PASSAGE-III: An Unidentified Flying Object (UFO) lands on a planet at a point 5 kilometres from an active volcano. There is a volcanic explosion. The time interval between the flash of light from the volcanic explosion and the sound of eruption was registered as 100 s. The time period of wave is 2 s.
Frequency of the wave is

Options

A. 0.001 Hz
B. 0.01 Hz
C. 0.5 Hz
D. 1.0 Hz

Explanation

To find the frequency of the sound wave produced by the volcanic eruption, we can use the relationship between frequency and time period. Here’s a step-by-step solution:

### Step 1: Understand the relationship between frequency and time period
Frequency (f) is defined as the number of oscillations (or cycles) per second. It is mathematically expressed as:
\[ f = \frac{1}{T} \]
where T is the time period of the wave.

### Step 2: Identify the given time period
From the question, we know that the time period (T) of the wave is given as 2 seconds.

### Step 3: Substitute the time period into the frequency formula
Now, we can substitute the value of T into the frequency formula:
\[ f = \frac{1}{T} = \frac{1}{2 \text{ s}} \]

### Step 4: Calculate the frequency
Now, calculate the frequency:
\[ f = \frac{1}{2} = 0.5 \text{ Hz} \]

### Step 5: State the final answer
The frequency of the sound wave from the volcanic eruption is:
\[ f = 0.5 \text{ Hz} \]

### Conclusion
The correct option that matches this frequency is option 3, which is 0.5 Hz.

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