The frequency of vibrations of a stretched string is ________wavelength

Options

A. directly 'proportional to
B. inversely proportional to
C. directly proportional to the square of
D. independent of

Explanation

To solve the question regarding the relationship between the frequency of vibrations of a stretched string and its wavelength, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Terms**:
- Frequency (f) is the number of vibrations or cycles per second.
- Wavelength (λ) is the distance between successive crests (or troughs) of a wave.

2. **Identify the Relevant Formula**:
- The relationship between wave speed (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \times \lambda \]
- Here, v is the speed of the wave, f is the frequency, and λ is the wavelength.

3. **Consider Constant Wave Speed**:
- For a stretched string, the speed of the wave (v) is constant when the tension and mass per unit length of the string are fixed.

4. **Rearranging the Formula**:
- We can rearrange the formula to express frequency in terms of wavelength:
\[ f = \frac{v}{\lambda} \]
- This shows that frequency is dependent on wavelength.

5. **Analyze the Relationship**:
- Since v is constant, if the frequency (f) increases, the wavelength (λ) must decrease to keep the product \(f \times \lambda\) constant.
- This indicates that frequency and wavelength are inversely related.

6. **Conclusion**:
- Therefore, we conclude that the frequency of vibrations of a stretched string is **inversely proportional** to its wavelength.

### Final Answer:
The frequency of vibrations of a stretched string is **inversely proportional** to wavelength.