A sound is produced by plucking a string in a musical instrument, then

Options

A. the velocity of the wave in the string is equal to the velocity of sound in the string
B. the frequency of wave in the string is equal to the frequency of the sound produced
C. the wave in the string is progrressive
D. the tension in the string varies from point to point

Answer

To solve the question regarding the sound produced by plucking a string in a musical instrument, we can break down the concepts involved step by step.

### Step-by-Step Solution:

1. **Understanding Wave Production**: When a string is plucked, it vibrates and produces a wave. This wave travels along the string and generates sound waves in the surrounding air.

2. **Velocity of the Wave**: The velocity of the wave in the string (v_string) is determined by the tension in the string and the mass per unit length (linear density) of the string. The formula for the velocity of a wave on a string is given by:
\[ v_{\text{string}} = \sqrt{\frac{T}{\mu}} \]
where \(T\) is the tension in the string and \(\mu\) is the linear density.

3. **Frequency of the Wave**: The frequency (f) of the wave produced by the vibrating string is related to the velocity of the wave and the wavelength (λ) by the equation:
\[ v_{\text{string}} = f \cdot \lambda \]
This means that the frequency of the wave in the string is directly linked to the frequency of the sound produced.

4. **Sound Wave Properties**: The sound produced by the vibrating string travels through the air (or any medium) as a sound wave. The speed of sound in air is different from the speed of the wave in the string, but the frequency remains the same.

5. **Conclusion**: The frequency of the wave in the string is equal to the frequency of the sound produced. This is a key property of wave behavior: the frequency of the wave is determined by the source (in this case, the plucked string).

### Final Answer:
The correct statement is that the frequency of the wave in the string is equal to the frequency of the sound produced.