question_answer

The equation \[y=4+2\sin \left( 6t-3x \right)\] represents a wave motion. Then wave speed and amplitude, respectively are

A) wave speed 1 unit, amplitude 6 unit

B) wave speed 2 unit, amplitude 2 unit

C) wave speed 4 unit, amplitude 1/2 unit

D) wave speed 1/2 unit, amplitude 5 unit

Correct Answer: B

Solution :

The shape of the wave is shown in the figure. From this graph we see that amplitude of wave is 2 unit. \[Wave\text{ }speed\text{ }v=\frac{coefficient\,of\,t}{coefficient\,of\,x}=\frac{6}{2}\text{ =}2\text{ }unit\]