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Since the wind is blowing from the source to the wall, we can assume that the apparent frequency of the source will be slightly higher when perceived by the observer due to the Doppler effect. Let's denote the frequency of the source as \(f_s\) and the velocity of sound with respect to the wind and wind speed as \(v\) and \(v_w\), respectively. We have: - \(f_s = 30\,\text{Hz}\), - \(v = 330\,\text{m/s}\), - \(v_w = 30\,\text{m/s}\). Using the Doppler effect formula for sound moving towards the observer, we get: \[f_o = f_s\frac{v + v_{o}}{v - v_{s}}\] Here, \(f_o\) is the frequency observed by the observer. Since the source is stationary, \(v_s = 0\), and we can ignore the wind velocity relative to the observer, so \(v_o = 0\). Then, the above formula becomes: \[f_o = f_s\frac{v}{v - 0}\] Let's find \(f_o\).

Now we have to consider the reflection of the wave off of the wall. When the wave is reflected, it will be traveling towards the source, and the perceived frequency will be higher. Let's denote the frequency of the reflected wave as \(f_r\). We can use the same Doppler effect formula, considering that the reflected wave is moving towards the source: \[f_r = f_o\frac{v + v_{s}}{v - v_{o}}\] Here, \(v_s\) represents the wind velocity relative to the reflected wave, and since the wind is moving in the same direction as the wave, we have \(v_s = v_w = 30\,\text{m/s}\). Also, \(v_o = 0\). Then, the above formula becomes: \[f_r = f_o\frac{v + v_w}{v}\] Let's find \(f_r\).

Now that we have the frequencies of the original and reflected waves (\(f_o\) and \(f_r\), respectively), we can determine the beat frequency, which is the difference in frequencies between these two waves. The beat frequency formula is given by: \[f_{beat} = |f_r - f_o|\] Using our previous calculations, we will find the number of beats heard by the observer.

Now that we have calculated the beat frequency (\(f_{beat}\)), we can compare it to the given options (A) 10, (B) 3, (C) 6, and (D) Zero. Choose the option that matches the value of \(f_{beat}\) calculated in Step 3. In conclusion, by analyzing the impact of the wind on the apparent frequencies of the source and reflected waves and using the beat frequency formula, we have determined the number of beats heard by the observer.