Hey, guys. If you've ever stood on the side of a road while an ambulance blaring its siren has moved past you, you might have noticed that the sound changes once it passes by. It sounds like eeew, and that's what the Doppler effect is. So in this video, I'm going to show you what causes the Doppler effect, but more importantly, I'm going to show you the one equation that you need to solve any kind of problem that deals with it. Let's check this out here. Basically, what the Doppler effect is is a shift in the frequency that you hear from the frequency of the sound source. So we call the frequency that you hear \(f_{\text{listener}}\) or \(f_L\) and the frequency of the sound source \(f_{\text{sound}}\) or \(f_S\). So it's not as if the ambulance actually produces a different sound as it passes by. What happens is that the frequency you hear gets shifted, so we call it sometimes a Doppler shift. Now this Doppler effect happens whenever the sound source, meaning the siren, or the sound listener, meaning you, are moving relative to each other. So you have to have some relative motion of the two objects in order for you to have a Doppler shift. Now I'm going to get back to the equation in just a second here, but I want to show you sort of visually what's going on here and why the Doppler effect gets produced. So if there's no relative motion, there's no Doppler effect. So if you are standing on the side of the road, your velocity of the listener is going to be 0, and if the ambulance is parked on the side of the road, the velocity of the sound source is going to be 0. So what happens is if this sound wave, or sorry, if this ambulance is producing waves at a rate of 5 hertz, so it's 5 waves per second, then what happens is that these waves are traveling towards you at the speed of sound. The ambulance is producing 5 waves every second, then what happens is that later on 5 waves are going to pass through you every second. So if nothing's moving, what's going to happen is that the frequency that you hear is going to be equal to the frequency of the sound source. So you're just going to hear 5 hertz. Right? Nothing gets shifted, nothing like that because 5 waves are going to pass through you. Now things get a little bit trickier whenever you do have some relative motion, and there's actually four different scenarios. You could have you, the listener, moving towards or away from the source or the source that's moving towards or away from you. So I'm going to show you these really where you see that there's only actually two scenarios. So now imagine that you're actually moving, running towards the sound source with some \(v_L\), and the sound source is basically just standing still. What happens is that the ambulance is still producing 5 waves a second, still producing a sound of 5 hertz. So what happens here though is that if you're moving towards the sound source, you're going to be able to cover more waves every second. You're going to be able to move through more waves as they're passing by you. So in general, what happens is you're going to hear something that's greater than 5 hertz. You're going to hear basically more waves per second. The exact same thing happens if the ambulance were actually moving towards you with some sound source like this. Basically, what happens is that these waves sort of get crammed up together in front of the sound source, and they sort of get stretched out or elongated behind it. But the effect is the same. You're going to hear more of these waves every second because the thing is actually moving towards you. So you're going to hear something that's greater than 5 Hertz. So, generally, what happens is that the listener and the sound source are moving towards each other, then the frequency you hear is going to be greater than the frequency of the source. That's the general rule. Now if you reverse everything, it's basically opposite. If you're moving away from this source or if the source is moving away from you, the exact opposite happens. Basically, you're going to hear fewer waves per second, so you're going to hear something that's less than 5 Hertz in both of these situations. So in if the listener and the source are moving away from each other, you're going to hear fewer waves per second and the frequency that you hear is going to be less than the source. So that's why what happens is that when the ambulance is moving towards you, you're going to hear a higher pitch or a higher