In a transverse progressive wave of amplitude A, the maximum particle velocity is four times its wave velocity. The wavelength of the wave is:-

Question

In a transverse progressive wave of amplitude A, the maximum particle velocity is four times its wave velocity. The wavelength of the wave is:- (A) π A (B) (π A/2) (C) (π A/1) (D) 2 π A

Tardigrade Admin · Accepted Answer

V max =A ω=4((ω/k)) ⇒ A=(4/k)=(4 λ/2 π) ⇒ λ=(π A/2)

Q. In a transverse progressive wave of amplitude $A$ , the maximum particle velocity is four times its wave velocity. The wavelength of the wave is:-

$π A$

$\frac{π A}{2}$

$\frac{π A}{1}$

$2 π A$

$V_{m a x} = A ω = 4 (\frac{ω}{k})$
$\Rightarrow A = \frac{4}{k} = \frac{4 λ}{2 π}$
$\Rightarrow λ = \frac{π A}{2}$

Q. In a transverse progressive wave of amplitude A, the maximum particle velocity is four times its wave velocity. The wavelength of the wave is:-

πA

2πA​

1πA​

2πA