A bat moving with a speed of 3.55 m/s and emitting sound of 34.0 kHz approaches a moth at rest on a tree trunk. What frequency is heard by the moth? Calculate the frequency heard by the moth when the speed of the bat is 5.55 m/s.

To calculate the frequency heard by the moth when the bat is moving, we need to consider the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave as observed by an observer moving relative to the source of the wave.

The formula to calculate the frequency observed (f') is:

f' = f * (v + vr) / (v + vs)

Where:
- f is the frequency of the source wave (emitted by the bat)
- v is the speed of sound (approximately 343 m/s in air at room temperature)
- vr is the speed of the moth relative to the air (since the moth is at rest on the tree trunk, its velocity is zero)
- vs is the speed of the bat relative to the air

Let's calculate the frequency heard by the moth when the bat's speed is 3.55 m/s:

f' = 34.0 kHz * (343 m/s + 0 m/s) / (343 m/s + 3.55 m/s)
= 34.0 kHz * (343 m/s) / (346.55 m/s)
≈ 33.7 kHz

Therefore, the frequency heard by the moth when the bat's speed is 3.55 m/s is approximately 33.7 kHz.

Now let's calculate the frequency heard by the moth when the bat's speed is 5.55 m/s:

f' = 34.0 kHz * (343 m/s + 0 m/s) / (343 m/s + 5.55 m/s)
= 34.0 kHz * (343 m/s) / (348.55 m/s)
≈ 33.3 kHz

Therefore, the frequency heard by the moth when the bat's speed is 5.55 m/s is approximately 33.3 kHz.