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: Option 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