Two sound sources of frequency `9Hz` and `11Hz` are sounded together then which plot is correct after superposition of sound waves.

Options

A.
B.
C.
D.

Answer

To solve the problem of determining the correct plot after the superposition of sound waves from two sources with frequencies of 9 Hz and 11 Hz, we can follow these steps:

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

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

### Step 3: Calculate the Time Period of the Beats
The time period \( T_b \) of the beats is given by the reciprocal of the beat frequency:
\[ T_b = \frac{1}{f_b} \]
Substituting the value of \( f_b \):
\[ T_b = \frac{1}{2 \, \text{Hz}} = 0.5 \, \text{seconds} \]

### Step 4: Analyze the Graphs
We need to find a graph that shows one beat occurring in 0.5 seconds. This means that in one complete cycle of the beat, we should observe a rise and fall in amplitude corresponding to the beat frequency.

### Step 5: Determine the Correct Plot
- In the correct plot, we should observe that within a time span of 0.5 seconds, there is one complete cycle (one beat).
- If we check the options, we will find that the plot that shows one complete cycle in 0.5 seconds is the correct one.

### Conclusion
Thus, the correct answer is the plot that shows one beat occurring in 0.5 seconds.

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