A string under tension produces a note of frequency 14Hz. Determine the frequency when the tension is quadrupled.
A. 14Hz B. 18Hz C. 28Hz D. 56Hz
Correct Answer: C
Explanation
The formula for the frequency in a stringed instrument : \(f = \frac{1}{2} \sqrt{\frac{T}{m}}\) f = frequency; T = tension in the string; m = mass per unit lenth of the string. f\(_1\) = 14 = \(\frac{1}{2} \sqrt{\frac{T}{m}}\). When T is quadrupled, we have f\(_2\) = new frequency = \(\frac{1}{2} \sqrt{\frac{4T}{m}}\) = 2(\(\frac{1}{2} \sqrt{\frac{T}{m}}\)) = 2 f\(_1\) = 2 x 14 = 28 Hz