frequency. It's going to sound like eeep, and then once it passes you, it's going to be moving away from you, and you're going to hear something that is a lower frequency. It just sounds like eeo as it passes by. So let me show you the equation real quick. Remember it's a shift between \(f_L\) and \(f_S\), and what goes inside here is really just a ratio. It's going to be \(\frac{v + v_L}{v + v_S}\). Now unfortunately, there are three \(v\)'s inside this equation, so I'm going to go through them very quickly. This \(v\) here with no subscripts is going to be the speed of sound. It's always going to be positive at 343 meters per second, no matter what. This \(v_L\) here is going to be the velocity of the listener, which is you, and this, the \(s\) here is going to be the velocity of the source, basically the velocity of the siren or the ambulance or whatever it is. Right? So that's just the one equation. It works for any kind of these situations here. Let's go ahead and take a look at our practice problem here. So we have the alarm of a car that's at rest and it produces sound waves of frequency 550. So this is actually the frequency that is produced by the sound source. It's going to be 550. Now you're on a motorcycle and you're traveling directly towards it. So what happens here is you have this \(f_S\), but you're going to be moving towards this sound source with some \(v_L\). And you're hearing an observed frequency of 600, so this is the frequency that you're actually hearing. So this is \(f_L\) at 600. So we want to calculate how fast must you be traveling. All right? So that's basically going to be this \(v_L\) over here. We have the velocity of the sound source, but remember the car is actually going to be at rest. So this velocity of the sound source is actually going to be 0. All right. So basically, now let's go ahead and take a look at our equation. So we have this equation here. This is \(f_L = \frac{v + v_L}{v + v_S} \times f_S\). So let's go through each one of our variables here. So I've got \(f_L\), right, that's just the 6600. Now I've got my \(v\) because it's always going to be positive, 343. What about this \(v_L\)? That's actually what I'm looking for here. We also know that \(v_S\) is going to be 0, so we just can cancel that out and we also have what the frequency of the sound source is. So you have one unknown. The problem here is that if you'll notice, what happens is this ambulance produces sound waves and remember these sound waves travel at the speed of sound that's going towards the listener, towards you. So what happens is we have these two arrows that are actually pointing in different directions. So in these kinds of problems, remember, velocity is a vector, we're going to have to establish a direction of positive here. And basically, here is the rule. The rule is that the direction of positive is always going to be from the listener to the source. So what happens here is that this is the listener and this is the source, so the direction of positive is always going to be from \(L\) to \(S\), from listener to source. So here is our direction of positive, and what that means is that this \(v_L\) is actually going to be positive. You're always going to write it like this, but depending on your sign, you actually might have to pick up a negative sign if that happens. All right. So let's take a look here. So we're going to plug in some numbers. Our \(f_L\) is 600, this equals 343. Now what happens is, remember, this 343 is always going to be positive. Even though the direction of positive is this way and your velocity, the speed of sound moves to the right, these sound waves, you're still going to actually write the 343 as positive. All right? So we have 343 plus \(v_L\), and then we're going to divide this by 343, and now we're going to multiply this by 550. So let's just go ahead and move this 550 over to the other side. Once you divide this 550, you're going to get 1.091, which equals \(\frac{343 + v_L}{343}\). So what happens is when you move this 343 up over here, you're going to get 374.2 equals 343 plus \(v_L\). All right. So all we have to do is just move this 343 over. We're going to get 374.2 minus 343, and this equals \(v_L\). And if you go ahead and work this out, you're going to get 31.2 meters per second. So that is the speed that you have while you are traveling towards the sound source. All right. So that's it for this one, guys. Let me know if you have any questions.

