Phys 101 Learning Object LO5 March 1 2015

Doppler Effect by Vivian Tsang 14153143

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)/vv0 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’=fv/(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 Note: the green wave has a smaller wavelength than the red wave

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’=fv/(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 Note: the green wave has a larger wavelength than the red wave

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…

Q: Which person will observe a larger frequency?

HintTry visualizing the question!

Person A Person B

AnswerThat’s right!Person A will observe a lower frequency than

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

Let’s clear up the informationGiven informationf= 70x10^3 HzVbaby=3m/sVwater=1484m/s

Steps:Part I

Let us consider the baby dolphin as the initial source of the sound waves

Use the doppler effect equation that we talked about in the previous slides and find the frequency that the mom hears her baby at

Part IIAfter the waves “hit” the mom, the mom now becomes

the source of the wavesThe baby then becomes the receiver of the sound wavesTherefore, we perform the doppler effect equation a

second time!

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

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