A wave traveling along a string is described by the equation y(x, t) = A sin(kx

A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What is the phase velocity of the wave?

A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What is the phase velocity of the wave?

Step 1: Identify the wave equation given, which is y(x, t) = A sin(kx - ωt).
Step 2: Recognize that in the equation, k represents the wave number and ω represents the angular frequency.
Step 3: Understand that the phase velocity (v) of a wave is the speed at which a point of constant phase travels.
Step 4: Use the formula for phase velocity, which is v = ω/k.
Step 5: Substitute the values of ω and k from the wave equation into the formula to find the phase velocity.

Wave Equation – The equation y(x, t) = A sin(kx - ωt) represents a sinusoidal wave, where A is amplitude, k is the wave number, and ω is the angular frequency.
Phase Velocity – Phase velocity is the speed at which a point of constant phase travels along the wave, calculated as v = ω/k.