Dolphins emit clicks of sound for communication and echolocation. A marine biologist is monitoring a dolphin swimming in seawater where the speed of sound is 1523 m/s. When the dolphin is swimming directly away at 5.5 m/s, the marine biologist measures the number of clicks occuring per second to be at a frequency of 2800 Hz. What is the difference (in Hz) between this frequency and the number of clicks per second actually emitted by the dolphin?

To find the difference in frequency between the observed frequency and the actual emitted frequency, we need to consider the Doppler effect. The Doppler effect describes the change in frequency of a wave (in this case, sound waves) due to the relative motion between the source of the wave (the dolphin) and the observer (the marine biologist).

In this scenario, the dolphin is swimming directly away from the biologist. As a result, the sound waves emitted by the dolphin are stretched out, resulting in a decrease in frequency observed by the biologist.

The formula we can use to calculate the observed frequency is:

Observed Frequency = Actual Frequency * (Speed of Sound + Speed of Observer) / (Speed of Sound + Speed of Source)

Let's calculate the observed frequency first:

Speed of Sound = 1523 m/s
Speed of Observer (marine biologist) = 0 m/s (since the biologist is stationary)
Speed of Source (dolphin) = -5.5 m/s (negative sign indicates that the source is moving away)

Observed Frequency = 2800 Hz * (1523 m/s + 0 m/s) / (1523 m/s - (-5.5 m/s))
= 2800 Hz * (1523 m/s / 1528.5 m/s)
≈ 2793.85 Hz

So, the observed frequency is approximately 2793.85 Hz.

To find the difference in frequency, we subtract the observed frequency from the actual frequency:

Difference in Frequency = Actual Frequency - Observed Frequency
= 2800 Hz - 2793.85 Hz
≈ 6.15 Hz

Therefore, the difference in frequency between the observed frequency and the actual emitted frequency is approximately 6.15 Hz.