Question

The transverse wave propagating through a medium is given by $y=A\cos 2\pi [ft-\frac{x}{\lambda }]$. If maximum particle velocity of medium is two times the velocity of wave through medium, then.

• A. $\lambda =3.14A$
• B. $\lambda =6.28A$
• C. $6.28\lambda =A$
• D. $3.14\lambda =A$

Answer 1

The correct option is A $\lambda =3.14A$

Velocity of a particle

$v_p=\nu \lambda$

$v_p=A\omega$

$=A2\pi \nu .....\left(1\right)$

Maximum velocity of a wave $v_g=\nu \lambda ............\left(2\right)$

It is given that $v_p=2v_g$

Using equation (1) and (2)

$A2\pi \nu =2\nu \lambda$

$\lambda =\pi A$

$\lambda =3.14A$