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

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

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

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 …

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

Harmonics in columns of Air One End Open Both Ends Open

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

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