The velocity of the plane wave sin2(ωt - βx) isa) 2ω / βb) ω / 2βc) ω2 / β2d) ω / βSelect one:badc

To determine the velocity of the plane wave given by the equation $\sin(2(\omega t - \beta x))$, we can analyze the wave function.

1. Break Down the Problem

Identify the parameters in the wave equation and what they represent:

• The term $\omega$ refers to the angular frequency.
• The term $\beta$ is the wave number.
• The form of the wave equation helps us find the wave velocity.

2. Relevant Concepts

The general form of a plane wave can be described as $A \sin(\omega t - kx)$, where:

• $k$ is the wave number, which in this case is $\beta$.
• The velocity $v$ of the wave is given by the formula: $v = \frac{\omega}{k}$

3. Analysis and Detail

Substituting $k$ with $\beta$: $v = \frac{\omega}{\beta}$

4. Verify and Summarize

From our analysis, the wave velocity derived from the equation is consistent with the standard wave velocity formula.

Final Answer

The velocity of the plane wave $\sin(2(\omega t - \beta x))$ is $\frac{\omega}{\beta}$. Thus, the correct answer is d) $\frac{\omega}{\beta}$.