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) =$Asin\left(\frac{x}{a}\right)$ where A and a are constants. Write the equation of the wave for a general time t, if the wave speed is v.

• A. $g\left(x\right)=Asin\left(\frac{x+vt}{a}\right)$
• B. $g\left(x\right)=Asin\left(\frac{x}{a}\right)$
• C. $g\left(x\right)=Asin\left(\frac{x-vt}{a}\right)$
• D. $g\left(x\right)=Asin\left(\frac{xt+v}{a}\right)$

Answer 1

The correct option is C

$g\left(x\right)=Asin\left(\frac{x-vt}{a}\right)$

Given shape of the wave at t=0

$g\left(x\right)=Asin\left(\frac{x}{a}\right)$

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 $g\left(x\right)=Asin\left(\frac{x}{a}\right)$

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 $\frac{x-vt}{a}$

Alternate Solution:- Given g(x) = A sin $\left(\frac{x}{a}\right)$

General equation A sin (kx - $\omega$t)