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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) + 2 sqrt("abxt")))` . 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^((- sqrt(ax) + sqrt(bt))^(2))`, It is a function of type y = f(x + vt)
`rArr ` speed of wave = `sqrt((b)/(a))`
Correct choice , a.
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