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Question:

A travelling harmonic wave is represented by the equation y(x,t)=10sin(50t+2x), where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?

The wave is propagating along the positive x-axis with speed 25ms⁻¹

negative x-axis with speed 25ms⁻¹

The wave is propagating along the positive x-axis with speed 100ms⁻¹

The wave is propagating along the negative x-axis with speed 25ms⁻¹

Solution:

The correct option is: The wave is propagating along the negative x-axis with speed 25ms⁻¹
y = asin(ωt+kx) ⇒ wave is moving along -ve x-axis
speed v = ω/k ⇒ v = 50/2 = 25m/sec.