Two simple harmonic waves having equal amplitudes of 8 cm and equal frequency of 10 Hz are moving along the same direction. The resultant amplitude is also 8 cm. The phase difference between the individual waves is _________ degree.

Solution

Physics sir · 3 steps

Two equal amplitudes, and the result is the same size: the phasor triangle is equilateral.

1. Add as phasors. Two waves of the same frequency add like vectors. The amplitudes a₁ and a₂ are the two arrows, and the phase difference φ is the angle between them.

   A² = a₁² + a₂² + 2a₁a₂cos φ

2. Put in numbers. With a₁ = a₂ = A = 8 cm: 64 = 64 + 64 + 128 cos φ. This gives 128 cos φ = -64, so cos φ = -1/2.
3. So. φ = 120°. The phase difference is 120 degrees.

The common slip: 60. Stopping at cos(φ/2) = 1/2 in A = 2a cos(φ/2) gives 60, which is only half the phase difference.

The idea to keep. For two equal amplitudes a, the resultant is 2a cos(φ/2). If it equals a, the phase difference is 120°. The frequency does not affect the answer.

Answer from the NTA final answer key. Solution by PrepWiser.