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Standing Waves. Nodes are where the resulting wave remains stationary. Anti-nodes are where the resulting wave has max amplitude. When an incident wave interferes with a reflected wave to form areas of constructive and destructive interference. Standing Waves on a String.

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## Standing Waves

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**Standing Waves**Nodes are where the resulting wave remains stationary. Anti-nodes are where the resulting wave has max amplitude. When an incident wave interferes with a reflected wave to form areas of constructive and destructive interference.**Standing Waves on a String**• Nodes must occur at the ends of the string because these points are fixed**Standing Waves on a String, final**• The lowest frequency of vibration (b) is called the fundamental frequency**Standing Waves in Air Columns**• If one end of the air column is closed, a node must exist at this end since the movement of the air is restricted • If the end is open, the elements of the air have complete freedom of movement and an antinode exists**Animation**http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html**Resonance in Air Column Open at Both Ends**• In a pipe open at both ends, the natural frequency of vibration forms a series whose harmonics are equal to integral multiples of the fundamental frequency**Open Tube Calculation**The range of a certain pipe organ is from 8.00 Hz to 30,000 Hz. What is the range of pipe lengths if they are opened at both ends (Assume that the speed of sound is 343 m/s.) L = 21.4 m L = 0.00572 m**PVC instrument**• Toccata and Fugue in D minor**Resonance in an Air Column Closed at One End**• The closed end must be a node • The open end is an antinode • There are no even multiples of the fundamental harmonic**Closed Tube Calc**The range of a certain pipe organ is from 8.00 Hz to 30,000 Hz. What is the range of pipe lengths if they are closed at one end (Assume that the speed of sound is 343 m/s.) L = 10.7 m L = 2.86 mm**Timbre**• In music, the characteristic sound of any instrument is referred to as the quality of sound, or the timbre, of the sound • The quality depends on the mixture of harmonics in the sound**Quality of Sound –Tuning Fork**• Tuning fork produces only the fundamental frequency**Quality of Sound – Flute**• The same note played on a flute sounds differently • The second harmonic is very strong • The fourth harmonic is close in strength to the first**Quality of Sound –Clarinet**• The fifth harmonic is very strong • The first and fourth harmonics are very similar, with the third being close to them

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