Answer :
Final answer:
To increase the frequency of a violin string by 20%, the tension must be increased by 44%, as the tension is proportional to the square of the frequency. Therefore, the answer is B) 44%.
Explanation:
To determine the change in tension required to increase the frequency of a violin string by 20%, we use the formula for the frequency of a vibrating string on a musical instrument, which is based on the wave speed on the string (c), the length of the string (L), and the tension in the string (T).
The formula for frequency is given as f = (1/2L) * sqrt(T/μ), where μ is the linear mass density of the string.
Increasing the frequency by 20% implies the new frequency is 1.20 times the original frequency.
Given that the wave speed c is proportional to the square root of the tension T, if the frequency increases by a factor of 1.20, then the wave speed must also increase by a factor of 1.20.
Since c^2 = T/μ, this means (1.20)^2 = 1.44.
This indicates that the tension must be increased by a factor of 1.44, or a 44% increase, to achieve a 20% increase in frequency.
Therefore, the answer is B) 44%.
