Detector \( D \) moves from \( A \) to \( B \) and observes the frequencies are differing by 10 Hz. The source is emitting frequency \( f_0 \) as shown: Speed of detector is 35 times less than speed of sound. Then \( f_0 \) is.
Show Hint
When solving Doppler effect problems, ensure the correct use of the formula for moving sources and observers, and apply the relative velocities correctly.
Step 1: Doppler effect formula.
The Doppler effect formula for the change in frequency when the detector moves towards or away from the source is given by:
\[
\Delta f = f_0 \left( \frac{v}{v - v_s} - \frac{v}{v + v_s} \right)
\]
where \( v \) is the speed of sound, \( v_s \) is the speed of the detector, and \( f_0 \) is the emitted frequency.
Step 2: Apply the given information.
We are given that the speed of the detector is 35 times less than the speed of sound. From the Doppler effect formula, we can calculate \( f_0 \) based on the frequency difference of 10 Hz.
Step 3: Conclusion.
After solving the equation, we find that \( f_0 = 250 \, \text{Hz} \).
Final Answer:
\[
\boxed{250 \, \text{Hz}}
\]
