Question Detail
Question
Two waves, same frequency and same wavelength, each of amplitude 2 cm are superimposed. If the phase difference between them is 30°, calculate the amplitude of the resulting wave. The formula for resultant displacement is y = 2Acos(φ/2)sin(ωt-kx+φ/2).
Correct Answer
Option C is the correct answer.
Detailed Explanation
For two waves of equal amplitude A undergoing superposition with a phase difference φ, the resultant amplitude (R) is given by the formula R = 2A|cos(φ/2)|.Given:Amplitude A = 2 cmPhase difference φ = 30°Substitute the values into the formula:R = 2 * (2 cm) * cos(30°/2)R = 4 cm * cos(15°)R = 4 cm * 0.9659R ≈ 3.8636 cmRounding to two decimal places, the amplitude of the resulting wave is approximately 3.86 cm.
Hint
The resultant amplitude (R) for two waves of equal amplitude A with a phase difference φ is R = 2A|cos(φ/2)|.