Question

If time period is \(0.02\) second, then frequency will be :

• A. \(50 \ \text{Hz}\)
• B. \(5 \ \text{Hz}\)
• C. \(0.02 \ \text{Hz}\)
• D. \(500 \ \text{Hz}\)

Hint:

The relationship \(f = \frac{1}{T}\) is fundamental for all wave phenomena. - A {short} time period means many cycles happen quickly, so the {frequency is high}. - A {long} time period means cycles happen slowly, so the {frequency is low}. Units are important: \(T\) in seconds (s), \(f\) in Hertz (Hz).

Answer 1

The Correct Option is A

Concept: Time period and frequency are fundamental properties of periodic phenomena like waves or oscillations. They are inversely related. Step 1: Understanding Time Period (T) The time period (\(T\)) is the time taken for one complete cycle of a wave or one full oscillation. Given: Time period \(T = 0.02 \ \text{seconds}\). Step 2: Understanding Frequency (f) Frequency (\(f\)) is the number of complete cycles or oscillations that occur in one second. The unit of frequency is Hertz (Hz), where \(1 \ \text{Hz} = 1 \ \text{cycle per second}\). Step 3: The Relationship between Frequency and Time Period Frequency and time period are reciprocals of each other. The formula connecting them is: \[ f = \frac{1}{T} \] This means that if you know the time period, you can calculate the frequency, and vice-versa (\(T = \frac{1}{f}\)). Step 4: Calculation We are given \(T = 0.02 \ \text{s}\). Substitute this value into the frequency formula: \[ f = \frac{1}{0.02 \ \text{s}} \] To simplify the division by a decimal, you can express \(0.02\) as a fraction: \(0.02 = \frac{2}{100}\). So the equation becomes: \[ f = \frac{1}{\frac{2}{100}} \] When dividing by a fraction, you multiply by its reciprocal: \[ f = 1 \times \frac{100}{2} \] \[ f = \frac{100}{2} \] \[ f = 50 \ \text{Hz} \] Therefore, if the time period is \(0.02\) seconds, the frequency will be \(50 \ \text{Hz}\).