Question

In a Doppler effect experiment, initially an observer and the source are moving towards each other with equal speeds. The observed frequency in this case is found to be \( f_0 \). The observed frequency once they cross each other is found to be \( f' \). If \( f \) is the frequency at the source, \( f' \) is equal to:

• A. \( \frac{f_0 + f}{\sqrt{f_0 f}} \)
• B. \( \frac{f_0 - f}{f_0} \)
• C. \( \frac{f_0}{f_0} \)
• D. \( f' = f \left( \frac{f_0}{f_0} \right) \)

Hint:

In Doppler effect problems, when both the observer and the source move towards each other, remember that the observed frequency will increase. Use the formula \( f' = f \left( \frac{f_0 + f}{\sqrt{f_0 f}} \right) \) to calculate the new frequency after crossing.

Answer 1

The Correct Option is A

In Doppler effect problems involving relative motion of both the observer and the source, the frequency observed by the observer changes depending on their relative speeds. When both the source and the observer move towards each other with equal speeds, the observed frequency is affected by the relative speed between the source and the observer. The formula for the Doppler effect when both the source and observer are moving towards each other is given by: \[ f' = f \left( \frac{f_0 + f}{\sqrt{f_0 f}} \right) \] where: - \( f_0 \) is the observed frequency, - \( f \) is the frequency at the source. Thus, once the source and observer cross each other, the observed frequency \( f' \) is given by the expression \( \frac{f_0 + f}{\sqrt{f_0 f}} \).