Table of contents

- 0. Math Review31m
- 1. Intro to Physics Units1h 23m
- 2. 1D Motion / Kinematics3h 56m
- Vectors, Scalars, & Displacement13m
- Average Velocity32m
- Intro to Acceleration7m
- Position-Time Graphs & Velocity26m
- Conceptual Problems with Position-Time Graphs22m
- Velocity-Time Graphs & Acceleration5m
- Calculating Displacement from Velocity-Time Graphs15m
- Conceptual Problems with Velocity-Time Graphs10m
- Calculating Change in Velocity from Acceleration-Time Graphs10m
- Graphing Position, Velocity, and Acceleration Graphs11m
- Kinematics Equations37m
- Vertical Motion and Free Fall19m
- Catch/Overtake Problems23m

- 3. Vectors2h 43m
- Review of Vectors vs. Scalars1m
- Introduction to Vectors7m
- Adding Vectors Graphically22m
- Vector Composition & Decomposition11m
- Adding Vectors by Components13m
- Trig Review24m
- Unit Vectors15m
- Introduction to Dot Product (Scalar Product)12m
- Calculating Dot Product Using Components12m
- Intro to Cross Product (Vector Product)23m
- Calculating Cross Product Using Components17m

- 4. 2D Kinematics1h 42m
- 5. Projectile Motion3h 6m
- 6. Intro to Forces (Dynamics)3h 22m
- 7. Friction, Inclines, Systems2h 44m
- 8. Centripetal Forces & Gravitation7h 26m
- Uniform Circular Motion7m
- Period and Frequency in Uniform Circular Motion20m
- Centripetal Forces15m
- Vertical Centripetal Forces10m
- Flat Curves9m
- Banked Curves10m
- Newton's Law of Gravity30m
- Gravitational Forces in 2D25m
- Acceleration Due to Gravity13m
- Satellite Motion: Intro5m
- Satellite Motion: Speed & Period35m
- Geosynchronous Orbits15m
- Overview of Kepler's Laws5m
- Kepler's First Law11m
- Kepler's Third Law16m
- Kepler's Third Law for Elliptical Orbits15m
- Gravitational Potential Energy21m
- Gravitational Potential Energy for Systems of Masses17m
- Escape Velocity21m
- Energy of Circular Orbits23m
- Energy of Elliptical Orbits36m
- Black Holes16m
- Gravitational Force Inside the Earth13m
- Mass Distribution with Calculus45m

- 9. Work & Energy1h 59m
- 10. Conservation of Energy2h 51m
- Intro to Energy Types3m
- Gravitational Potential Energy10m
- Intro to Conservation of Energy29m
- Energy with Non-Conservative Forces20m
- Springs & Elastic Potential Energy19m
- Solving Projectile Motion Using Energy13m
- Motion Along Curved Paths4m
- Rollercoaster Problems13m
- Pendulum Problems13m
- Energy in Connected Objects (Systems)24m
- Force & Potential Energy18m

- 11. Momentum & Impulse3h 40m
- Intro to Momentum11m
- Intro to Impulse14m
- Impulse with Variable Forces12m
- Intro to Conservation of Momentum17m
- Push-Away Problems19m
- Types of Collisions4m
- Completely Inelastic Collisions28m
- Adding Mass to a Moving System8m
- Collisions & Motion (Momentum & Energy)26m
- Ballistic Pendulum14m
- Collisions with Springs13m
- Elastic Collisions24m
- How to Identify the Type of Collision9m
- Intro to Center of Mass15m

- 12. Rotational Kinematics2h 59m
- 13. Rotational Inertia & Energy7h 4m
- More Conservation of Energy Problems54m
- Conservation of Energy in Rolling Motion45m
- Parallel Axis Theorem13m
- Intro to Moment of Inertia28m
- Moment of Inertia via Integration18m
- Moment of Inertia of Systems23m
- Moment of Inertia & Mass Distribution10m
- Intro to Rotational Kinetic Energy16m
- Energy of Rolling Motion18m
- Types of Motion & Energy24m
- Conservation of Energy with Rotation35m
- Torque with Kinematic Equations56m
- Rotational Dynamics with Two Motions50m
- Rotational Dynamics of Rolling Motion27m

- 14. Torque & Rotational Dynamics2h 5m
- 15. Rotational Equilibrium3h 39m
- 16. Angular Momentum3h 6m
- Opening/Closing Arms on Rotating Stool18m
- Conservation of Angular Momentum46m
- Angular Momentum & Newton's Second Law10m
- Intro to Angular Collisions15m
- Jumping Into/Out of Moving Disc23m
- Spinning on String of Variable Length20m
- Angular Collisions with Linear Motion8m
- Intro to Angular Momentum15m
- Angular Momentum of a Point Mass21m
- Angular Momentum of Objects in Linear Motion7m

- 17. Periodic Motion2h 9m
- 18. Waves & Sound3h 40m
- Intro to Waves11m
- Velocity of Transverse Waves21m
- Velocity of Longitudinal Waves11m
- Wave Functions31m
- Phase Constant14m
- Average Power of Waves on Strings10m
- Wave Intensity19m
- Sound Intensity13m
- Wave Interference8m
- Superposition of Wave Functions3m
- Standing Waves30m
- Standing Wave Functions14m
- Standing Sound Waves12m
- Beats8m
- The Doppler Effect7m

- 19. Fluid Mechanics2h 27m
- 20. Heat and Temperature3h 7m
- Temperature16m
- Linear Thermal Expansion14m
- Volume Thermal Expansion14m
- Moles and Avogadro's Number14m
- Specific Heat & Temperature Changes12m
- Latent Heat & Phase Changes16m
- Intro to Calorimetry21m
- Calorimetry with Temperature and Phase Changes15m
- Advanced Calorimetry: Equilibrium Temperature with Phase Changes9m
- Phase Diagrams, Triple Points and Critical Points6m
- Heat Transfer44m

