A string under tension produces a note of frequency 14Hz. Determine the frequency when the tension is quadrupled.
Answer Details
The frequency of a note produced by a string under tension is directly proportional to the square root of the tension. This relationship is given by the equation:
f = (1/2L) √(T/μ)
Where f is the frequency, T is the tension, L is the length of the string and μ is the linear mass density of the string.
Since the length and mass density of the string are constant, we can say that the frequency is directly proportional to the square root of the tension:
f ∝ √T
So, if we quadruple the tension, the frequency will double. Therefore, the frequency produced by the string when the tension is quadrupled will be:
f' = 2f = 2 × 14Hz = 28Hz
Therefore, the correct answer is 28Hz.