If the speed of a transverse wave on a stretched string of length 1 m is `60 m s^-1`, what is the fundamental frequency of vibration ?

Explanation

To find the fundamental frequency of vibration for a transverse wave on a stretched string, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We are given the speed of a transverse wave on a stretched string and the length of the string. We need to find the fundamental frequency of vibration.

2. **Identify the Parameters**:
- Length of the string, \( L = 1 \, \text{m} \)
- Speed of the wave, \( v = 60 \, \text{m/s} \)

3. **Determine the Wavelength for the Fundamental Frequency**:
- For a string fixed at both ends, the fundamental mode (first harmonic) has a wavelength \( \lambda \) that is twice the length of the string. This relationship can be expressed as:
\[ \lambda = 2L \]
- Substituting the length of the string:
\[ \lambda = 2 \times 1 \, \text{m} = 2 \, \text{m} \]

4. **Calculate the Fundamental Frequency**:
- The fundamental frequency \( f \) can be calculated using the formula:
\[ f = \frac{v}{\lambda} \]
- Substituting the values we have:
\[ f = \frac{60 \, \text{m/s}}{2 \, \text{m}} = 30 \, \text{Hz} \]

5. **Conclusion**:
- The fundamental frequency of vibration for the string is \( 30 \, \text{Hz} \).

### Final Answer:
The fundamental frequency of vibration is \( 30 \, \text{Hz} \).