Question

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 `sqrt(1/sqrt(b)`
D. wave moving in +x direction with speed `sqrt(a//b)`

Answer 1

Correct Answer - b
`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(omegat+kx)`
`therefore y(x,t)` represents wave travelling along -x direction.
Speed of wave `=omega/k=sqrt(b)/sqrt(a)=sqrt(b/a)`