Date post: | 07-Aug-2015 |
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Education |
Upload: | vivian-tsang |
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What is this?This phenomenon occurs when the frequency
emitted by the source of the waves and the frequency at which the observer notes the waves are different!
The Doppler Effect occurs when the observer and the source of the waves are moving relative to each other!
Let’s break it downFirst consider when the source and the
observer are both at rest. Let f = the frequency of the source and f’ be the frequency observed by the blue man
Here, there is no Doppler shift: f = f’
Now let’s consider four examplesNow let’s imagine the blue man running towards the source.Here, the Doppler effect comes into play as there is a difference in
their relative speeds f’=f(v+vo/v) v0 refers to the observer’s speed while v refers to the speed of the waveThe (+) sign is used because the observer is going towards the source
Example 2Now let’s imagine the blue man running away from the source.Here, the Doppler effect comes into play as there is a difference in
their relative speeds f’=f(v-vo/v) v0 refers to the observer’s speed while v refers to the speed of the waveThe (-) sign is used because the observer is going away from the source
Example 3 Now let’s imagine the blue man stationary but the source of the wave moving
closer to the man. Here, the Doppler effect comes into play as there is a difference in their
relative speeds f’=f(v/v-vs) vs refers to the source speed while v refers to the speed of the wave The (-) sign is used because the source is coming closer to the observer
Example 4 Now let’s imagine the blue man stationary but the source of the wave moving
farther from the man Here, the Doppler effect comes into play as there is a difference in their relative
speeds f’=f(v/v+vs) vs refers to the source speed while v refers to the speed of the wave The (+) sign is used because the source is moving further from the observer
So what if everything’s moving all at the same time?!?!?! Now that we know the basics, there are multiple combinations possible. Let’s imagine the blue man running away from the source and the source of the
wave moving farther from the man Here, the Doppler effect comes into play as there is a difference in their relative
speeds f’=f(v-v0/v+vs) vs refers to the source speed while v refers to the speed of the wave v0 refers to the observer’s speed while v refers to the speed of the wave The (-) sign is used in the numerator because the object is moving further from the
observer The (+) sign is used in the denominator because the source is moving further from
the observer
Let’s apply this! Question 1A brand new ferrari
is moving along a straight section of a road with its engine in constant full blast away from personA and towards personB. If fA is the frequency observed by observer A and fB is the frequency observed by observer B…
AnswerThat’s right!Person A will observe a lower frequency that
person B
This is because the wave fronts in the direction of the car’s travel is going to be more compressed than the wave fronts opposite to the car’s travelling direction!
Further applications! Question 2This baby dolphin sends out underwater
sound waves at 70 kHz to try and find its mom
The baby dolphin is swimming at 3m/s and the mom who is looking for her baby is waiting anxiously!
What is the frequency of the echo that is heard by the baby dolphin?
HintsLet’s assume that mom’s motion can be
ignored compared to that of the frantic baby dolphin
The baby is going towards its mom! It’s getting closer!
The “echo” can be thought of as the waves reflected from the mother dolphin
Solution
Notice that the mom has zero speed throughout our calculations
We first find the frequency that the mom hears her baby at
Next, we find the frequency that the baby hears the echo back at. Note that fbaby differs from f’baby