First slide

Interference

Question

Two sinusoidal waves of same amplitude of 1 cm propagate in opposite directions along x-axis. Wavelength of each wave is 6 cm speed of each wave is 0.5 cm/s. Then at any time t, displacement of a particle from its equilibrium position is zero at

Difficult

A

x = 1 cm
B

x = 2cm
C

x = 3cm
D

x = 4cm

Solution

Frequency $f = \frac{V}{λ} = \frac{0 .5}{6} Hz = \frac{1}{12} Hz$
Wave number $K = \frac{2 π}{λ} = \frac{2 π}{6} {cm}^{- 1} = \frac{π}{3} {cm}^{- 1}$
Equation of wave-1, $y_{1} = 1 \sin (\frac{πx}{3} - 2 π . \frac{1}{12} t)$ and equation of wave-2, $y_{2} = 1 . \sin (\frac{πx}{3} + 2 π . \frac{1}{12} . t)$
$∴$ Equation of resultant wave is
$y = y_{1} + y_{2} = 2 . \sin \frac{πx}{3} . \cos \frac{πt}{6} cm$
For the particles which are permanently at rest, y = 0
$\begin{array}{l} ∴ \sin \frac{πx}{3} = 0 \Rightarrow \frac{πx}{3} = nπ (n = 1, 2, 3, . ....) \\ \Rightarrow x = 3 n cm \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App