Honors Physics - Chapter 14: Lesson 2

Chapter 14: Lesson 2

Transverse and Longitudinal Waves

Chapter 14: Lesson 2 - Transverse and Longitudinal Waves

Types of Waves

A mechanical wave required a mechanical medium. A medium can be defined as a substance through which a vibration travels. A medium can be air, liquid, rope, slinkies, water, anything with particles that the vibration can travel through.

An electromagnetic wave does not require a medium for motion to occur. An electromagnetic wave can travel through a vacuum. A vacuum is space devoid of matter. An electromagnetic wave has two parts, an electric field and a magnetic field. They are perpendicular to each other because the two different fields repel each other. Light, radio, and x-rays are examples of electromagnetic waves.

Transverse Waves

Transverse waves cause the particles of the medium to vibrate perpendicularly to the direction of the motion of the wave. Piano and guitar strings that are in motion are examples of a transverse wave.

Longitudinal Waves

Longitudinal waves occur when particles of a medium move parallel to the direction of the waves. Fluids, liquids, gases, or plasma usually only transmit longitudinal waves.

Longitudinal vs Transverse Waves

Watch this quick video to see the difference between longitudinal and transverse waves.

Surface Waves

Surface waves are a mixture of transverse and longitudinal waves. The particles move both parallel and perpendicular to the direction of the wave. Each particle moves in a circular shape.

Wave Pulse

A wave pulse is a single disturbance that travels through a medium. Look at the rope animation to the right. The hand makes one wave pulse and the wave pulse travels through the rope, which is the medium.

Traveling Wave

A traveling wave is a moving periodic disturbances in a medium or field. The top animation shows a traveling wave.

The bottom animation is a standing wave. We will be talking about a standing wave in a little bit.

Wavelength of a Wave

The shortest distance between points where the wave pattern repeats itself is called the wavelength. Wavelength is abbreviated with the greek letter, lambda, λ. Wavelength is measured in meters because it is a length.

Parts of a Wave

It is important to be able to know what the parts of a wave are.

The crests are the high point of a wave. The troughs are the low points of each wave motion. Amplitude is the maximum displacement from the rest or equilibrium position.

The equilibrium position is the dotted line in the first picture and the red line in the second picture.

Amplitude and Energy

In order to produce a wave with a larger amplitude, more work has to be done. Waves with larger amplitudes transfer more energy.

When talking about mediums, what the wave is traveling through, we often look at the density of the wave as that affects our wave. Different things happen to a wave when we travel from a less dense medium to a more dense medium or from a more dense medium into a medium that is less dense. Keep reading to find out more!

More Wave Vocabulary

We call the initial wave sent the incident wave. The wave that is moved into another medium is the transmitted wave. The reflected wave is the wave the moves back from the boundary into the original medium.

The hand on the left sends an incident pulse to the right. When the red incident pulse hits the boundary between the red and the blue rope, the blue wave that travels into the new blue rope medium is the transmitted wave and the red wave that bounces back into the original red rope medium is the reflected wave.

The speed of a mechanical wave does not depend on the amplitude or the frequency. It depends on the medium through which it is traveling. The amplitude of a wave changes as it enters or exits different mediums.

Whenever a wave passes from a less dense to a denser medium, the reflected wave is inverted, meaning it comes back on the opposite side of the equilibrium line as the incident wave was originally. You can see in the first animation that when the incident wave hits the more dense blue dot, the reflected wave is inverted. In the second picture, the incident wave is should in figure A. In figure B, the wave has hit the block on the right and has been reflected upside down, or inverted.

Less Dense Medium to a More Dense Medium

You can see that the incident wave is traveling to the right. The transmitted wave's is erect (it is on the same side as the incident wave) and the amplitude is less than the incident wave's amplitude and the reflected wave is inverted and has a smaller amplitude than the incident wave.

More Dense Medium to a Less Dense Medium

This incident wave is traveling to the right and is in a medium that is more dense than the medium on the right. When the wave moves into the less dense medium, the amplitude increases and the wave is erect. The reflected waves's amplitude decreases and is erect.

