A flying bat emits squeaks at a frequency of 80 kHz. If a stationary observer picks up the frequency of the squeaks as 78 kHz, determine the speed at which the bat is flying
To determine the speed at which the bat is flying, we will use the Doppler Effect formula:
Δf/f₀ = v/c,
where Δf is the change in frequency, f₀ is the original frequency, v is the velocity of the source (in this case, the bat), and c is the speed of sound in air.
In this scenario, the original frequency (f₀) is 80 kHz, and the observed frequency (f) is 78 kHz. The change in frequency (Δf) can be calculated by subtracting the observed frequency from the original frequency:
Δf = f - f₀ = 78 kHz - 80 kHz = -2 kHz.
Since the bat is flying towards the observer, the change in frequency is negative. Now, we can rearrange the Doppler Effect formula to solve for the velocity (v) of the bat:
v = (c * Δf) / f₀.
The speed of sound in air (c) is approximately 343 m/s. Substituting the given values into the equation:
v = (343 m/s * -2 kHz) / 80 kHz.
Simplifying:
v = (343 m/s * -2) / 80 = -8.575 m/s.
The negative sign indicates that the bat is flying towards the observer at a speed of 8.575 m/s.