Sound WavesHard
Question
The equation of a travelling wave is y = 60 cos (1800t - 6x) where y is in microns, t in second and x in metre. The ratio of maximum particle velocity to the velocity of wave propagation is :
Options
A.3.6 × 10-4
B.3.6 × 10-6
C.3.6 × 10-8
D.none of these
Solution
y = 60cos(1800t - 6x), y is in microns.
y = 60cos(1800 t - 6 x) × 10-6
v =
= particle velocity
60 × 10-6 × 1800 sin (1800t - 6x)
vmax = 6 × 18 × 10-3
vwave =
; ω = 1800; K = 6
vwave =
= 300
36 × 10-5 = 3.6 × 10-4
y = 60cos(1800 t - 6 x) × 10-6
v =
= particle velocity 60 × 10-6 × 1800 sin (1800t - 6x)
vmax = 6 × 18 × 10-3
vwave =
; ω = 1800; K = 6vwave =
= 300 36 × 10-5 = 3.6 × 10-4
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