A bat flies toward a wall at a speed of 3.5 m/s. As it flies, the bat emits an ultrasonic sound wave with frequency 30.5 kHz. What frequency does the bat hear in the reflected wave?

kHz

To find the frequency of the reflected wave, we need to consider the Doppler effect. The Doppler effect refers to the change in frequency of a wave due to the relative motion between the source of the wave and the observer.

In this scenario, the bat is emitting an ultrasonic sound wave towards a wall. As the wave hits the wall, it gets reflected back towards the bat. The frequency of the reflected wave observed by the bat will be different from the emitted frequency due to the relative motion.

The Doppler effect formula for frequency is:

f' = (v + v₀) / (v - vₑ) * f,

Where:
f' is the frequency of the reflected wave (what the bat hears),
v is the speed of sound in air,
v₀ is the velocity of the bat,
vₑ is the velocity of the wall (assuming it's stationary),
f is the frequency of the emitted wave.

Given:
v = speed of sound in air = approximately 343 m/s,
v₀ = velocity of the bat = 3.5 m/s,
vₑ = velocity of the wall (assumed stationary) = 0 m/s,
f = frequency of the emitted wave = 30.5 kHz = 30,500 Hz.

Substituting these values into the formula:

f' = (343 + 3.5) / (343 - 0) * 30,500,
f' = (346.5 / 343) * 30,500,
f' = 30,849 Hz.

Therefore, the frequency that the bat hears in the reflected wave is approximately 30,849 Hz, or 30.8 kHz.