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A displacement wave is represented by ...

A displacement wave is represented by
`xi=0.25xx10^(-3)sin(500t-0.025x)`
Deduce (i) amplitude (ii) period (iii) angular frequency (iv)wavelength (v) amplitude of particle velocity (vi) amplitude of particle acceleration . `xi`, t and x are in cm, sec, and metre respectively.

Text Solution

Verified by Experts

The correct Answer is:
`0.25 xx 10^(-3)` cm
In the given equation =
`y = 0.25 xx 10^(-3) sin(500t - 0.25x)`
Comparing with
`y = A sin (omegat - kx)`
(a) Amplitude
`A = 0.25 xx 10^(-3)` cm
(b) Time period
`T = (2pi)/(omega) = (2pi)/(500) = (pi)/(250)x`
(C) Angular frequency
`omega = 500` rad/s
(d) wavelength
`lambda = (2pi)/(k) = (2pi)/(0.25) = 8pi` cm
("E") Particle velocity amplitude
`v_(max) = Aomega = 0.25 xx 10^(-3)xx 500`
`6.25 cm//s^(2)`
(f) Particle acceleration amplitude
`a_(max) = omega^(2)A = (500)^(2)xx0.25 xx 10^(-3)`
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