1. Part 3 Harmonics Standing Waves and Pitch
Sound
Part 3
Harmonics
Standing Waves and Pitch

2. Determining Natural frequency
The possible wavelengths of standing waves in/on an object depend on:
Length of the vibrating object
Where the vibrating object is or isn’t free to move.
The frequency is determined by the velocity of the waves possible and their length
f = v/λ
This is the frequency you hear

3. The Speed of the Waves
The speed of the waves in most objects is known at given temperature, it is the speed of sound (p410) The speed of waves on a string, wire or drum head is directly related to the tension in the string And inversely to the mass per unit length (thickness) Thus thicker strings have slower waves and thus lower frequencies Tighter strings have faster waves and thus higher frequencies

4. Finding the possible wavelengths
Assume nodes were the object is held or tube is closed.
Put Antinodes at free or open ends and between the nodes
From a Node to Antinode is ¼ λ, count the nodes to antinodes and set it equal to L, the length of the object column of air.
Solve for λ
The simplest pattern is the longest wave
and is called
The Fundamental or 1st Harmonic
5. If you add Nodes/antinodes to make more complex patterns you can find other possible harmonic or …

5. Overtones
More complex patterns create “Overtones” Here are the Harmonics of a String:

6. Harmonics in columns of Air
One End Open
Both Ends Open

7. A Octave
An octave in music (one “scale” of 8 notes) is a doubling of frequency
Middle “C” is 256 Hz
The “C” an octave higher is 512 Hz
An octave lower 128 Hz
Thus doubling length of an instrument
Doubles wavelength thus
halving the frequency
And lowering the pitch an octave

8. Interference, Beats and Noise Cancelation
When sound waves interfere the intensity changes. If the frequencies are different the wave will alternately reinforce and cancel causing a rhythmic pattern of louder and softer sound called beats. fb = | f1 – f2 | If the frequencies are the same but completely out of phase they will cancel and If intensities are equal they will Cancel completely This is how noise canceling headphones work