THE DOPPLER EFFECT

POLICE PATROL CAR, AMBULANCE AND FIRE TRUCKS What have you observed with the sound

of these vehicles as they pass by at a certain speed?

What explanation can offer to account for this observation?

What are the key variable involved?

OBSERVE…

WHAT IS DOPPLER EFFECT? The apparent change in the frequency

of a source of wave due to the motion of the source and/or the observer

Developed by Christian Doppler in 1842 The difference of the true frequency and

the apparent frequency is called the Doppler Shift

KEY VARIABLESThe following symbols will be used in the

definitions: f is the true frequency f’ is the apparent frequency v is the velocity of the sound (air) vs is the velocity of the source vo is the velocity of the observer λ is the true wavelength λ’ is the apparent wavelength

CASE 1:OBSERVER IS IN MOTION AND THE SOURCE IS AT REST

f ’ = [ ( v ± vo ) / v ] f ( + ) means the observer is moving

towards the source ( - ) means the observer is moving

away from the source

CASE 2:OBSERVER IS AT REST AND THE SOURCE IS IN MOTION f ’ = [ v / ( v ± vs ) ] f ( + ) means the source is moving away

from the observer ( - ) means the source is moving

towards the observer

CASE 3:BOTH THE OBSERVER AND THE SOURCE ARE IN MOTION

f ’ = [ ( v ± vo ) / ( v ± vs ) ] f NOTE: please refer to case 1 and

case 2 and analyze the situation of the observer and the source respectively.

CONCEPTUAL UNDERSTANDING When a wave source moves toward a

receiver, does the receiver encounter an increase in wave frequency, wave speed ,or both?

Does the Doppler Effect occur for only some types of waves or all types of waves?

THE MACH NUMBER named after Austrian physicist and

philosopher Ernst Mach Used to describe speed of objects that

are travelling close to, or above the speed of sound.

The ratio of the speed of the object and the speed of sound in the medium.

M = speed of object / speed of sound

SHOCK WAVES this is heard as a sonic boom when an

airplane passes over; this is the result of the compilation of sound waves generated by a source that moves at equal or greater velocity than the sound it creates

SAMPLE PROBLEMS:DOPPLER EFFECT1. An ambulance traveling at 20. m/s sounds its siren

at a frequency of 256Hz. What apparent frequency will you hear if the ambulance is: ( assume air temperature to be at 25°C )

a. approaching you?b. moving away from you?

2. A car traveling at 30. m/s sounds its horn as it overtakes and pass another car traveling at 20. m/s in the same direction. If the frequency of the horn is 500. Hz, what is the frequency heard by the driver in the slower car:

a.) beforeb.) after the car has passed?

Assume sound speed to be at 350. m/s.