Question

Two identical sinusoidal waves each of amplitude 10 mm with a phase difference of 120° are travelling in the same direction in a string. The amplitude of the resultant wave is

• A. 5 mm
• B. 10 mm
• C. 15 mm
• D. 20 mm

Answer 1

Answer: (B)

10 mm

Answer 2

Since the two waves are identical, they have same amplitudes.

The amplitude of the resultant wave is

$A = 2a\cos\frac{\varphi}{2}$

Here, a = 10 mm, $\varphi = 120{^\circ}$

A = 2 (10 mm)$\cos\frac{120{^\circ}}{2}$

$= 2 \times 10 \times \frac{1}{2}mm = 10mm$