Fore a transverse wave on a string, the string displacement is describrd by
`y(x,t)=f(x-at)`
where f represent a function and a is a negative constant. Then which of the following is//are correct statement(S)?

Options

A. Shape of the string at time `t=0` is given by `f(x)`.
B. The shape of waveform does not change as it moves along the string.
C. waveform moves in `+ve` x-direction.
D. The speed of wveform is `a`.

Answer

a., b., d.

Explanation

`y(x,0)=f(x)`. So shape of string at `t-0` is given by `=f(x)`.
As velocity of wave `(dx)/(dt)=+a`, is a constant, so shape of string doesn't change, or we can say `(x-at)` is constant. Thus, the shape of string remains the same.
As a is -ve and constant, so `(dx)/(dt)=-` ve and hence, wave is moving along-ve x-direction.