Today s Topic: The Doppler Effect

Transcription

1 Today s Topic: The Doppler Effect Learning Goal: SWBAT explain what the Doppler Effect is and why it occurs. A person operating a wave generator finds that when she sets the function generator to 116 Hz, she sees a string with 5 nodes. What frequency corresponds to the 7 th harmonic?

2 Homework Due Tuesday, 6/9: Complete the Wave Interference Worksheet Two Days Late: Complete the Wave Speed Worksheet

3 Movement of Waves We are going to watch two very short clips. I want you to compare the sound of the train horn as it passes us by and the sound of the racecar as it passes us by. What do these objects have in common? What are we hearing?

4 Weeee-ooooo What we re hearing is something known as the Doppler Effect. The apparent change in frequency due to the motion of the source of the sound is called the Doppler Effect. If you, the receiver of the frequency, also move you can also experience the Doppler Effect. But let s back up for a minute.

5 The Doppler Effect While this effect happens with all types of waves, it s easiest to talk about the Doppler Effect when we discuss sound. But because it s impossible to see sound waves, we re going to need to create an analogy of what s happening. Let s imagine there s a small bug standing in the middle of a puddle, but it is vibrating up and down, creating ripples in the puddle.

6 The Doppler Effect If the bug vibrates up and down with a constant frequency, the waves are going to produce concentric circles, like in this figure: The waves will reach points A and B at the same time, with the same frequency.

7 The Doppler Effect Now imagine that the bug now travels to point B slower than the wave travels. The waves no longer appear as concentric circles. The centers of the circles now move in the direction of the swimming bug.

8 The Doppler Effect As a result, an observer at B would encounter wave crests more often. More waves per second There s a term for that The observer at B encounters a higher frequency. This again, is because the bug is moving towards B, so B sees the waves more frequently than if the bug were not moving. The waves don t travel as far.

9 The Doppler Effect An observer at A, on the other hand, encounters the wave at a lower frequency. The waves take a longer time to get to A, as there is more of a distance the waves need to travel to get to A.

10 The Doppler Effect As a wave source moves towards an observer, the observer encounters waves with a higher frequency. As the wave moves away from an observer, the observer encounters waves with a lower frequency.

11 The Doppler Effect Water waves travel across the surface of water, but sound waves travel like a sphere. The Doppler effect is very noticeable when you hear a train passing by, a car horn, police siren, or an ambulance.

12 The Doppler Effect Oddly enough, the Doppler effect also occurs in light too. When a light source approaches an observer, there is an increase in the perceived frequency. When a light source travels away from an observer, there is a decrease in the perceived frequency.

13 The Doppler Effect An increase in frequency is called a blue shift, because the increase is towards the high-frequency, or blue, end of the spectrum.

14 The Doppler Effect A decrease in frequency is called a red shift, referring to the low-frequency, or red, end of the spectrum.

15 The Doppler Effect Distant galaxies show a red shift when they are observed. What does that mean about the motion of these galaxies relative to Earth? Looking at that color, astronomers are able to determine how quickly they re traveling from Earth.

16 The Doppler Effect Rapidly spinning stars will show both a blue shift and red shift. A blue shift will appear on half of the planet, while the red shift will occur on the other half. This information tells astronomers how fast a star is spinning. This video explains it a bit more.

17 Physics Fun Fact: Radar Guns Police officers utilize the Doppler effect in their cars to catch speeders. Radar guns emit microwaves towards a moving car, which then bounce back. The reflections are received by the gun, and the speeder s speed is calculated.

18 Doppler Effect Formula We have a formula that mathematically explains what our ears and eyes perceive. The formula depends on your situation:

19 Doppler Effect Formula If neither your wave source or observer is moving, will the Doppler Effect be observed? No. If neither the source nor the observer are moving, there is no change in the apparent frequency.

20 Doppler Effect Formula If the wave source is moving towards an observer at rest: f = v f (v v ) s Where: v = velocity of sound or light in medium v s = velocity of the source f = real frequency f = apparent frequency

21 Doppler Effect Formula If the wave source is moving away from an observer at rest: f = v f (v + v ) s Where: v = velocity of sound or light in medium v s = velocity of the source f = real frequency f = apparent frequency

22 Doppler Effect Formula If the observer is moving towards a stationary wave source: f = (v + v o ) Where: v = velocity of sound or light in medium v o = velocity of the observer f = real frequency f = apparent frequency v f

23 Doppler Effect Formula If the observer is moving away from a stationary wave source: f = (v v o ) Where: v = velocity of sound or light in medium v o = velocity of the observer f = real frequency f = apparent frequency v f

24 Doppler Effect Formula This formula can be combined to the following combination: f = (v ± v o ) (v v s ) f Where: v = velocity of sound or light in medium v s = velocity of the source v o = velocity of the observer f = real frequency f = apparent frequency

25 Sample Problems On a 16 ⁰C day, a police car produces a siren with a frequency of 1200 Hz while traveling at 30 m/s towards a stationary passerby. What is the apparent frequency experienced by the observer? What frequency do they hear as the car drives away?

26 Sample Problems On a stormy 24 ⁰C day in Indiana, a tornado siren emits an alarm at 2500 Hz. What frequency does someone hear while they stand up (not moving) to leave their house? What frequency does the driver hear as they drive away from the siren at a rate of 8 m/s?