Overview
This lecture explains the Doppler effect, which is the change in observed frequency or pitch of a sound due to relative motion between the sound source and the observer.
The Doppler Effect: Concept & Explanation
- The Doppler effect is a change in frequency or pitch detected by an observer when the sound source and observer move relative to each other.
- If the source moves toward the observer, the observed wavelength shortens and frequency increases (higher pitch).
- If the source moves away from the observer, the wavelength lengthens and frequency decreases (lower pitch).
- The speed of sound in air is constant, so changes in wavelength directly affect frequency.
Mathematical Formulation: Moving Source
- For a stationary observer and moving source:
- Observed frequency ( f_o = f_s \frac{v}{v \mp v_s} )
- ( v ) = speed of sound, ( v_s ) = speed of source, ( f_s ) = source frequency.
- Use minus sign if the source moves toward the observer; plus sign if moving away.
Example: Passing Train Problem
- Given train speed (44.7 m/s), horn frequency (415 Hz), and speed of sound (343 m/s).
- Approaching observer: observed frequency ≈ 477 Hz.
- Receding (leaving) observer: observed frequency ≈ 367 Hz.
- The observed frequency is higher when the source approaches and lower when it recedes.
- Wavelength can be found using ( \lambda = v / f_o ).
Doppler Effect: Moving Observer
- For a moving observer and stationary source:
- Observed frequency ( f_o = f_s (1 \pm v_o / v) )
- ( v_o ) = speed of observer; use plus sign when moving toward, minus when moving away from the source.
General Doppler Effect Equation
- Most general case:
- ( f_o = f_s \frac{(v \pm v_o)}{(v \mp v_s)} )
- Plus in numerator when observer moves toward the source; minus in denominator when source moves toward observer.
Key Terms & Definitions
- Doppler Effect — observed change in frequency due to relative motion between a wave source and an observer.
- Frequency (( f )) — number of wave cycles per second (Hz).
- Wavelength (( \lambda )) — distance between successive wave peaks.
- Speed of Sound (( v )) — speed at which sound travels through a medium (usually ≈ 343 m/s in air).
Action Items / Next Steps
- Watch the optional Doppler effect demonstration video in the course playlist.
- Review sound applications in the medical field in the next course video.