You are flying in an ultra-light aircraft at a speed of 41.4 m/s. An eagle, whose speed is 21.7 m/s, is flying directly toward you. Each of the given speeds is relative to the ground. The eagle emits a shrill cry whose frequency is 3680 Hz. The speed of sound is 330 m/s. What frequency do you hear?
I got 3020 Hz, but that's wrong apparently, pls help!!!
the transmitter is coming toward you at a relative speed of 63.1 m/s
You will therefore hear a HIGHER frequency.
http://hyperphysics.phy-astr.gsu.edu/hbase/Sound/dopp.html
f' = [ v/(v-vs) ] f
f' = [330 / (330 - 63.1) ] 3680
F = ((Vs+Va)/(Vs-Ve)) * Fe.
F = ((330+41.4)/(330-21.7)) * 3680 = 4433.2 Hz.
Vs = Velocity of sound.
Va = velocity of the aircraft.
Ve = velocity of the eagle.
Fe = Freq. emitted by the eagle.
To find the frequency you hear, we need to consider the Doppler effect. The Doppler effect occurs when there is relative motion between the source of a sound wave and the observer.
In this case, the eagle is the source of the sound wave (shrill cry), and you are the observer. The frequency you hear will be affected by the relative motion between the two.
To calculate the frequency you hear, we can use the following formula for the Doppler effect on sound waves:
f' = f * (v + vo) / (v + vs)
Where:
f' is the frequency the observer hears,
f is the frequency emitted by the source,
v is the speed of sound,
vo is the speed of the observer (you), and
vs is the speed of the source (the eagle).
Let's substitute the given values into the formula:
f = 3680 Hz (frequency emitted by the eagle)
v = 330 m/s (speed of sound)
vo = 41.4 m/s (your speed)
vs = -21.7 m/s (negative sign indicates the source is moving towards you)
Plugging in the values:
f' = 3680 * (330 + 41.4) / (330 - 21.7)
Now let's calculate the value:
f' = 3680 * 371.4 / 308.3
= 4435720 / 308.3
≈ 14381 Hz
Therefore, the frequency you hear is approximately 14381 Hz.