A flying bat emits squeaks at a frequency of 80 MHz, if a stationary observer picks up the frequency of the squeaks as 78 MHz, is the bat moving towards or away from the listener? Determine the speed of the bat.
Fb = 80 kHz = Freq. emitted by the bat.
Fh = 78 kHz = Freq. heard.
Vs = 343 m/s = Velocity of sound in air.
a. The bat is moving away.
b. Fh = (Vs-Vr)/(Vs+Vb) * Fb = 78 kHz
(343-0)/(343+Vb) * 80 = 78
Solve for Vb, the velocity of the bat.
To determine if the bat is moving towards or away from the listener, we need to consider the concept of the Doppler effect.
The Doppler effect states that when a source of sound waves, like the flying bat, is moving relative to an observer, the frequency of the sound waves changes. If the source is moving towards the observer, the frequency appears higher, whereas if the source is moving away, the frequency appears lower.
In this case, we're given that the bat emits squeaks at a frequency of 80 MHz (80 million hertz). The stationary observer picks up the frequency as 78 MHz (78 million hertz). Since the observed frequency is lower than the emitted frequency, we can conclude that the bat is moving away from the listener.
Now, let's determine the speed of the bat. We can use the formula for the Doppler effect:
\(f = f_0 \cdot \dfrac{v + v_o}{v + v_s}\)
Where:
\(f\) is the observed frequency,
\(f_0\) is the emitted frequency,
\(v\) is the speed of sound (assumed to be constant),
\(v_o\) is the velocity of the observer relative to the medium,
\(v_s\) is the velocity of the source relative to the medium.
In this case, the observed frequency (\(f\)) is 78 MHz, the emitted frequency (\(f_0\)) is 80 MHz, and we want to find \(v_s\).
The formula can be rearranged as:
\(v_s = v \cdot \dfrac{f_0 - f}{f_0 + f}\)
Given that the speed of sound (\(v\)) is approximately 343 meters per second (in air at room temperature), we can substitute the values into the formula:
\(v_s = 343 \, \text{m/s} \cdot \dfrac{80 \times 10^6 - 78 \times 10^6}{80 \times 10^6 + 78 \times 10^6}\)
Now, we can calculate the value of \(v_s\) to find the speed of the bat.