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. (a) wave moving in -x direction with speed `sqrt((b)/(a))`
B. (b) standing wave of frequency `sqrt(b)`
C. ( c ) standing wave of frequency `(1)/sqrt(b)`
D. (d) wave moving in +x direction with speed `sqrt((a)/(b))`

Answer 1

Correct Answer - A
(a) Given wave equation is `y(x, t)= e ^(-(ax^(2) + bt^(2) + 2sqrt((ab))xt)`
`= e^(-[sqrt(ax^(2)) + (sqrt(bt))^(2) + 2sqrt(a x). sqrt(b t)] = e^(-(sqrt(ax) + sqrt(bt)^(2))`
`=e^(-(x+ sqrt(b/a) t)^2`
It is a function of type `y = f(x + vt)`
rArr Speed of wave `= sqrt((b)/(a))`