A bat flying at 5.5 m/s emits a chirp at 35 kHz. If this sound pulse is reflected by a wall, what is the frequency of the echo received by the bat?
______ kHz (Assume the speed of sound is 345 m/s.)
thanks for any help
To find the frequency of the echo received by the bat, we need to consider the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the waves.
In this case, the bat is the source of the sound wave and the wall is the reflecting surface. When the sound wave is reflected by the wall, its frequency will change relative to the bat.
The formula for the Doppler effect in terms of frequency is:
f' = f * (v + v₀) / (v - v₀)
Where:
f' is the frequency observed by the observer (bat) after reflection
f is the frequency of the sound wave emitted by the bat before reflection
v is the speed of sound
v₀ is the velocity of the bat
We are given:
f = 35 kHz (35,000 Hz)
v = 345 m/s (speed of sound)
v₀ = 5.5 m/s (velocity of the bat)
By substituting the given values into the formula, we can calculate the frequency of the echo received by the bat.
f' = 35 kHz * (345 m/s + 5.5 m/s) / (345 m/s - 5.5 m/s)
Simplifying the formula, we have:
f' = 35 kHz * (350.5) / (339.5)
Calculating this expression gives us the frequency of the echo received by the bat.
f' ≈ 36.26 kHz
Therefore, the frequency of the echo received by the bat is approximately 36.26 kHz.