A wave pulse is travelling on a string with a speed v towards the positive X-axi

Question

A wave pulse is travelling on a string with a speed v towards the positive X-axis. The shape of the string at t = 0 is given by g(x) =

A s i n (\frac{x}{a})

where A and a are constants. Write the equation of the wave for a general time t, if the wave speed is v.

Options:

A . g(x)=A sin(x+vta)

B . g(x)=A sin(xa)

C . g(x)=A sin(x−vta)

D . g(x)=A sin(xt+va)

Answer: Option C
:
C
Given shape of the wave at t=0

g (x) = A s i n (\frac{x}{a})

let's say the wave looks like

It's wave speed is v. After time t, the wave would have moved vt.
Now if at t = 0
The equation is

g (x) = A s i n (\frac{x}{a})

This wave was at x = x, t= t will be same as the wave at x= x-vt at t = 0
So at t = 0 g(x) = A sin

\frac{x - v t}{a}

Alternate Solution:- Given g(x) = A sin

(\frac{x}{a})

General equation A sin (kx -

ω

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