If the bat emits a sound at a frequency of 80.0 kHz and hears it reflected at a frequency of 83.3 kHz while traveling at a speed of 3.9 m/s , calculate the speed of the insect.
So using the doppler effect I got that
1.04=(344+3.9)/(344-vbug) This is because 83.3/80=1.04 and the frequency incr therefore lambda decr.
I am getting vbug=9.89m/s but apparently it is only 2.0m/s?
Where am I going wrong?
Thank you!
the first thing: what is the direction the bug is flying in relation to the bat? Same direction, opposite direction, or some other direction? You used the speed of sound at 20C, that is pretty cool for bugs flying.
Otherwise, your calculations are OK if they are both approaching each other.
To find the speed of the insect, we can use the doppler effect equation:
f observed = (v sound + v observer) / (v sound + v source) * f source
In this case, the frequency observed (f observed) is 83.3 kHz, the frequency emitted (f source) is 80.0 kHz, the speed of sound (v sound) is 344 m/s, and the speed of the observer (v observer) is 3.9 m/s.
Let's plug in the values and solve for the speed of the insect (v source):
83.3 kHz = (344 m/s + 3.9 m/s) / (344 m/s + v source) * 80.0 kHz
First, let's convert the frequencies from kHz to Hz:
83.3 kHz = 83300 Hz
80.0 kHz = 80000 Hz
Now, let's solve the equation:
83300 Hz = (347.9 m/s) / (344 m/s + v source) * 80000 Hz
Next, let's cross-multiply:
83300 Hz * (344 m/s + v source) = (347.9 m/s) * 80000 Hz
Now, let's cancel out the Hz units:
(83300 Hz) * (344 m/s + v source) = (347.9 m/s) * (80000 Hz)
Next, let's distribute:
28635200 Hz * m/s + 83300 Hz * v source = 27832000 Hz * m/s
Now, let's isolate v source:
83300 Hz * v source = 27832000 Hz * m/s - 28635200 Hz * m/s
Subtracting the terms on the right side:
83300 Hz * v source = -7.032 * 10^5 Hz * m/s
Dividing both sides by 83300 Hz:
v source = -7.032 * 10^5 Hz * m/s / 83300 Hz
Calculating the result:
v source = -84.39 m/s
From your calculations, it looks like you made an error in the math. The correct speed of the insect should be approximately -84.39 m/s. However, since speed cannot be negative in this scenario, it suggests there might be an error in the problem setup or the calculation. Please double-check your formulas and values to ensure accuracy.