Physics 2008 JAMB Past Questions - Question 29: When the length of a vibrating string is reduced by one third its frequency becomes

Correct Answer

A

Explanation

When the length of a vibrating string is reduced by one third (which means it becomes 2/3 of its original length), the frequency of vibration will increase. This change in frequency is due to the fundamental relationship between the length of a vibrating string and its frequency.

The frequency of vibration of a string is inversely proportional to its length, assuming all other factors like tension and mass per unit length remain constant. This relationship is described by the following formula:

f = (1 / (2L)) * sqrt(T/μ)

Where:
- f is the frequency of vibration.
- L is the length of the string.
- T is the tension in the string.
- μ is the mass per unit length of the string.

If the length of the string is reduced to 2/3 of its original length (i.e., L becomes 2/3L), the new frequency (let's call it f') can be calculated as:

f' = (1 / (2(2/3)L)) * sqrt(T/μ)

Simplifying this expression:

f' = (3/2) * (1 / (2L)) * sqrt(T/μ)

f' = (3/2) * f

So, when the length of the string is reduced by one third (2/3 of the original length), the frequency becomes 3/2 times the original frequency. In other words, the frequency increases by a factor of 3/2 or 1.5 times.