Sound WavesEasy
Question
The displacement y of a particle executing periodic motion is given by
Y = 4 cos2
sin(1000t)
This expression may be considered to be a result of the superposition of ........ independent harmonic motion
Y = 4 cos2
sin(1000t)This expression may be considered to be a result of the superposition of ........ independent harmonic motion
Options
A.two
B.three
C.four
D.five
Solution
The equation can be written as
y = 2(2cos2
) sin (1000 t)
y = 2(cost + 1) sin (1000t)
y = 2 cos t sin 1000t + 2sin(1000t)
y = sin(1001t) + sin(999t) + 2sin(1000t)
i.e., the given expression is a resultant of superposition of three independent harmonic motions of angular frequencies 999, 1000 and 1001 rad/s.
y = 2(2cos2
) sin (1000 t)y = 2(cost + 1) sin (1000t)
y = 2 cos t sin 1000t + 2sin(1000t)
y = sin(1001t) + sin(999t) + 2sin(1000t)
i.e., the given expression is a resultant of superposition of three independent harmonic motions of angular frequencies 999, 1000 and 1001 rad/s.
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