Revise Doppler effect for sound waves for Cambridge 9702 (7.3)

At its core, the Doppler effect describes how you perceive a different frequency from what a source actually emits, simply because either you, the source, or both are moving. For sound, this means the pitch you hear changes. It's not the source altering its sound; it's the motion altering how those sound waves reach you. When the source and observer are stationary relative to each other, the observed frequency is the same as the source frequency.

Sound waves travel as a series of compressions (regions of high pressure) and rarefactions (regions of low pressure). When a sound source moves, it essentially 'chases' its own wavefronts in the direction of motion, squeezing them together. In the opposite direction, it pulls away from the wavefronts, stretching them out. This changes the spacing between successive wavefronts, which is the wavelength.

To quantify this change in frequency, we use a specific formula. It allows us to calculate the observed frequency ($f_o$) based on the source's emitted frequency ($f_s$), the speed of sound ($v$), and the speed of the source ($v_s$). Remember, this formula applies when the observer is stationary and the source is moving.

$f_o = \frac{f_s \cdot v}{v \pm v_s}$

The diagram for this topic illustrates the effect of a moving source on its emitted wavefronts. In front of the moving source, the wavefronts bunch up, leading to a shorter observed wavelength ($\lambda_o < \lambda_s$) and thus a higher frequency ($f_o > f_s$). Behind the source, the wavefronts spread out, resulting in a longer observed wavelength ($\lambda_o > \lambda_s$) and a lower frequency ($f_o < f_s$). This direct relationship between wavelength and frequency is governed by the wave speed equation, $v = f\lambda$.

It is important to note the limitations of the formula $f_o = f_s \cdot v / (v \pm v_s)$. This version is simplified for the case where the observer is stationary and the source is moving along the line connecting them. Different formulas are required if the observer is also moving or if the motion is not directly along the line of sight. Additionally, this formula assumes the source's speed ($v_s$) is less than the speed of sound ($v$). If $v_s \ge v$, a shock wave (sonic boom) is created.