Questions and Example Problems from Chapter 17

Question I'(a) when an orchestra waflns up, the players' warm breath increases the temperature of the airwithin the wind instruments (and thus decreases the density ofthat air). Do the resonantfrequencies oftlose instruments increase or decrease? (b) When *re slide ofa slide trombone ispushed outward, do the resonant frequencies ofthe instrument increase or decrease?

co) f "=ryt ^ fn=DL V )xw.tta.t-od Pte )/"sMu'S

(b)Question 2For a particular tube, here are four ofthe six harmonic ftequencies below 1000 Hz: 300, 600,750, and 900 FIz. What two frequencies are missing from the list?

@^a7;i4Question 3A tuning fork ofunknown frequency makes three beats per second with a standard fork offrequency 384 Hz. The beat frequency decreases when a small piece of wax is put on a prong ofthe fust fork. What is the frequency of this fork?

Sxql+z+ 3ltL ) fk":3ztftz::--

T= J..56^ ld'sProblem 1Devise a rule for finding your distance in kilometers (and miles) frorrr a lightning flash bycounting the seconds from the time you see the flash until you hear the thunder. Assume that thesound travels to you along a straight line.

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T-'wt / I

| = / ( : - - , P - - - )| / T 3z"l*z

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^t= Ax (zbd,)(W) =$ou aX = -l-,,i ---)

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Problem 2ln the figure below, sound with a 40.0 cm wavelength travels rightward from a source andthrough a tube that consists ofa straight portion and a half-circle. Part ofthe sound wave travelsthrough the half-circie and then rejoins the rest of the wave, which goes directly through thestraight portion. This rejoining results in interference. Whal is the smallest radius r that results inan intensity minimum at the detector?

AL=rTt--!,n-- r (tt--O

Source Detector

),'ru.lJd f -) ,r = o I -

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r(-n-r) = (t*/"r)z\ / l , \ \---) p -- ( fct + AJ z\/n-a1

) ; - / * ^ \ - - - ' - 7

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Problem 3The figure below shows an air-filled, acoustic interferometer, used to demonstrate theinterference of sound waves. Sound source S is an oscillating diaphragm; D is a sound detector,such as the ear or a microphone. Path SBD can be varied in length, but path SAD is fixed. At D,the sound wave coming along path SBD interferes with that coming along path SAD. In onedemonstration, the sound intensity at D has a minimum value of 100 r.rnits at one position of themovable arm and continuously climbs to a maximum value of 900 units when that arrn is shiftedby 1.65 cm. Find the ffequency of the sound emitted by the source.

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=o?) . r ) , - - -

r l :o r l t ) , - - -

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/r+ AJ

f = s"r." Ioellz

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LL= Ad ' y" ^"*" , tJE o n -X,) )r)n rPr\t^LLD M^f

AL = Y^-'=::-

)=qJ=4(1.65..)-= 6.too .

"1 = O ,o 61eo rn

=

343,/sO

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Problen 4In the figure below, s is a small loudspeaker driven by an audio oscillator and amplifier,adjustable in frequency from 1000 to 2000 Hz only. Tube D is apiece of cylindrical sheelmetalpipe 45 .7 cm long and open at both ends. (a) If the speed of sound in air is 344 m/s at the existingtemperatue, at what tequencies will resonance occur in the pipe when the fiequency emitted bythe speaker is varied from 1000 FIz to 2000 Hz? (b) sketch the standing wave for each resonantfrequency.

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\ : l

s\AL

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( b)

Problem 5Q=5

A tube 1.20 m long is closed at one end. A stretched wire is placed near the opea end. The wireis 0.330 m long and has a mass of 9.60 g. It is fixed at both ends and oscillates in its fundamentalmode. By resonance, it sets the air column in the tube into oscillation at the tubes fundamentalfrequency. Find (a) that frequency and (b) the tension in the wire.

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Problem 6An acoustical burglar alarm consists ofa source emitting waves offrequency 28.0 kHz. what isthe beat ftequency between the source waves and the waves reflected from an intruder walkine atan average speed of 0.950 nrls direcfly away from the alarm? .\_-.,

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V+Vs 19. c>.11onf s at rnS -l"tn a.o\rt4> (u.t- - l/yt ru;ruts,)

Probrem? +*'ole=ot= e{|Gz-[ '=T7GTJIn the figure below, a French submarine and a U.S. submarine move toward each ofiiE-dffi'ljmaneuvers in motionless water in the North Atlantic. The French sub moves at speed vp : 50.00km./h, and the u.S. sub at vus : 70.00 km/h. The French sub sends out a sonar signal (sound wavein water) at 1.00 x 103 Hz. sonar waves travel at 5470 km/h. (a) what is the signal's frequency asdetected by the U.S. sub? (b) What frequency is detected by the French sub in the signal reflectedback to it by the U.S. sub? \_/

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