Physics 2011 JAMB Past Questions - Question 26: A length of wire has a frequency of 255Hz when stretched by a force of 225N. If the force increases to 324N , what is new frequency of vibration ?

Correct Answer

B

Explanation

To determine the new frequency of vibration when the force increases, we can use the formula for the relationship between frequency and tension in a stretched wire. The formula is given by:

f = (1/2L) * √(T/μ)

Where:
f is the frequency of vibration,
L is the length of the wire,
T is the tension in the wire, and
μ is the linear mass density of the wire.

In this case, we are given the initial frequency (f = 255 Hz) and the initial force (T = 225 N). We need to find the new frequency when the force increases to 324 N.

Since the length of the wire and the linear mass density are not given, we can assume that they remain constant. Therefore, we can set up a proportion to solve for the new frequency:

f1 / T1 = f2 / T2

Substituting the given values:

255 Hz / 225 N = f2 / 324 N

Now we can solve for f2, the new frequency:

f2 = (255 Hz / 225 N) * 324 N
f2 ≈ 365.6 Hz

Therefore, the new frequency of vibration when the force increases to 324 N is approximately 365.6 Hz.