If the distance between successive compressions and rarefactions is 1 m and velocity of sound is `360 m s^(-1)`, then the frequency is

Options

A. 180 Hz
B. 45 Hz
C. 120 Hz
D. 90 Hz

Explanation

To find the frequency of sound based on the given distance between successive compressions and rarefactions and the velocity of sound, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Distance Between Successive Points**:
- The distance between successive compressions and rarefactions is given as 1 meter. This distance corresponds to half of a wavelength (λ/2).

2. **Calculate the Wavelength (λ)**:
- Since the distance between a compression and the next rarefaction is λ/2, we can express this as:
\[ \frac{\lambda}{2} = 1 \text{ m} \]
- To find the full wavelength (λ), we multiply both sides by 2:
\[ \lambda = 2 \times 1 = 2 \text{ m} \]

3. **Use the Velocity of Sound**:
- The velocity of sound (V) is given as 360 m/s.

4. **Apply the Formula for Frequency (f)**:
- The frequency can be calculated using the formula:
\[ f = \frac{V}{\lambda} \]
- Substituting the known values:
\[ f = \frac{360 \text{ m/s}}{2 \text{ m}} = 180 \text{ Hz} \]

5. **Final Answer**:
- The frequency of the sound is 180 Hz.