The velocity of waves in a string fixed at both ends is 2 m / s . The string forms standing waves with nodes 5.0 cm apart. The frequency of vibration of the string in Hz is

Answer

To solve the problem step by step, we will follow these calculations:

1. **Identify the given values:**
- Velocity of the wave (v) = 2 m/s
- Distance between nodes = 5 cm

2. **Convert the distance between nodes to meters:**
- Since 1 cm = 0.01 m, we convert 5 cm to meters:
\[ 5 \text{ cm} = 5 \times 0.01 \text{ m} = 0.05 \text{ m} \]

3. **Relate the distance between nodes to the wavelength (λ):**
- For standing waves on a string fixed at both ends, the distance between two consecutive nodes is half the wavelength (λ/2).
- Therefore, we can express this as:
\[ \frac{\lambda}{2} = 0.05 \text{ m} \]

4. **Calculate the wavelength (λ):**
- To find λ, we multiply both sides of the equation by 2:
\[ \lambda = 2 \times 0.05 \text{ m} = 0.10 \text{ m} \]

5. **Use the wave speed formula to find the frequency (f):**
- The relationship between wave speed (v), frequency (f), and wavelength (λ) is given by:
\[ v = f \lambda \]
- Rearranging this formula to solve for frequency gives:
\[ f = \frac{v}{\lambda} \]

6. **Substitute the known values into the frequency formula:**
- Substitute v = 2 m/s and λ = 0.10 m:
\[ f = \frac{2 \text{ m/s}}{0.10 \text{ m}} = 20 \text{ Hz} \]

7. **Conclusion:**
- The frequency of vibration of the string is 20 Hz.

### Summary of the Solution:
The frequency of vibration of the string is **20 Hz**.