How does relative motion between source and observer influence the Doppler effect?

Relative motion between the source and observer changes the perceived frequency and wavelength, causing the Doppler effect.

The Doppler effect is a phenomenon in physics that describes how the frequency and wavelength of a wave change when the source of the wave and the observer are in relative motion. This effect is commonly observed with sound waves, but it also applies to light waves and other types of waves. The change in frequency and wavelength is what causes the characteristic shift in pitch that you hear when a vehicle with a siren passes by, for example.

When the source and the observer are moving towards each other, the observer perceives a higher frequency (or shorter wavelength) than the actual frequency of the wave. This is because the relative motion decreases the distance between the observer and each successive wavefront, causing the waves to reach the observer more frequently. This results in a shift to a higher pitch for sound waves, or a shift to the blue end of the spectrum for light waves (known as blue shift).

Conversely, when the source and the observer are moving away from each other, the observer perceives a lower frequency (or longer wavelength) than the actual frequency of the wave. This is because the relative motion increases the distance between the observer and each successive wavefront, causing the waves to reach the observer less frequently. This results in a shift to a lower pitch for sound waves, or a shift to the red end of the spectrum for light waves (known as red shift).

The magnitude of the Doppler effect depends on the relative speed of the source and the observer. The faster the relative speed, the greater the change in perceived frequency and wavelength. However, the direction of the relative motion also matters. If the source and the observer are moving at right angles to each other, there is no Doppler effect because the distance between the observer and each successive wavefront does not change.

In summary, the relative motion between the source and the observer influences the Doppler effect by changing the perceived frequency and wavelength of the wave. This change is due to the variation in the distance between the observer and each successive wavefront caused by the relative motion.