Preview of the Math:

Frequency is the number of complete revolutions per second. We abbreviate frequency with a fancy f, ƒ. Frequency is measured in hertz, Hz. A hertz is one vibration per second.

Waves passing from one medium to another have the same frequency. The wavelength change depends on the velocity change, so that ƒ=v/λ is constant. If the velocity increases, the wavelength also increases.

Wavelength and Frequency

As the frequency increases, the wavelength decreases. As the frequency decreases, the wavelength increases.

Superposition and Interference

The principal of superposition states that the displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves. This just means that when you have two waves in a medium and they meet, their amplitudes can be added or subtracted.

Interference is the result that you get when you have the superposition of two or more waves. You can have constructive interference or destructive interference. If you were on one side of a slinky and I was on the other side and we both sent a wave pulse into the slinky, the slinky does not split to show our individual waves when the waves meet. The waves add together. The two waves can either add together to get taller, subtract to get smaller, or totally cancel each other out.

Constructive Interference

When you construct something, you make it taller, so when you think of constructive interference, think of taller waves! Constructive interference occurs when the wave displacements are on the same side of the wave. The result is a wave with a larger amplitude than any of the individual waves.

Destructive Interference

When you destruct something, you make it smaller. Destructive interference occurs when you have one wave on one side of the equilibrium position and another wave on the other side of the equilibrium position.

Total destructive interference occurs when you have one wave traveling on one side and another wave traveling on the opposite side with the same amplitude. The result is a wave with zero amplitude.

Destructive interference occurs when the wave pulses on opposite sides of the equilibrium position have unequal amplitudes. In this case, destructive interference is not complete. The result is a wave with a smaller amplitude.

The animation above shows constructive interference twice. Can you catch both instances of constructive interference?

The top picture shows constructive interference. The bottom picture shows total destructive interference.

Nodes and Antinodes

A node is a point in the medium that is completely undisturbed at all times. A node is produced by destructive interference of waves. A node occurs where the wave crosses the equilibrium position.

An antinode is a point of maximum displacement. An antinode is formed from constructive interference.

Antinodes are crests and troughs. They just represent the point of maximum displacement.

Standing Wave

When the antinodes appear to be stationary, the wave appears to be standing still. That is called a standing wave.

If you increase the frequency of a standing wave, you will see more nodes and the wavelength decreases.

Watch this quick video for an explanation on standing waves.

Waves Explained

I use a wave demonstrator to demonstrate nodes, antinodes, wavelength, and interference. Watch this quick video to see waves in action.

This is a picture of one wavelength with the wave generator. One wave has both a crest and a trough.

These are pictures from the wave generator. The top picture is half wavelength. There is only a crest or a trough in this picture.

The middle picture shows 1.5 wavelengths. Follow one line, crest, through, crest.

The bottom picture has 2 wavelengths.

Check Your Understanding:

Click on the down arrow when you have your answer to check to see if you are correct.

How many nodes does the standing wave in the picture to the left have?

There are 8 nodes in the standing wave. To count the number of nodes, you need to see how many times the wave crosses the equilibrium position.

Use the picture below to answer the next 3 questions.

2. In the standing wave above, what is the amplitude?

Amplitude is measured from the equilibrium position to the maximum displacement. It is 20 cm from the crest to the trough. The amplitude is 10 cm, the distance from the crest to the equilibrium position.

3. In the standing wave above, what is the wavelength?

You are looking at a standing wave, so you only need to look at one of the waves, crest then trough. There are 2.5 waves (one wave is one crest and one trough.). Since there are 2.5 waves and it is 2.5 meters from the tree to the girl, then each wave is 1.0 m.

4. In the standing wave above, how many nodes are there?

There are 6 nodes in this wave. Picture the equilibrium position going straight through the middle of the wave. The wave crosses the equilibrium position 6 times.

Before the Next Class Period:

Label the wave...

In the next class meeting time, we will be labeling this wave with the following...

Equilibrium Position
Crests
Troughs
Nodes
Antinodes
Amplitude
Wavelength
One Wave

Try it on your own and be ready to go over it when we meet!

You have finished Lesson 2!

Be sure to head over to google classroom and fill out the exit pass.

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