Final answer:
The frequency heard by the moth as a bat approaches it is calculated using the Doppler effect formula. With an emitted frequency of 35.0 kHz and bat speed of 3.25 m/s, the frequency heard by the stationary moth is approximately 35.353 kHz.
Step-by-step explanation:
The question is asking for the frequency heard by the moth when a bat approaches it while emitting sound. To find this, we apply the Doppler effect formula for sound. The Doppler effect describes the change in frequency (or wavelength) of a wave in relation to an observer moving relative to the source of the waves.
The formula for the frequency heard by a stationary observer when the source is moving toward the observer is:
f' = f (v + vo) / (v - vs)
where:
f' is the observed frequency,
f is the emitted frequency,
v is the speed of sound,
vo is the speed of the observer (moth, which is 0 in this case as the moth is at rest),
vs is the speed of the source (bat).
Given:
f = 35.0 kHz,
vs = 3.25 m/s,
Assuming v (the speed of sound) is approximately 343 m/s at room temperature,
Let's plug in the values:
f' = 35.0 kHz * (343 m/s + 0) / (343 m/s - 3.25 m/s) = 35.0 kHz * (343 m/s) / (339.75 m/s) = 35.353 kHz
So, the frequency heard by the moth will be approximately 35.353 kHz.