Final answer:
To determine how fast the osprey is approaching using the observed frequency shift, we apply the Doppler Effect formula rearranged to solve for the osprey's speed. The formula includes the natural frequency of the osprey's call, the observed frequency, and the speed of sound.
Step-by-step explanation:
The question involves the application of the Doppler Effect, which describes the change in frequency of a wave in relation to an observer who is moving relative to the wave source. The osprey's call, which has a natural frequency (f0) of 2200 Hz, is heard at 2315 Hz. To solve this problem, we use the Doppler Effect formula for a source moving towards a stationary observer:
f = f0 * (v / (v - vs))
Where:
f is the observed frequency (2315 Hz).
f0 is the emitted frequency (2200 Hz).
v is the speed of sound.
vs is the speed of the source (osprey).
Rearrange the formula to solve for vs:
vs = v(1 - (f0/f))
Substituting our known values, we find:
vs = v(1 - (2200/2315))
To solve the mathematical problem completely, simply plug in the known value for v (the speed of sound), which is typically around 340 m/s under standard conditions, and calculate the osprey's speed vs. Please replace v with its specific numerical value in your calculations when it is provided.