InterferenceInterference

ObjectivesObjectives

• Investigate wave interference.

• Describe constructive and destructive interference.

1. Which of the following is not an example of wave interference and the superposition principle?

AssessmentAssessment

A. A car muffler produces sound to counteract noise from the engine.

B. Ocean waves hit the shore and are absorbed by the beach.

C. Noise-canceling headphones eliminate background noise by producing sound that is out of phase with the background noise.

D. Light shown through two thin slits creates a diffraction pattern.

2. Describe how two wave pulses can combine destructively.

AssessmentAssessment

3. In your own words, describe the difference in appearance between a wave with a single frequency and a wave composed of more than one frequency.

Physics termsPhysics terms

• superposition principle

• interference

• constructive interference

• destructive interference

• phase

Examine this picture of the ocean.

Notice that there are ripples on top of the waves. These ripples are actually smaller waves that are combining with larger waves.

Multiple wavesMultiple waves

Examine this picture of the ocean.

Notice that there are ripples on top of the waves. These ripples are actually smaller waves that are combining with larger waves.

Waves of different amplitudes, wavelengths, and frequencies are often present at the same time.

Multiple wavesMultiple waves

How are small ripples and the huge walls of water called “rogue waves” related?

The answer lies in an understanding of interference.

Rogue wavesRogue waves

The simplest wave can be described by a single amplitude, wavelength, and frequency.

These are referred to as sine waves.

Sine waves Sine waves

Sine waves Sine waves The simplest wave can be described by a single amplitude, wavelength, and frequency.

These are referred to as sine waves.

Graphs of amplitude vs. position and amplitude vs. time can be modeled using the sine function.

Sine waves Sine waves The sine function repeats every cycle, or every 2π radians.

The sine function repeats every cycle, or every 2π radians.

What happens when two or more of these simple waves combine with each other?

Sine waves Sine waves

In Investigation 15C you will experiment with multi-frequency waves composed of multiple sine waves.

The investigation is found on page 427.

InvestigationInvestigation

InvestigationInvestigation

•Select the Analyze Waveform tab.

•Turn on the green sine wave.

•Adjust the amplitude frequency, and phase of the wave.

Open the Physics of Sound application.

Adjust the green wave.

Part 1: Constructive and destructive interference

InvestigationInvestigation

1. Create a wave that has a frequency of 50 Hz; adjust the axes so you can see about 5 cycles.

2. Add a second red wave of the same frequency and set the display to show the sum of the two waves.

Adjust the green wave. Adjust the red wave.

3. Adjust the phase and amplitude of the individual waves to make the largest possible or the smallest possible sum.

InvestigationInvestigationPart 1: Constructive and destructive interference

a. Describe what the phase and amplitude variables do.

b. Describe how you can create constructive interference.

c. Describe how you can create destructive interference.

InvestigationInvestigationQuestions for Part 1

1. Create a wave that has a frequency of 50 Hz; adjust the axes so you can see about 5 cycles.

2. Add a second wave of a different frequency and set the display to show only the sum of the two waves.

InvestigationInvestigationPart 2: Superposition principle

Turn Show Sum ON and Show Sines OFF.

InvestigationInvestigationPart 2: Superposition principle

3. Vary the frequency difference between the waves and observe the waveform on both a short time scale (3-5 periods) and a long time scale (1 second or more).

What do you notice?

InvestigationInvestigation

a. Describe the difference in appearance of a single frequency and multi- frequency wave.

b. Describe how amplitude changes over time when waves interfere that differ in frequency by a small amount (such as 2 Hz out of 100 Hz).

c. In your own words, what does the superposition principle mean?

Questions for Part 2

The superposition principle says that the total amplitude at any point equals the sum of the amplitudes of all of the waves that occur at that same place and time.

Superposition principleSuperposition principle

When more than one wave is present, they can sum to make a larger or smaller amplitude wave.

Superposition principleSuperposition principle

When more than one wave is present, they can sum to make a larger or smaller amplitude wave.

If the result is a larger amplitude wave, constructive interference has occurred.

Constructive interferenceConstructive interference

Two waves can also add up to make a smaller wave.

Destructive interferenceDestructive interference

Destructive interferenceDestructive interferenceTwo waves can also add up to make a smaller wave.

When two or more waves add up to make a smaller amplitude wave, destructive interference has occurred.

If the amplitudes are exactly matched, there can be total destructive interference.

Interference and superpositionInterference and superpositionIn most real situations, many waves will be present.

Some will interfere constructively; others will interfere destructively.

Interference and superpositionInterference and superpositionIn most real situations, many waves will be present.

Some will interfere constructively; others will interfere destructively.

The interference is often temporary, lasting only until the waves pass by each other.

Temporary interferenceTemporary interferenceTwo opposite pulses start at opposite ends of this spring.

Temporary interferenceTemporary interference

When they meet in the middle, they cancel.

Two opposite pulses start at opposite ends of this spring.

They re-appear after passing through each other.

When they meet in the middle, they cancel.

Temporary interferenceTemporary interferenceTwo opposite pulses start at opposite ends of this spring.

AssessmentAssessment1. Which of the following is not an example of wave interference and

the superposition principle?

A. A car muffler produces sound to counteract noise from the engine.

B. Ocean waves hit the shore and are absorbed by the beach.

C. Noise-canceling headphones eliminate background noise by producing sound that is out of phase with the background noise.

D. Light shown through two thin slits creates a diffraction pattern.

AssessmentAssessment1. Which of the following is not an example of wave interference and

the superposition principle?

A. A car muffler produces sound to counteract noise from the engine.

B. Ocean waves hit the shore and are absorbed by the beach.

C. Noise-canceling headphones eliminate background noise by producing sound that is out of phase with the background noise.

D. Light shown through two thin slits creates a diffraction pattern.

2. Describe how two wave pulses can combine destructively.

AssessmentAssessment

AssessmentAssessment2. Describe how two wave pulses can combine destructively.

If a “up” pulse traveling to the left and a “down” pulse traveling the right reach each other, they will interfere destructively. If they have equal amplitudes, they will cancel each other out.

The cancellation is temporary. In the next instant they will reappear and continue on as before.

3. In your own words, describe the difference in appearance between a wave with a single frequency and a wave composed of more than one frequency.

AssessmentAssessment

Single frequency waves can be represented as simple sine waves.

Multi-frequency waves are more complex in appearance; a multi-frequency wave typically has peaks within peaks, giving the repeating waveform a more serrated shape.

AssessmentAssessment3. In your own words, describe the difference in appearance between

a wave with a single frequency and a wave composed of more than one frequency.