Derive an expression of wave velocity in terms of frequency and wavelength of the wave.

Answer

To derive the expression for wave velocity in terms of frequency and wavelength, we can follow these steps:

### Step 1: Understand the definitions
- **Frequency (f)** is defined as the number of waves that pass a point in one second. It is measured in Hertz (Hz).
- **Wavelength (λ)** is the distance between two consecutive points that are in phase on the wave, such as crest to crest or trough to trough.

### Step 2: Relate frequency and time period
- The **time period (T)** is the time taken for one complete wave to pass a point. It is the reciprocal of frequency:
\[ T = \frac{1}{f} \]

### Step 3: Define wave velocity
- The **wave velocity (v)** is the distance traveled by a wave in a unit of time. For one complete wave, the distance traveled is the wavelength (λ), and the time taken is the time period (T):
\[ v = \frac{\text{Distance}}{\text{Time}} = \frac{\lambda}{T} \]

### Step 4: Substitute the time period with frequency
- We already established that \( T = \frac{1}{f} \). Therefore, we can substitute T in the wave velocity equation:
\[ v = \frac{\lambda}{T} = \frac{\lambda}{\frac{1}{f}} = \lambda \cdot f \]

### Step 5: Final expression
- Thus, the expression for wave velocity in terms of frequency and wavelength is:
\[ v = \lambda f \]

### Summary
- The wave velocity (v) is equal to the product of the wavelength (λ) and the frequency (f):
\[ v = \lambda f \]