The Doppler Effect: How Waves Are Received at Destination with Altered Wavelength

The Doppler Effect is a phenomenon observed when waves or particles change their frequency due to relative motion between the source and the observer. This phenomenon is crucial in various fields, from astronomy to telecommunications. In this article, we will explore the mechanism of the Doppler Effect and how it affects the received waves at their destination with altered wavelengths.

Understanding the Doppler Effect

The Doppler Effect is caused by relativistic motion relative to each other. Whether the source of a signal is moving relative to the observer or vice versa, as long as either one is in motion, the frequency of the signal changes. What matters is the change in the distance between the source and the observer, not which entity is moving.

Frequency and Wavelength Alteration

When the distance between the source and the observer decreases, the frequency of the signal increases, and the wavelength shortens. Conversely, when the distance increases, the frequency decreases, and the wavelength lengthens. This alteration is governed by the principle of conservation of energy. The energy in the relativistic motion involved in this energetic transaction is reflected in the change of frequency and wavelength.

Consequences of Relativistic Motion

Let's consider a scenario where you are moving away from a source of sound. The source emits a pure tone, a sound wave consisting of alternating peaks and troughs of pressure and density. These peaks and troughs form spherical surfaces known as wavefronts in space.

The Wavefronts and Relativistic Motion

At a certain initial time, you receive a maximum positive wavefront at a distance d from the source. The source then emits the maximally negative wavefront 10 ms later, indicating a frequency of 100 Hz. From the source's perspective, the wavefronts are separated by a distance of half-wavelength, (frac{lambda}{2} v_s t), where (v_s) is the speed of sound, and (t) is the time difference between the emission of wavefronts.

However, since you are moving away from the source at speed (v), in that 10 ms, you have moved farther by a distance (vt). Consequently, the second wavefront has to travel a longer distance to reach you. This delay in the arrival of successive wavefronts from your perspective results in a longer time interval between the two wavefronts being received compared to the time interval between their emission from the source. This change in time interval leads to a lower perceived frequency and a longer wavelength.

Conclusion

The Doppler Effect is a fascinating phenomenon that showcases the interplay between waves and motion. Whether it's sound, light, or any other form of wave, understanding the Doppler Effect is essential for comprehending how and why the perceived frequency and wavelength of a wave can change due to the motion of the source or the observer. This knowledge has wide-ranging applications, from medical imaging to space exploration.