To determine the frequency of a wave on a string that oscillates in segments, we need to understand the relationship between the number of segments, the length of the string, and the velocity of the wave.
- The string is fixed at both ends and oscillates in 5 segments. This implies that the string is vibrating in its fifth harmonic.
- The formula for the wavelength of the nth harmonic for a string fixed at both ends is given by: \(\lambda_n = \frac{2L}{n}\), where \(L\) is the length of the string and \(n\) is the harmonic number.
- For the fifth harmonic (\(n=5\)), the wavelength will be: \(\lambda_5 = \frac{2 \times 10 \, \text{m}}{5} = 4 \, \text{m}\).
- The wave velocity \((v)\) is given as 20 m/s, and we know the relationship between wave velocity, frequency, and wavelength is: \(v = f \cdot \lambda\).
- Substitute the known values into this formula: \(20 = f \times 4\) which simplifies to: \(f = \frac{20}{4}\).
- Thus, the frequency \((f)\) is calculated to be 5 Hz.
Hence, the correct answer is 5 Hz.