Interference and beats

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Interference and beats
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Echoes 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.
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Echoes and reverberation
Reverberation is the addition of multiple
reflections of a sound to the original sound.
This adds liveliness, depth, and richness to
sound. In an auditorium you hear music directly
from the stage AND a multiple echo called
reverberation.
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Phase
A full wave has a phase of 360 degrees.
Interference between two or more sound waves
depends on their phase difference.
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Constructive interference
Two waves are in phase when both begin at the
same point in their cycle. Waves that are in
phase interfere constructively.
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Destructive 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.
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Beats

• 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.

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What do beats sound like?
Click on this simulation on page 456 to explore
beats
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Engaging with the concepts

• 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?

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Engaging with the concepts

• Change the frequencies to 440 Hz and 442 Hz.
• How does the beat frequency change?
• Does it increase or decrease?

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Engaging 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?
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Test your knowledge
What is the beat frequency between a 120 Hz wave
and a 140 Hz wave?
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Test your knowledge
What is the beat frequency between a 120 Hz wave
and a 140 Hz wave?
20 Hz (20 beats per second).
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Assessment

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

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Assessment

• 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.

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Assessment

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

• harmonic motion
• refraction
• Fourier's theorem
• superposition principle

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Assessment

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

• harmonic motion
• refraction
• Fourier's theorem
• superposition principle