Solution:

Given,
Length of the string, L = 10 m
Number of segments, n = 5
Velocity of wave, v = 20 m/s

We know that the frequency of vibration of a string is given by:

f = (nv)/(2L)

where n is the number of segments and v is the velocity of wave in the string.

Substituting the given values, we get:

f = (5 x 20)/(2 x 10) = 5 Hz

Therefore, the frequency of vibration of the string is 5 Hz.

Explanation:

- Understanding Standing Waves: Standing waves are formed when two identical waves travelling in opposite directions interfere with each other. In a standing wave, the points on the wave that are stationary are called nodes, while the points that undergo maximum displacement are called antinodes.
- Relationship between Frequency, Velocity and Wavelength: The frequency of a wave is inversely proportional to its wavelength and directly proportional to its velocity. That is, f = v/λ.
- Deriving the Formula for Frequency of Vibration of a String: For a string fixed at both ends, the wavelength of the standing wave that is formed is given by λ = 2L/n, where L is the length of the string and n is the number of segments. Therefore, the frequency of the standing wave is given by f = v/λ = (nv)/(2L).
- Solving the Given Problem: In the given problem, we are given the length of the string, the number of segments and the velocity of the wave. We can use the formula for frequency of vibration of a string to find the frequency of the standing wave. Substituting the given values, we get the frequency to be 5 Hz.
- Answer and Explanation: Therefore, the correct answer is option (b) 5 Hz.