Question

If a wave is represented by $y(x,t)=A\sin (kx-\omega t+\varphi )$,

• A. $\varphi$ has no impact on particle acceleration
• B. $\varphi$ has an impact on particle acceleration
• C. $\varphi$ has an impact on particle acceleration at some times
• D. None of these

Answer 1

Answer: (B)

$\varphi$ has an impact on particle acceleration

We know that, the displacement of a transverse wave is given by $y=A\sin (kx-\omega t+\varphi )$

Thus, the particle acceleration is given by $a=\frac{d^{2}y}{d{t}^2}=-A{\omega }^2\sin (kx-\omega t+\varphi )$

Thus, at any instant, the particle acceleration is given by $a=-{\omega }^{2}y$ which depends on $\varphi$.

However, the amplitude doesn't depend on $\varphi$.