Sound and adding wavesInterference

Types of Waves

• Longitudinal– Sound waves– Motion of the

medium is parallel to the wave

• Transverse– Motion of the

medium is perpendicular to the wave

– Waves in a string

Remember, for waves, there is no net displacement of the medium

Two waves at the same place• When multiple waves meet at the same spot

in the same medium, they interact. This is called wave interference.

• At the moment they overlap, their amplitudes add, so we get a bigger wave for a moment

• This only lasts until they pass by each other.

• Positive (red) combines with positive (blue) and add to result in a bigger amplitude (green)

• Negative(red) combines with negative (blue) and add to result in a bigger amplitude (green)

Constructive Interference

Destructive Interference

• Negative (blue) meets positive (red), so a portion or all of the wave is canceled, resulting in a smaller amplitude (green)

Beats• Beats are alternations in loudness, due to interference• Waves have slightly different frequencies and the time

between constructive and destructive interference alternates• The beat frequency equals the difference in frequency

between the two sources:

2 1ƒ ƒ ƒb

• Beats make a “wah, wah” sound• Happens only when the two frequencies are

close• Instruments or voices close, but out of tune• Different from really bad musicians

• The two small graphs below are sine plots of two different but similar frequencies. Notice that the wave crests are closer together on the first graph.

• Y = 3sin(5x) Y = 3sin(4x)

Note the difference

Notice that at times the waves are perfectly matching and at

others they are exactly opposite. When they interfere

When the waves match perfectly they will add and when they are opposite the cancel each other out. The result is the pattern

below and is termed beats.

In a series of waves, all the waves interfere making huge wave

patterns• Think of “donuts” while tubing at the lake