THE DOPPLER EFFECT
(Page 69 to 74)
The Doppler Effect was named after Christian Doppler, who first came up with the idea in 1842.
Definition: The change in electromagnetic (or sound) frequency that occurs when the source of the radiation (or sound) and its observer move toward or away from each other.
It is best understood considering the object emitting the waves and it is most easily represented and understood using sound waves.
Like ripples in a pond when an object is dropped into it so sound waves radiate outwards evenly from any stationary object producing them. An observer will hear the same pitch no matter where he is situated relative to the object.
However, if the object is moving in a straight line then the wavelength (and hence frequency) of the waves in front and behind the object will be altered.
As can be seen above (circles represent crests) the moving object compresses the waves in its direction of motion and stretches them out in the opposite direction.
Thus:
To an observer ahead of the object the sound will have a higher pitchthan it
actually emits because if the wavelength is shorter then the frequency is higher .
To an observer behind of the object the sound will have a lower pitch than it
actually emits because if the wavelength is longer then the frequency is lower .
(Reminder: frequency is the number of waves to pass a point per second)
Therefore when a noise emitting object passes an observer the frequency and pitch drop.
Explain, in your own words, why the wavelength of the sound in front of a moving object is shorter than the actual sound being emitted.
………The object emitting the sound is moving in the direction of the sound wave moving to the listener. This bunches the waves and shortens the wavelength......
Explain, in your own words, why the wavelength of the sound behind a moving object is longer than the actual sound being emitted.
...... The object emitting the sound is moving in the opposite direction to the sound wave moving towards the listener. This spreads the waves and lengthens the wavelength....
NOTE: If the emitting object is stationary and the observer moves towards or away from it, then the Doppler effect occurs. It is the RELATIVE motion which is important.
When the relative motion of the observer and emitting object is towards each
other then the observed frequency is ……………………. than the emitted frequency.
When the relative motion of the observer and emitting object is away from each
other then the observed frequency is ……………………. than the emitted frequency.
Questions
Explain in detail, in your own words, why a cyclist riding at constant speed past a siren (on a stationary police car) heard a drop in pitch as he passed it.
...... As he moves towards the siren the wavelength of the sound received by the cyclist is decreased(compressed) and so the pitch increases. Once he has passed the siren the wavelength of the sound received by the cyclist increases (stretched)and so the pitch drops...
What change in pitch would the cyclist hear if he approached the siren at a constantly increasing speed?
...... He would hear a constantly increasing pitch as he got faster – which would always be higher than the frequency of the source......
THE DOPPLER EFFECT EQUATION
If an object emitting a sound with a frequencyfS travels at a velocity vSthen the frequency fLheard by a listener moving in the same line at a velocity vL will be:
NOTE
Velocity is a vector and has a direction – hence the ± sign. We usually take the direction of source to listener (or observer) of the sound as positive (AND REPLACE THE ± SIGN WITH MINUS ONLY TO START WITH).
Examples (use 340 m.s-1 for speed of sound and 3 x 108 m.s-1 for speed of light)
1.An ambulance drives towards a stationary man at a constant speed of 40 m.s-1 with its siren emitting a sound with an average frequency of 320 Hz.
a)What average frequency does the man hear?
b) By how much does the average frequency he hears drop as the ambulance passes him?
c) If, once past, the ambulance accelerates will the pitch of sound the man hears INCREASE, DECREASE or STAY THE SAME?
2.Bobby is driving down a straight road at 35 m.s-1 and hears a siren with a frequency of 400 Hz. He sees a police car behind him. If the actual frequency of the police car siren is 407, what was the speed of the police car?
3.A boy sprints towards his sister at 12 m.s-1 shouting with sound of frequency 280 Hz. If she is running towards her brother at 8 m.s-1, what is the frequency of the sound she hears?
4.Most galaxies are moving away from ours. The fastest recorded is moving away from us at 1,89 x 107 m.s-1. If an object there produced light at a frequency of 5,2 x 1014 Hz, what would be the frequency of that photon when recorded on the earth?
5.A speed gun uses microwaves with a frequency of 37,4 GHz. If the microwaves bounce off a car moving towards the gun at 160 km.h-1, what will be the frequency of the reflected microwaves?
Uses in syllabus: Page 72 (Blood flow meter and heartbeat monitor using ultrasound.)
General interest
At speed of sound
When the moving object or airplane reaches the speed of sound, it catches up to the sound waves it is creating, and they bunch up at the front end of the object, forming a shock wave. This is a reason that it is difficult for an airplane to break the sound barrier.
Supersonic speeds
When an aircraft travels at supersonic speeds or is moving faster than sound, it leaves the sound waves it makes behind it. These waves fan out and cause a sonic boom.
Other examples of sonic booms
A whip cracks because the end breaks the sound barrier.
A passing bullet cracks because its speed exceeds the sound barrier.
Red shift
Most galaxies are moving away from us. Scientists can look at the light signatures of the galaxies and see how the much lower the frequency patterns are. This “red-shift” can be used to calculate the relative speed of the distant galaxy. See page 72. It turns out that the further away they are from us the faster they are moving away from us.