What is the plane’s altitude?    $ \times10^{4 }$ m

  The wake of a speedboa ad *a)qxedi44t is 15 $^{\circ} $ in a lake where the speed of the water wave is 2.2 km/h What is the speed of the boat?    km/h