Interference and beats. Objectives Investigate and analyze characteristics of waves, including frequency and amplitude. Investigate and analyze behaviors.

Interference and beatsInterference and beats

ObjectivesObjectives

• Investigate and analyze characteristics of waves, including frequency and amplitude.

• Investigate and analyze behaviors of waves, including constructive and destructive interference.

• Describe the role of wave interference in industrial applications such as noise cancellation technology.

AssessmentAssessment1. What happens when two sound waves of the same frequency

interfere with each other if they are 180° out of phase?

2. Noise canceling headphones use destructive interference. Which of the following explains destructive interference?

A. harmonic motion

B. refraction

C. Fourier's theorem

D. superposition principle

Physics termsPhysics terms• echo

• reverberation

• phase

• beats

• active noise cancellation

An echo is a reflected sound wave.

If you clap your hands 170 meters away from a large wall . . .

Echoes and reverberationEchoes and reverberation

An echo is a reflected sound wave.

If you clap your hands 170 meters away from a large wall . . .

the sound will echo back to you one second later.

Echoes and reverberationEchoes and reverberation

What happens if you clap or sing in a shower stall, where the wall is much closer? What do you hear?

In an auditorium you hear music directly from the stage AND a multiple echo called reverberation.

Sound from this performer travels to the listener via three paths.

•Which path is the direct path?•Which paths are the echoes?•Do they all arrive at the same time?

Echoes and reverberationEchoes and reverberation

A

B

C

In an auditorium you hear music directly from the stage AND a multiple echo called reverberation.

Sound from this performer travels to the listener via three paths.

•Which path is the direct path? B•Which paths are the echoes? A, C•Do they all arrive at the same time?

Echoes and reverberationEchoes and reverberation

A

B

C

A and C are almost simultaneous with B.

Reverberation is the addition of multiple reflections of a sound to the original sound. This adds liveliness, depth, and richness to sound.

Reverberation is why it’s so fun to sing in the shower.

Echoes and reverberationEchoes and reverberation

Echoes and reverberationEchoes and reverberationAcoustical engineers design concert halls to create the right amount of “reverb”.

There should be no “dead” spots where sound waves interfere destructively.

Absorbent wall panels dampen side reflections

Angled back walls help project sound forward

Echoes and reverberationEchoes and reverberationAcoustical engineers design concert halls to create the right amount of “reverb”.

There should be no “dead” spots where sound waves interfere destructively.

Some auditoriums have panels that can be rearranged to balance the reverberation for different performances.

A full wave has a phase of 360 degrees. Interference between two or more sound waves depends on their phase difference.

Phase Phase

Two waves are in phase when both begin at the same point in their cycle.Waves that are in phase interfere constructively.

Constructive interferenceConstructive interference

Two waves are out of phase if one wave begins half a cycle ahead or behind the other. Waves that are out of phase interfere destructively.

Destructive interferenceDestructive interference

When two frequencies are close but not the same, the sound waves drift in and out of phase, making beats.

•When the waves are in phase, they add to create a louder wave.

•When the waves are out of phase they cancel, reducing the sound.

•The result is a “beat envelope” with its own beat frequency.

BeatsBeats

Click on this simulation on page 456 to explore beats

What do beats sound like?What do beats sound like?

Create a set of two sound waves at 440 Hz and 441 Hz. Set time to 5 s.

•Can you hear the beats?

•Can you see the beats?

•What is the beat frequency?

Engaging with the conceptsEngaging with the concepts

Change the frequencies to 440 Hz and 442 Hz.

•How does the beat frequency change?

•Does it increase or decrease?

Engaging with the conceptsEngaging with the concepts

What do you think the formula is for the beat frequency?

Test your hypothesis with a new set of frequencies. You may need to adjust the time scale to see the beats.

What wave behavior causes beats?

Engaging with the conceptsEngaging with the concepts

What is the beat frequency between a 120 Hz wave and a 140 Hz wave?

Test your knowledgeTest your knowledge

20 Hz (20 beats per second).

Test your knowledgeTest your knowledge

What is the beat frequency between a 120 Hz wave and a 140 Hz wave?

Beats and tuningBeats and tuning

Musicians listen for beats when tuning their instruments.

When the beats disappear, the instruments are in tune with each other.

Applications of interferenceApplications of interference

Tuning an instrument by using beats is one application of interference.

Can you think of any other applications?

Why might you want to use destructive interference?

There are sounds you WANT to hear and sounds you DON’T want to hear.

Sound wave interference can be used to help get rid of unwanted sound.

Noise reductionNoise reduction

Typical background noise has:

Sound you WANT to hear generally has:

Noise reductionNoise reduction

• amplitude that changes quickly

• frequency above a few hundred hertz.

• amplitude that is relatively constant

• typically low frequency

A microphone in these noise-canceling headphones samples the external noise.

The microphone is connected to a computer chip that controls a miniature amplifier.

The amplifier drives a speaker inside the head phones that sends canceling sound waves directly into your ear.

Active noise cancellationActive noise cancellation

Noise + anti-noise = quiet Noise + anti-noise = quiet

1. What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase?

AssessmentAssessment

1. What happens when two sound waves of the same frequency interfere with each other if they are 180° out of phase?

Two waves that are 180° apart in their cycles will be out of phase, because they will be one half wavelength apart.

These waves will interfere destructively. If the waves have the same amplitude, they will cancel each other out completely. This is the idea behind noise-cancelling headphones.

AssessmentAssessment

AssessmentAssessment

A. harmonic motion

B. refraction

C. Fourier's theorem

D. superposition principle

2. Noise-canceling headphones use destructive interference. Which of the following explains destructive interference?

AssessmentAssessment

A. harmonic motion

B. refraction

C. Fourier's theorem

D. superposition principle

2. Noise-canceling headphones use destructive interference. Which of the following explains destructive interference?