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

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