Chapter 25, Problem 35A

If you double the frequency of a vibrating object, what happens to its period?

To determine

To estimate: The effect of doubling the frequency of a vibrating object on its period.

Answer to Problem 35A

The period gets halved

Explanation of Solution

Given:

The frequency of a vibrating object is doubled from its original value.

Formula used:

The frequency f of a wave is defined as the number of cycles completed in one second and the fundamental period or period, T is the duration for completing one full cycle. They are related mathematically as,

  $f=\frac{1}{T}$

Thus, frequency is inversely proportional to the time period of a vibration.

Calculation:

Here, the new frequency is double the initial value. Considering this fact in the above equation,

  $\begin{array}{c}2f=\frac{2}{T}\\ =\frac{1}{T/2}\end{array}$

This implies that, when frequency is doubled, the time period gets halved.