Traveling Waves and Sound

Student Learning Objectives
Lessons / Lecture Notes
Important Equations
Example Problems
Applets and Animations

Student Learning Objectives

To use the wave model and understand how it differs from the particle model.
To understand the difference between transverse and longitudinal waves.
To become familiar with the properties of sinusoidal waves, such as wavelength, wave speed, amplitude, and frequency.
To become familiar with the properties of sinusoidal waves, such as wavelength, wave number, phase, and frequency.
To study important characteristics of sound waves and light waves.
To understand the Doppler effect.
To understand how waves travel through a medium.
To apply the wave model generally, and understand how it applies to the specific cases of waves on strings, sound waves, and light waves.
To apply energy and power concepts to waves.

Lessons / Lecture Notes

The Physics Classroom (conceptual)

PY105 Notes from Boston University (algebra-based):

Physics 2C notes from Dr. Bobby W.S. Lau (algebra-based)

HyperPhysics (calculus-based)

Physics 4C notes from Dr. Bobby W.S. Lau (calculus-based)

Important Equations (for algebra-based Physics)



word	pdf

Example Problems

Example Problems for algebra-based physics (from College Physics 2^nd Edition by Knight, Jones, and Field):

Example Problems (Waves and Superposition)
Solutions to Example Problems (Waves and Superposition)

Example Problems for calculus-based physics (from Physics for Scientists and Engineers 4^th Edition by Knight):

Example Problems (Traveling Waves and Superposition)
Solutions to Example Problems (Traveling Waves and Superposition)

Applets and Animations

Waves Intro Make waves with a dripping faucet, audio speaker, or laser! Adjust frequency and amplitude, and observe the effects. Hear the sound produced by the speaker, and discover what determines the color of light.

Transverse Traveling Wave
Nice animation showing a transverse traveling wave.

A Transverse Wave Another nice animation showing a transverse traveling wave. The user can adjust the frequency, amplitude, tension, and linear mass density.

Transverse Wave As the animation starts, you see a vibration which begins at the left end traveling towards right. If you observe any particle you would find it vibrating up and down. You would say to yourself, something is moving to the right here, it is not the particles, they are only vibrating up and down - it is a shape or a vibration that is moving to the right- being passed on from particle to particle. That is what wave motion is - a moving vibration or a moving shape.

Transverse Wave
Animation shows a vibration being transmitted from left to right. The position of the left most particle is also shown on a circle of reference. This should be helpful in appreciating relation between the phase of a wave and phase of a vibrating particle.

Longitudinal Traveling Wave
Nice animation showing a longitudinal traveling wave.

A Sound Wave
A simple animation showing a traveling sound wave. The user can adjust the frequency and amplitude of the sound wave.

Longitudinal Wave You are shown vibrating layers of air in a horizontal tube. The layer at the extreme left is the one disturbed earliest. A vibrating piston at the left end is causing these disturbances. So the layer at the left extreme is always ahead in phase of the layers to its right. The time lag between the moments when different layers begin oscillating causes the layers to come closer to each other at some moments and move farther at some other moments.

Sound This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears. (Note: this is an old applet and may not run on some computers)

Visualizing a Sound Wave
A simple animation showing the propogation of a sound wave.

Types of Waves This is an awesome applet showing transverse and longitudinal traveling and standing waves.

Pendulum Waves A very cool animation showing pendulum waves from different perspectives.

Ripple Tank Great animation showing a ripple tank with numerous very cool options. I highly recommend exploring the many different setups.

Forces on a Waving String
A very nice animation showing the forces acting on a waving string. The user can adjust the frequency, amplitude, and highlighted portion of the string.

A Movie and a Graph This animation shows a movie of a transverse traveling wave (y vs. x) as well as a graph of the position versus time for a particular string element (at x = 0).

Wave Reflections Fun animation showing the reflection of a wave from both a fixed end and a free end.

Pulse Reflection at String End Another animation showing the reflection of a wave on a string from either a fixed end or a free end.

Wave Pulse In this useful applet, you can investigate the reflection and transmission of waves on a string at an interface between strings of different linear mass densities.

Wave on a String Explore the wonderful world of waves! Even observe a string vibrate in slow motion. Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator.

Speed of Sound and Lightning Fun animation showing why we see lightning before we hear thunder.

Measuring the Speed of Sound This is a simulation of a standard physics demonstration to measure the speed of sound in air. A vibrating tuning fork is held above a tube - the tube has some water in it, and the level of the water in the tube can be adjusted. This gives a column of air in the tube, between the top of the water and the top of the tube. By setting the water level appropriately, the height of the air column can be such that it gives a resonance condition for the sound wave produced by the tuning fork. In the real experiment, resonance is found by listening - the sound from the tube is loudest at resonance. In the simulation, resonance is shown by the amplitude of the wave in the air column. The larger the amplitude, the closer to resonance. Note that at certain special heights of the air column, no sound is heard - this is because of completely destructive interference.

Sound Waveforms This cool animation lets you hear what different shaped sounds waves (sinusoidal, square, triangle, ...) sound like.

