Doppler Effect: Observed Frequency and Wavelength

Flashcards covering the derivation, formulas, and concepts of observed frequency and wavelength in the Doppler effect for stationary and moving sources.

What determines the speed $v$ of a sound wave as it travels through the air?

The speed of a wave depends only on the medium it is travelling through and is unaffected by the speed of the source.

For a stationary source, what is the formula for the observed wavelength $\lambda_o$ in terms of wave speed $v$ and source frequency $f_s$?

$$\lambda_o = \frac{v}{f_s}$$

When a sound source moves away from an observer at speed $v_s$, what is the length of the section of $f_s$ wavelengths emitted in $1\,s$?

$$v + v_s$$

What is the formula for the observed wavelength $\lambda_o$ when a source moves away from a stationary observer at speed $v_s$?

$$\lambda_o = \frac{v + v_s}{f_s}$$

What is the formula for the observed frequency $f_o$ when a source moves away (receding) from an observer?

$$f_o = \frac{f_s \times v}{v + v_s}$$

When a source moves towards an observer at speed $v_s$, what is the compressed length of the section of $f_s$ wavelengths emitted in $1\,s$?

$$v - v_s$$

What is the formula for the observed frequency $f_o$ when a source moves towards (approaching) an observer?

$$f_o = \frac{f_s \times v}{v - v_s}$$

In the general Doppler effect equation $f_o = \frac{f_s \times v}{v \pm v_s}$, when do the plus and minus signs apply?

The plus sign applies to a receding source, and the minus sign applies to an approaching source.

How does the movement of a sound source affect its source frequency $f_s$ and the wave speed $v$ through the medium?

Neither the frequency $f_s$ of the source nor the wave speed $v$ through the medium is affected by the movement of the source.

Under what conditions other than a source moving relative to a stationary observer can a Doppler effect be heard?

When an observer is moving relative to a stationary source, and when both source and observer are moving.