A string under tension produces a note of frequency 14Hz. Determine the frequency when the tension is quadrupled.
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
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