First slide

Travelling wave

Question

The angular frequency of a particle in a progressive wave in an elastic medium is 100 $π$ rads^-1 and it is moving with a velocity of 200ms^-1. The phase difference between two particles separated by a distance of 20m is

Moderate

A

31.4 rad
B

$π$ rad
C
$\frac{3}{4} π r a d$
D

36 rad

Solution

$ω = 100 π rad / s; V = 200 m / s; Δ x = 20 m$
$\begin{array}{l} Δ ϕ = \frac{2 π}{λ} Δ x \\ w = 2 π n = 100 π \Rightarrow n = 50 Hz \\ V = n λ \Rightarrow λ = \frac{v}{n} = \frac{200}{50} = 4 m \\ Δ ϕ = \frac{2 π}{4} (20) = 10 π = 10 \times 3.14 = 31.4 rad \end{array}$

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