Homework SourseA train blos its whistle as it passes a platform An observer
A train blos its whistle as it passes a platform. An observer hears a frequency of 570 as the train comes close and 490 as the train leaves. What is the speed of the train? What is the frequency of the whistle as heard by someone on the train? If the whistle is open on both ends, and the sound produced is first harmonic, what is the length of the tube? With first harmonic, where is the location in the tube where air molecules have maximum displacement?
A train blos its whistle as it passes a platform. An observer hears a frequency of 570 as the train comes close and 490 as the train leaves. What is the speed of the train? What is the frequency of the whistle as heard by someone on the train? If the whistle is open on both ends, and the sound produced is first harmonic, what is the length of the tube? With first harmonic, where is the location in the tube where air molecules have maximum displacement?
Solution
Using Doppler\'s effect,
f = (v + vr)f0 / (v + Vs)
v = speed of sound = 343 m/s
vr = speed of receiver = 0
vs = speed of source (vt when train goes away and -vt when train comes closer)
hence, 570 = 343f0 / (343 - vt)
and 490 = 343f0 / (343 + vt)
dividing equation,
570/490 = 343 + vt / 343 - vt
1.163*343 - 1.163vt = 343 + vt
vt = 25.84 m/s ..........ans (Speed of train)
putting value of vt in equation,
570 = 343f0 / (343 - 25.84)
f0 = 527 Hz ....Ans
for tube open at both end and fundamental,
lambda = 2L
and lambda = v / f0 = 343/527 = 0.65 m
and L = 0.65/2 =0.325 m .........Ans
Maximum displacement of air molecule = at ends and in middle position
