The wavelength of a periodic wave is 0.750 m. If the frequency is 425 Hz, then what is the velocity of the wave?

1. Break Down the Problem

We need to calculate the velocity of a wave, given its wavelength and frequency. The relationship between these quantities can be stated in a single formula.

2. Relevant Concepts

The formula to determine the velocity $v$ of a wave is given by: $v = f \cdot \lambda$ where:

• $v$ is the wave velocity,
• $f$ is the frequency of the wave,
• $\lambda$ is the wavelength of the wave.

3. Analysis and Detail

Let's substitute the given values into the formula:

• Wavelength $\lambda = 0.750$ m
• Frequency $f = 425$ Hz

Now calculate the wave velocity: $v = 425 \, \text{Hz} \times 0.750 \, \text{m}$ $v = 318.75 \, \text{m/s}$

4. Verify and Summarize

The calculations seem correct. The steps used are consistent with the formula for wave velocity. Thus, the calculated velocity aligns with the physical principles:

Final Answer

The velocity of the wave is $318.75 \, \text{m/s}$.