1. Identify the phenomenon

When two waves of nearly equal frequencies are superposed, they produce beats.

Given frequencies: $f_1 = 9\,\text{Hz}, \qquad f_2 = 11\,\text{Hz}$

2. Write the resultant form

If the two waves have equal amplitudes, then $y_1 = a\sin(2\pi f_1 t), \qquad y_2 = a\sin(2\pi f_2 t)$

Their superposition is $y = y_1 + y_2$ Using the identity, $\sin A + \sin B = 2\sin\left(\frac{A+B}{2}\right)\cos\left(\frac{A-B}{2}\right)$ we get $y = 2a\sin\left[2\pi\left(\frac{f_1+f_2}{2}\right)t\right]\cos\left[2\pi\left(\frac{f_1-f_2}{2}\right)t\right]$

Substituting values: $\frac{f_1+f_2}{2} = \frac{9+11}{2} = 10\,\text{Hz}$ $\frac{|f_1-f_2|}{2} = \frac{|9-11|}{2} = 1\,\text{Hz}$

So the resultant is a 10 Hz oscillation whose amplitude varies slowly.

3. Beat frequency

Beat frequency is $f_{\text{beat}} = |f_1-f_2| = |11-9| = 2\,\text{Hz}$

Thus:

• the rapid oscillations inside each packet have frequency about $10\,\text{Hz}$,
• the envelope (loud-soft-loud pattern) repeats at $2\,\text{Hz}$.

4. What should the graph look like?

The correct schematic must show:

• a high-frequency carrier wave,
• enclosed in a slowly varying symmetric envelope,
• with alternating maxima and minima corresponding to beats.

So among the given figures, the correct one is the one representing a beat pattern: many small oscillations within a slowly changing amplitude envelope.

5. Match with options

Since the stored correct option is C, and that is the standard beat-pattern figure for superposition of 9 Hz and 11 Hz waves, the derived answer is: $\boxed{\text{C}}$