- 21. Kinetic Theory of Ideal Gases1h 50m
- 22. The First Law of Thermodynamics1h 26m
- 23. The Second Law of Thermodynamics3h 11m
- 24. Electric Force & Field; Gauss' Law3h 42m
- 25. Electric Potential1h 51m
- 26. Capacitors & Dielectrics2h 2m
- 27. Resistors & DC Circuits3h 8m
- 28. Magnetic Fields and Forces2h 23m
- 29. Sources of Magnetic Field2h 30m
- Magnetic Field Produced by Moving Charges10m
- Magnetic Field Produced by Straight Currents27m
- Magnetic Force Between Parallel Currents12m
- Magnetic Force Between Two Moving Charges9m
- Magnetic Field Produced by Loops and Solenoids42m
- Toroidal Solenoids aka Toroids12m
- Biot-Savart Law (Calculus)18m
- Ampere's Law (Calculus)17m

- 30. Induction and Inductance3h 37m
- 31. Alternating Current2h 37m
- Alternating Voltages and Currents18m
- RMS Current and Voltage9m
- Phasors20m
- Resistors in AC Circuits9m
- Phasors for Resistors7m
- Capacitors in AC Circuits16m
- Phasors for Capacitors8m
- Inductors in AC Circuits13m
- Phasors for Inductors7m
- Impedance in AC Circuits18m
- Series LRC Circuits11m
- Resonance in Series LRC Circuits10m
- Power in AC Circuits5m

- 32. Electromagnetic Waves2h 14m
- 33. Geometric Optics2h 57m
- 34. Wave Optics1h 15m
- 35. Special Relativity2h 10m

18. Waves & Sound

The Doppler Effect

18. Waves & Sound

# The Doppler Effect - Online Tutor, Practice Problems & Exam Prep

Created using AI

The Doppler effect describes the change in frequency of sound waves due to the relative motion between a sound source and a listener. When moving towards the source, the listener perceives a higher frequency, while moving away results in a lower frequency. The equation to calculate the observed frequency (f_{listener}) is given by: f = v+v_{l}v+v_{s}f_{s}. Understanding this effect is crucial in acoustics and various applications, including radar and astronomy.

concept

### The Doppler Effect

Video duration:

7mPlay a video:

#### Video transcript

## Do you want more practice?

More sets### Your Physics tutor

Additional resources for The Doppler Effect

PRACTICE PROBLEMS AND ACTIVITIES (22)

- The shock-wave cone created by a space shuttle at one instant during its reentry into the atmosphere makes an ...
- The siren of a fire engine that is driving northward at 30.0 m>s emits a sound of frequency 2000 Hz. A truc...
- The siren of a fire engine that is driving northward at 30.0 m>s emits a sound of frequency 2000 Hz. A truc...
- A railroad train is traveling at 30.0 m>s in still air. The frequency of the note emitted by the train whis...
- A railroad train is traveling at 30.0 m>s in still air. The frequency of the note emitted by the train whis...
- An avant-garde composer wants to use the Doppler effect in his new opera. As the soprano sings, he wants a lar...
- A bat locates insects by emitting ultrasonic 'chirps' and then listening for echoes from the bugs. Suppose a b...
- A physics professor demonstrates the Doppler effect by tying a 600 Hz sound generator to a 1.0-m-long rope and...
- A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25.0 m/s on a day when ...
- BIO Ultrasound has many medical applications, one of which is to monitor fetal heartbeats by reflecting ultras...
- (II) A bat at rest sends out ultrasonic sound waves at 50.0 kHz and receives them returned from an object movi...
- A fish finder uses a sonar device that sends 20,000-Hz sound pulses downward from the bottom of the boat, and ...
- (II) Two trains emit 508-Hz whistles. One train is stationary. The conductor on the stationary train hears a 4...
- Two loudspeakers face each other at opposite ends of a long corridor. They are connected to the same source wh...
- (II) A police car sounding a siren with a frequency of 1580 Hz is traveling at 120.0 km/h . ...
- (III) A factory whistle emits sound of frequency 770 Hz. The wind velocity is 15.0 m/s from the north (heading...
- (III) A factory whistle emits sound of frequency 770 Hz. The wind velocity is 15.0 m/s from the north (heading...
- (III) A factory whistle emits sound of frequency 770 Hz. The wind velocity is 15.0 m/s from the north (heading...
- (II) A police car sounding a siren with a frequency of 1580 Hz is traveling at 120.0 km/h .(c) The police car ...