A certain transverse sinusoidal wave of wavelength 20 cm is moving in the positive x -direction. The transverse velocity of the particle at x=0 as a function of time is shown. The amplitude of the motion is :

Question

A certain transverse sinusoidal wave of wavelength 20 cm is moving in the positive x -direction. The transverse velocity of the particle at x=0 as a function of time is shown. The amplitude of the motion is : (A) (5/π) cm (B) (π/2) cm (C) (10/π) cm (D) 2 π cm

Tardigrade Admin · Accepted Answer

We use maximum particle velocity v max =A ω=5 cm / s ; T=4 s ⇒ ω =(2 π/4)=(π/2) ⇒ A =(5/π / 2)=(10/π) cm.

Q. A certain transverse sinusoidal wave of wavelength $20 c m$ is moving in the positive $x$ -direction. The transverse velocity of the particle at $x = 0$ as a function of time is shown. The amplitude of the motion is :

$\frac{5}{π} c m$

$\frac{π}{2} c m$

$\frac{10}{π} c m$

$2 π c m$

We use maximum particle velocity
$v_{m a x} = A ω = 5 c m / s; T = 4 s$
$\Rightarrow ω = \frac{2 π}{4} = \frac{π}{2}$
$\Rightarrow A = \frac{5}{π /2} = \frac{10}{π} c m .$

Q. A certain transverse sinusoidal wave of wavelength 20cm is moving in the positive x -direction. The transverse velocity of the particle at x=0 as a function of time is shown. The amplitude of the motion is :

π5​cm

2π​cm

π10​cm

2πcm