The correct figure that shows , schematically , the wave pattern produced by superposition of two waves of frequencies 9 Hz and 11 Hz, is :

Options

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Explanation

To solve the problem regarding the wave pattern produced by the superposition of two waves with frequencies of 9 Hz and 11 Hz, we can follow these steps:

### Step 1: Identify the Frequencies
We have two frequencies:
- \( f_1 = 9 \, \text{Hz} \)
- \( f_2 = 11 \, \text{Hz} \)

### Step 2: Calculate the Beat Frequency
The beat frequency is calculated using the formula:
\[ f_{\text{beat}} = |f_2 - f_1| \]
Substituting the values:
\[ f_{\text{beat}} = |11 \, \text{Hz} - 9 \, \text{Hz}| = 2 \, \text{Hz} \]

### Step 3: Determine the Time Period of the Beats
The time period of the beats can be found using the formula:
\[ T_{\text{beat}} = \frac{1}{f_{\text{beat}}} \]
Substituting the beat frequency:
\[ T_{\text{beat}} = \frac{1}{2 \, \text{Hz}} = 0.5 \, \text{seconds} \]
This means that in 0.5 seconds, there will be one complete cycle of rise and fall in the intensity of the resultant wave.

### Step 4: Analyze the Wave Pattern
Since the beat frequency is 2 Hz, this indicates that the wave pattern will show a rise and fall in intensity twice every second. Thus, the wave pattern will have a periodicity of 0.5 seconds.

### Step 5: Choose the Correct Figure
To find the correct schematic representation of the wave pattern, we look for a graph that shows:
- A complete cycle of rise and fall occurring in 0.5 seconds.
- The wave pattern should reflect the superposition of two waves, showing alternating constructive and destructive interference.

### Conclusion
The correct figure will be the one that depicts the wave pattern with a cycle of rise and fall every 0.5 seconds, corresponding to the calculated beat frequency of 2 Hz.

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