Question

A plane transverse harmonic wave travels through a medium. The maximum particle velocity equals the wave velocity. Then

• A. $\lambda =2\pi A$
• B. $\lambda =\pi A$
• C. $A=2\pi \lambda$
• D. $\lambda =\frac{\pi A}{2}$

Answer 1

Answer: (A)

$\lambda =2\pi A$

A transverse wave is described by the equation,

$y=A\sin 2\pi (ft-\frac{x}{\lambda })$

The maximum velocity of the particle will be

$v_{max}=amplitude\times 2\pi f=A\times 2\pi f$

velocity of wave, $v_{wave}=\lambda \times f$

By the condition of the problem

$v_{max}=v_{wave}$

$\Rightarrow A\times 2\pi f=\lambda \times f$

$\Rightarrow \lambda =2\pi A$