Question

The frequency of the periodic wave for the following figure is 


 

• A. 1 MHz
• B. 0.25 MHz
• C. 0.5 MHz
• D. 0.1 MHz
• E. 0.05 MHz

Hint:

To find frequency from a wave graph, measure the time for one full cycle (from one crest to the next crest). Then use \(f = 1/T\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question asks for the frequency of a periodic wave shown in a graph. Frequency is the number of complete cycles of a wave that occur in one unit of time. It is the reciprocal of the time period (\(T\)), which is the time taken to complete one full cycle.
Step 2: Key Formula or Approach:
The relationship between frequency (\(f\)) and time period (\(T\)) is:
\[ f = \frac{1}{T} \] Step 3: Detailed Explanation:
First, we need to determine the time period (\(T\)) from the given graph.
The graph shows the wave's amplitude (\(y\)) as a function of time (\(t\)). The x-axis represents time in microseconds (\(\mu\)s).
A complete cycle of the wave is the smallest repeating pattern. Looking at the graph:
- The wave starts at \(t=0\), goes up, and stays high.
- At \(t=2 \, \mu\)s, it goes down and stays low.
- At \(t=4 \, \mu\)s, it goes up again, starting the next cycle.
Therefore, the time taken for one complete cycle (the time period) is \(T = 4 \, \mu\)s.
Convert the time period to seconds:
\[ T = 4 \, \mu\text{s} = 4 \times 10^{-6} \, \text{s} \] Now, calculate the frequency using the formula:
\[ f = \frac{1}{T} = \frac{1}{4 \times 10^{-6} \, \text{s}} \] \[ f = 0.25 \times 10^{6} \, \text{Hz} \] The unit \(10^6\) Hz is equivalent to Megahertz (MHz).
\[ f = 0.25 \, \text{MHz} \] Step 4: Final Answer:
The frequency of the periodic wave is 0.25 MHz, which corresponds to option (B).