The frequency of a sound wave is n and its velocity is v. If the frequency is increased to 4n the velocity of the wave will be

Options

A. v
B. 2v
C. 4v
D. `v//4`

Answer

To solve the problem, we need to analyze the relationship between frequency, velocity, and wavelength of a sound wave.

### Step-by-Step Solution:

1. **Identify the Given Information**:
- Initial frequency of the sound wave, \( n \).
- Initial velocity of the sound wave, \( v \).
- New frequency after increase, \( 4n \).

2. **Use the Wave Equation**:
- The fundamental relationship between the velocity \( v \), frequency \( n \), and wavelength \( \lambda \) of a wave is given by the equation:
\[ v = n \lambda \]
- Here, \( v \) is the velocity of the wave, \( n \) is the frequency, and \( \lambda \) is the wavelength.

3. **Understand the Dependency**:
- The velocity of sound in a medium is primarily determined by the properties of the medium (like temperature) and is generally constant for a given medium under constant conditions.
- The frequency can be changed by altering the source of the sound (like changing the tuning fork), but this does not affect the velocity of sound in that medium.

4. **Analyze the Change in Frequency**:
- When the frequency is increased to \( 4n \), we can express the new velocity \( v' \) as:
\[ v' = 4n \lambda' \]
- However, since the medium does not change, the velocity \( v \) remains constant regardless of the frequency change.

5. **Conclusion**:
- Since the velocity of sound in a medium is independent of the frequency, the velocity of the wave when the frequency is increased to \( 4n \) will still be \( v \).

### Final Answer:
The velocity of the wave will remain \( v \).

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