Two eagles fly directly toward one another, the first at 15.0 m/s and the second at 21.0 m/s. Both screech, one emitting a frequency of 3200 Hz and the other one of 3800 Hz. What frequencies do they receive if the speed of sound is 330 m/s?
To determine the frequencies that the eagles receive, we need to consider the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave when the source and observer are in relative motion.
For the first eagle, since it is moving towards the source of the sound, the frequency it receives will be higher than the emitted frequency. This can be calculated using the formula:
f1 = (v + vo) / (v + vs) * fs
Where:
f1: Frequency received by the first eagle
v: Speed of sound
vo: Velocity of the first eagle (towards the source)
vs: Velocity of the sound source (second eagle)
fs: Frequency emitted by the second eagle
Substituting the given values:
f1 = (330 + 15) / (330 - 21) * 3800 Hz
Now, let's calculate the frequency received by the first eagle:
f1 = (345 / 309) * 3800 Hz
f1 ≈ 4244.69 Hz
Therefore, the first eagle receives a frequency of approximately 4244.69 Hz.
For the second eagle, since it is moving away from the source of the sound, the frequency it receives will be lower than the emitted frequency. Using the same formula, we can find the frequency received by the second eagle:
f2 = (v - vo) / (v - vs) * fs
Substituting the given values:
f2 = (330 - 15) / (330 + 21) * 3200 Hz
Now, let's calculate the frequency received by the second eagle:
f2 = (315 / 351) * 3200 Hz
f2 ≈ 2856.13 Hz
Therefore, the second eagle receives a frequency of approximately 2856.13 Hz.
In summary, the frequencies received by the two eagles are approximately 4244.69 Hz and 2856.13 Hz, respectively.