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

Answer

a.,b.,d.

Explanation

`y(x,0)=f(x)`. So, shape of string at `t=0` is given by `y=f(x)`
As velocity of wave `dx//dt=+a`, is constant, so shape of string does not 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.
speed `=-a` and not a as speed cannot `be-ve`