Quality of Sound Mix in different overtones with the fundamental frequency and hear the result. Great for investigating timbre and the quality of sound.

Doppler Effect Fun Doppler Effect applet that let's you place a microphone at diferent locations and hear the sound pulse.

An Example of Doppler Effect An emergency ambulance with switched on siren passes a person who is standing at the street.

Shock Waves Great applet that demonstrates shock waves and lets you hear what one might sound like!

Beats Simple animation where you can vary the frequencies of two sound wave and see the resulting beats. The sound waves can also be placed out of phase.

Beats Nice animation showing the formation of beats.

Forming Beats Simple yet effective. Play two different sound waves at the same time (or individually) and hear the resulting beats.

Waves Intro		Make waves with a dripping faucet, audio speaker, or laser! Adjust frequency and amplitude, and observe the effects. Hear the sound produced by the speaker, and discover what determines the color of light.
Transverse Traveling Wave		Nice animation showing a transverse traveling wave.
A Transverse Wave		Another nice animation showing a transverse traveling wave. The user can adjust the frequency, amplitude, tension, and linear mass density.
Transverse Wave		As the animation starts, you see a vibration which begins at the left end traveling towards right. If you observe any particle you would find it vibrating up and down. You would say to yourself, something is moving to the right here, it is not the particles, they are only vibrating up and down - it is a shape or a vibration that is moving to the right- being passed on from particle to particle. That is what wave motion is - a moving vibration or a moving shape.
Transverse Wave		Animation shows a vibration being transmitted from left to right. The position of the left most particle is also shown on a circle of reference. This should be helpful in appreciating relation between the phase of a wave and phase of a vibrating particle.
Longitudinal Traveling Wave		Nice animation showing a longitudinal traveling wave.
A Sound Wave		A simple animation showing a traveling sound wave. The user can adjust the frequency and amplitude of the sound wave.
Longitudinal Wave		You are shown vibrating layers of air in a horizontal tube. The layer at the extreme left is the one disturbed earliest. A vibrating piston at the left end is causing these disturbances. So the layer at the left extreme is always ahead in phase of the layers to its right. The time lag between the moments when different layers begin oscillating causes the layers to come closer to each other at some moments and move farther at some other moments.
Sound		This simulation lets you see sound waves. Adjust the frequency or volume and you can see and hear how the wave changes. Move the listener around and hear what she hears. (Note: this is an old applet and may not run on some computers)
Visualizing a Sound Wave		A simple animation showing the propogation of a sound wave.
Types of Waves		This is an awesome applet showing transverse and longitudinal traveling and standing waves.
Pendulum Waves		A very cool animation showing pendulum waves from different perspectives.
Ripple Tank		Great animation showing a ripple tank with numerous very cool options. I highly recommend exploring the many different setups.
Forces on a Waving String		A very nice animation showing the forces acting on a waving string. The user can adjust the frequency, amplitude, and highlighted portion of the string.
A Movie and a Graph		This animation shows a movie of a transverse traveling wave (y vs. x) as well as a graph of the position versus time for a particular string element (at x = 0).
Wave Reflections		Fun animation showing the reflection of a wave from both a fixed end and a free end.
Pulse Reflection at String End		Another animation showing the reflection of a wave on a string from either a fixed end or a free end.
Wave Pulse		In this useful applet, you can investigate the reflection and transmission of waves on a string at an interface between strings of different linear mass densities.
Wave on a String		Explore the wonderful world of waves! Even observe a string vibrate in slow motion. Wiggle the end of the string and make waves, or adjust the frequency and amplitude of an oscillator.
Speed of Sound and Lightning		Fun animation showing why we see lightning before we hear thunder.
Measuring the Speed of Sound		This is a simulation of a standard physics demonstration to measure the speed of sound in air. A vibrating tuning fork is held above a tube - the tube has some water in it, and the level of the water in the tube can be adjusted. This gives a column of air in the tube, between the top of the water and the top of the tube. By setting the water level appropriately, the height of the air column can be such that it gives a resonance condition for the sound wave produced by the tuning fork. In the real experiment, resonance is found by listening - the sound from the tube is loudest at resonance. In the simulation, resonance is shown by the amplitude of the wave in the air column. The larger the amplitude, the closer to resonance. Note that at certain special heights of the air column, no sound is heard - this is because of completely destructive interference.
Sound Waveforms		This cool animation lets you hear what different shaped sounds waves (sinusoidal, square, triangle, ...) sound like.
Quality of Sound		Mix in different overtones with the fundamental frequency and hear the result. Great for investigating timbre and the quality of sound.
Doppler Effect		Fun Doppler Effect applet that let's you place a microphone at diferent locations and hear the sound pulse.
An Example of Doppler Effect		An emergency ambulance with switched on siren passes a person who is standing at the street.
Shock Waves		Great applet that demonstrates shock waves and lets you hear what one might sound like!
Beats		Simple animation where you can vary the frequencies of two sound wave and see the resulting beats. The sound waves can also be placed out of phase.
Beats		Nice animation showing the formation of beats.
Forming Beats		Simple yet effective. Play two different sound waves at the same time (or individually) and hear the resulting beats.