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
Verified Correct Answer: C.
Physical Principles & Numerical Solution
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
Source: Myschool Past Questions Archive (Record #35682)