Chapter 10, Problem 1RQ

Review Question 10.1

Can we say that the period of vibration depends on the frequency or that the frequency depends on the period? Explain your answer.

To determine

Whether it is correct to say that the period of a vibration depends on the frequency or conversely, frequency depends on the period.

Answer to Problem 1RQ

Solution:

Frequency depends on the time period.

Explanation of Solution

Introduction:

The time period of a vibrating object is the time interval needed for the object to complete one cycle.

The frequency of the vibrational motion is the number of complete vibrations of the system in one second. The frequency is expressed as,

$f=\frac{1}{T}$

Here, $T$ represents time period.

Explanation:

Frequency is defined as the number of the complete vibrations of a system within one second.

On the other hand, the time period of a motion is defined as the time needed to complete one vibration of the motion.

For example: Consider spring and mass system,

Here time period $\left(T\right)$ of oscillation it depends only on mass $\left(m\right)$ and stiffness of spring $\left(k\right)$ as

$T=2\pi \sqrt{\frac{m}{k}}$

Now frequency and time period are related as

$f=\frac{1}{T}$

According to the above equations, the frequency of a vibrational motion is inversely proportional to the time period, that is, the frequency of a vibrational motion is dependent on the time period.

Conclusion:

Therefore, frequency depends on the time period, and time period depends on the mass and other factors.