a flying bat emits squeaks of frequency 80 kHz.if a stationary observer hears the frequency of the squeaks as 78kHz,is the bat moving towards or away from the observer?determine the speed at which the bat is flying.
away of course
in general for non-relativistic Doppler effect
f heard = f emmitted (c+vr)/(c+vs)
c = v of wave
vr = v receiver (plus if toward source)
vs = v source, (plus if source moving away from receiver)
use your c of sound
78 = 80 (c+0)/(c+vs)
given:
fl = 78kHZ
Fs = 80kHz
vl = o (stationary)
vs =?
v =340 m.s-1
fl =v-vl/v+vs•Fs
78 =340-0/340+vs x80
therefore vs=8.72 m.s-1
To determine whether the bat is moving towards or away from the observer, we need to apply the Doppler effect formula. The formula is given by:
f' = (v + vr) / (v + vs) * f
Where:
- f' is the observed frequency
- v is the speed of sound in air
- vr is the velocity of the receiver (observer) relative to the medium (air)
- vs is the velocity of the source (bat) relative to the medium (air)
- f is the emitted frequency
First, let's determine the velocity of the bat.
Given:
- The emitted frequency (f) = 80 kHz
- The observed frequency (f') = 78 kHz
We can rearrange the Doppler effect formula to solve for the velocity of the source:
vs = ((f' / f) - 1) * v
Substituting the given values:
vs = ((78 kHz / 80 kHz) - 1) * v
Now, let's calculate vs:
vs = (0.975 - 1) * v
vs = -0.025 * v
Since there is a negative sign, it indicates that the bat is moving away from the observer.
To determine the speed at which the bat is flying, we need to know the speed of sound in air (v). Let's assume it is 343 m/s, which is approximately the speed of sound at sea level.
Using the formula:
vs = -0.025 * v
Substituting v = 343 m/s:
vs = -0.025 * 343
vs = -8.575 m/s
Therefore, the bat is flying with a velocity of approximately 8.575 m/s away from the observer.