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The transverse displacement y(x, t) of a...

The transverse displacement `y(x, t)` of a wave on a string is given by `y(x, t)= e ^(-(ax^(2) + bt^(2) + 2sqrt((ab))xt)`. This represents a :

A

wave moving `+x-`direction with speed `sqrt((a)/(b))`

B

wave moving in `-x`direction with speed `sqrt((b)/(a))`

C

standing wave of frequency `sqrt(b)`

D

standing wave of frequency `(1)/(sqrt(b))`

Text Solution

Verified by Experts

The correct Answer is:
2
`y(x,t) = e^(-[sqrt(ax)+sqrt(bt)]^(2))`
it is transverse type , `y(x,t) = e^(-(ax + bt)^(2))`
Speed `v = (sqrt(b))/(sqrt(a))`
and wave is moving along `-x` direction.
`y(x,t) = e^(-[sqrt(ax)+sqrt(bt)]^(2))`
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