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Understanding how to calculate frequency is crucial when dealing with the Doppler Effect. It's a phenomenon observed when the source and the observer are moving relative to each other. In this exercise, we are dealing with sound frequency that changes due to this relative motion.

The Doppler Effect provides us with a formula to calculate the observed frequency, taking into account the speeds of both the source and the observer relative to the medium through which the sound travels (often air, where sound speed is given). Here's the key formula we use:\[f_{observed} = f_{source} \left( \frac{v_{sound} + v_{observer}}{v_{sound} - v_{source}} \right)\]

• \(f_{observed}\) is the frequency heard by the observer.
• \(f_{source}\) is the original frequency of the sound, which in this case is the eagle's cry at 3400 Hz.
• \(v_{sound}\) is the speed of sound in the medium, here it's 330 m/s.
• \(v_{observer}\) and \(v_{source}\) are the speeds of the observer and the source relative to the ground.

By substituting the given values, we determine the frequency that the observer, or pilot, hears. Calculating this frequency helps to understand how sound waves behave when there is motion involved.

Relative motion is the movement of one object with respect to another. It's an essential concept in physics, especially when analyzing situations involving the Doppler Effect.

In our situation, the observer (pilot in the ultralight aircraft) and the source (eagle) are moving towards each other relative to the ground. This relative motion affects how sound waves are perceived.

The speeds of both the observer and the source must be considered as they move in opposite directions towards one another. These speeds directly affect the frequency of the sound wave that the observer hears.

• The observer's speed, in this case, is 39 m/s.
• The source's speed is 18 m/s.

This closing speed is crucial for applying the Doppler Effect formula correctly; it accounts for the increase in perceived frequency because the two are moving closer.

Understanding this relative motion allows us to apply the correct mathematical adjustments in the formula, leading to an accurate calculation of the observed frequency.

Sound waves are fundamental to understanding the Doppler Effect. They are longitudinal waves that travel through various media and are affected by factors such as speed of the medium and objects within it.

The speed of sound in air is a common reference, typically about 330 m/s under normal conditions, and it plays a key role in determining how sound is propagated when either the source or the observer is moving.

• Sound waves consist of compressions and rarefactions.
• They are subject to changes in frequency and wavelength based on relative motion.

When the source or observer moves, the frequency and wavelength adjust in such a way that the observer hears a different frequency from the source frequency. This change is precisely what we calculate using the Doppler Effect formula.

Sound waves are an excellent example of how wave properties like frequency and wavelength can be affected by motion. Learning how these waves behave helps in understanding and predicting phenomena like the sonic boom or the varying pitch of a passing siren.