If two sound waves, `y_(1) = 0.3 sin 596 pi[t - x//300]` and` y_(2) = 0.5 sin 604 pi [t - x//330]` are superimposed, what will be the
(a) frequencyof resultant wave

Explanation

To find the frequency of the resultant wave when two sound waves are superimposed, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angular Frequencies:**
The given sound waves are:
- \( y_1 = 0.3 \sin(596 \pi [t - \frac{x}{300}]) \)
- \( y_2 = 0.5 \sin(604 \pi [t - \frac{x}{330}]) \)

From these equations, we can identify the angular frequencies (\( \omega_1 \) and \( \omega_2 \)):
- \( \omega_1 = 596 \pi \)
- \( \omega_2 = 604 \pi \)

2. **Calculate the Average Angular Frequency:**
The average angular frequency (\( \omega_{\text{avg}} \)) can be calculated using the formula:
\[ \omega_{\text{avg}} = \frac{\omega_1 + \omega_2}{2} \]
Substituting the values:
\[ \omega_{\text{avg}} = \frac{596 \pi + 604 \pi}{2} = \frac{1200 \pi}{2} = 600 \pi \]

3. **Relate Angular Frequency to Frequency:**
The relationship between angular frequency (\( \omega \)) and frequency (\( f \)) is given by:
\[ \omega = 2 \pi f \]
Thus, we can express the frequency of the resultant wave as:
\[ f_{\text{resultant}} = \frac{\omega_{\text{avg}}}{2 \pi} \]

4. **Substitute the Average Angular Frequency:**
Now substituting \( \omega_{\text{avg}} \):
\[ f_{\text{resultant}} = \frac{600 \pi}{2 \pi} = 300 \text{ Hz} \]

5. **Final Answer:**
Therefore, the frequency of the resultant wave is:
\[ \boxed{300 \text{ Hz}} \]