Question

Standing waves are produced by the superposition of two waves:

y₁ = 0.05 sin(3πt - 2X) and y₂ = 0.05 sin(3πt + 2X), where x and y are expressed in metres and t is in seconds. Find the amplitude of a particle at x = 0.5m. (Given cos1 = 0.54; sin1 = 0.84; angle is in radian)

1. 5.4 cm
2. .54 m
3. .84 m
4. 8.4 cm

Answer 1

Correct Answer - Option 1 : 5.4 cm

y = y₁ + y₂ according to superposition of waves.

= 0.05 sin (3πt - 2x) + 0.05 sin (3πt + 2x)

As 2sinAcos B = sin (A + B) + sin (A - B)

= (0.05) × 2sin(3πt)cos(2x) = 2(0.05) cos(2x)× sin(3πt)

amplitude is (0.1 cos 2x)

at x = 0.5 : A = 0.1cos 2(0.5) = 0.1× cos1 = 0.1× cos 57.3⁰ = 0.1 × 0.54 = 5.4 cm