Answer :
The new frequency of the violin string after the tension is decreased by a factor of 2.5 is roughly 186 Hz, calculated by using the relationship between tension and frequency for a string fixed at both ends.
The frequency of a string fixed at both ends, like a violin string, is determined by the string's length, tension, and mass per unit length.
When the tension in a violin string tuned to a frequency of 294 Hz is reduced, the new frequency can be found by using the properties of wave motion.
The equation for the frequency f of a string is given by: f = (1/2L) * sqrt(T/μ), where L is the length, T is the tension, and μ is the mass per unit length.
The frequency is directly proportional to the square root of the tension.
If the tension is decreased by a factor of 2.5, the new tension T' is T/2.5. We can calculate the new frequency f' using the following steps:
- Determine the initial tension (which is not necessary for the calculation as we are looking for a ratio).
- Apply the change in tension: T' = T/2.5.
- Calculate the square root of the tension ratio: sqrt(T'/T) = sqrt(1/2.5).
- Calculate the new frequency: f' = f * sqrt(T'/T).
Carrying out the calculation:
- sqrt(1/2.5) ≈ 0.6325
- f' = 294 Hz * 0.6325 ≈ 186 Hz
Therefore, the new frequency of the string is 186 Hz.
