Length of 0.3 m wire vibrates in fundamental mode at frequency 480Hz. Then the velocity of sound wave in air is

Options

A. 330m/s
B. 320m/s
C. 300m/s
D. 288m/s

Explanation

To find the velocity of sound waves in air based on the given information about a vibrating wire, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Length of the wire (L) = 0.3 m
- Frequency of vibration (f) = 480 Hz

2. **Understand the Fundamental Frequency Formula**:
- The fundamental frequency (f₀) of a vibrating wire is given by the formula:
\[ f₀ = \frac{V}{2L} \]
where V is the velocity of the wave in the wire.

3. **Rearrange the Formula to Solve for V**:
- To find the velocity (V), rearrange the formula:
\[ V = 2L \cdot f₀ \]

4. **Substitute the Known Values into the Formula**:
- Substitute L = 0.3 m and f₀ = 480 Hz into the equation:
\[ V = 2 \cdot 0.3 \cdot 480 \]

5. **Calculate the Velocity**:
- Calculate the value:
\[ V = 2 \cdot 0.3 \cdot 480 = 0.6 \cdot 480 = 288 \text{ m/s} \]

6. **Conclusion**:
- The velocity of sound waves in air is **288 m/s**.