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

B

standing wave of frequency `sqrt(b)`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
`y(x, t) = e^(-(ax^(2)+bt^(2)+2sqrt(ab) xt))=e^(-(sqrt(a)x+sqrt(b)t)^(2)`
It is a function of type
`y = f(omega t + kx)`
`therefore y (x, t)` represents wave travelling along - x-direction,
Speed of wave = `(omega)/(k)=(sqrt(b))/(sqrt(a))=sqrt((b)/(a))`
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