Concepts Of Physics MCQ Edition [Volume 1]PhysicsWave Motion and Waves on a String

The equation y = A ^2(kx - t) characterizes a wave motion with

Options

Aamplitude A , frequency 2
Bdoes not characterize a wave motion
Camplitude 2A , frequency 4
Damplitude A 2 , frequency

Correct answer

D. amplitude A 2 , frequency

Step-by-step solution

Given equation of the wave is y = A ^2(kx - t) Using the trigonometric identity ^2 = 1 - 2 2 , we get: y = A 2 [1 - (2kx - 2 t)] y = A 2 - A 2 (2kx - 2 t) This represents a wave superimposed on a constant displacement of A 2 . The amplitude of the wave is the magnitude of the coefficient of the cosine term, which is A 2 . The angular frequency of the wave is ' = 2 . The frequency of the wave is f = ' 2 = 2 2 = .

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