A bat is flitting about in a cave, navigating via ultrasonic bleeps. Assume that the sound emission frequency of the bat is 39 .000 Hz. During one fast swoop directly toward a flat wall surface, the bat is moving at 0.020 times the speed of sound in air. What frequency does the bat hear reflected off the wall?

Explanation

To solve the problem, we will use the Doppler effect equations for sound. The bat is emitting sound waves and moving towards a wall, which acts as a reflector. We will calculate the frequency of the sound that the bat hears after it reflects off the wall.

### Step-by-step solution:

1. **Identify the Given Values:**
- Emission frequency of the bat, \( f_0 = 39 \, \text{Hz} \)
- Speed of the bat, \( v_b = 0.02 \times v \) (where \( v \) is the speed of sound in air)
- The speed of sound in air is denoted as \( v \).
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