Bats navigate and search out prey by emitting, and then detecting reflections of, ultrasonic waves, which are sound waves with frequencies greater than can be heard by a human. Suppose a bat emits ultrasound at frequency `f_(be)` = 82.52 kHz while flying with velocity `vecv_b = (9.00 m//s) hati` as it chases a moth that flies with velocity `vecv_m =(8.00 m//s) hati`. What frequency does the moth detect? What frequency `f_(md)` does the bat detect in the returning echo from the moth?

Explanation

To solve the problem, we will use the Doppler Effect formula for sound waves. The Doppler Effect describes how the frequency of a wave changes for an observer moving relative to the source of the wave.

### Step 1: Determine the frequency detected by the moth

1. **Identify the parameters:**
- Frequency emitted by the bat (source): \( f_{be} = 82.52 \, \text{kHz} = 82,520 \, \text{Hz} \)
- Velocity of the bat (source): \( v_b = 9.00 \, \text{m/s} \)
- Velocity of the moth (observer): \( v_m = 8.00 \, \text{m/s} \)
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