Doppler effect Eeeeeee – yowwwwwwwwww A change in frequency or pitch of a sound detected by an observer. Unless specified – assume that the speed of sound waves in the air is 343 m/s This velocity is a fair estimate under most daily conditions

Stationary source production of sound waves Velocity of source (vs) = 0 Both women hear the same sound (pitch)

Moving source production of sound waves Velocity vector in direction (vs) has positive value Hears lower pitch – longer λ hears higher pitch – shorter λ

HOW DOES IT WORK??? Let’s start with a review of equations: λ = V(wave) / f units: m (per wave) f = V(wave) / λ units: waves / s T = λ / V(wave) = 1 / f units: s / wave

How about a visual here Stationary source: 1 pulse/s (siren)  Moving pulse: 1 pulse/s (siren v = .5m/s)

A distinction: λ = the wavelength that is emitted by a source = what is observed by someone who is moving along with that source. λ’ = the wavelength that an observer hears when not moving along with the source

λ = 1m λ’ = .5m λ’ (in m/wave) = the wavelength that the observer hears as the sound source moves toward them λ’ = λ - V sound source x period (if the source is moving toward the observer) λ’ = λ - (V source) (T) (if the source is moving toward the observer) Or: λ’ = λ + (V source) (T) (if the source is moving away from the observer) And another relationship for you: The change in wavelength (from what is produced to what is observed by an external observer) = the velocity of the source times the wavelength being emitted divided by the velocity of the sound in the air Δ λ = (V source) (λ) / V sound

A few Doppler questions: A police car is chasing a speeder at 45 m/s and emitting a siren with a 2.6m λ, and 131.9 Hz. What λ does an observer standing on the side of the road hear as the police car approaches? What does the observer hear as the police car passes? Assuming v wave in air = 343 m/s, what is the change in wavelength for each condition mentioned above?

The key man: 1) 2.258 m = λ’ when moving toward 2) 2.94 m = λ’ when moving away

Fun and exciting question for you: If a siren wave frequency is 1600 Hz And the V of the siren source is 25 m/s Then what is the frequency of the siren as heard by an observer (as the siren moves toward the observer)?

You need the λ and the period to solve λ = V sound / f = 343 / 1600 = .214 m T = 1/f = 1/1600 = 6.25 x 10-4 s/wave Now calculate λ’ λ’= λ – V siren (T) =.214 m/wave – (25 m/s x 6.25 x 10-4 s/wave) = .198 m f’ = V sound / λ’ = 343 / .198 = 1732 Hz

Another fun one for you!!! A motorcycle with a wavelength exhaust note of .83m (414 Hz) is moving away from you at 54 m/s. What wavelength do you hear as it moves away? 0.965 m (a frequency of 355 Hz)

If a car moving at 50 m/s sounds a horn with a frequency of 280 Hz, then: 1) What frequency will the driver of the car hear? 2) What frequency will an observer watching the car approach hear? 3) What frequency will an observer watching the car pass hear?  Hint: Calculate the wavelength, and the period! 1) answer: 280 Hz 2) answer: 327 Hz 3) answer: 244 Hz

Well DONE!