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

2. Standing Waves on a String Nodes must occur at the ends of the string because these points are fixed

3. Standing Waves on a String, final The lowest frequency of vibration (b) is called the fundamental frequency The lowest frequency of vibration (b) is called the fundamental frequency

4. 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 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 If the end is open, the elements of the air have complete freedom of movement and an antinode exists

5. Animation http://www.physics.smu.edu/~olness/www/05f all1320/applet/pipe-waves.html

6. Tube Open at Both Ends

7. 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 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

8. 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

9. PVC instrument PVC instrument PVC instrument PVC instrument Toccata and Fugue in D minor Toccata and Fugue in D minor Toccata and Fugue in D minor Toccata and Fugue in D minor

10. Tube Closed at One End

11. Resonance in an Air Column Closed at One End The closed end must be a node The closed end must be a node The open end is an antinode The open end is an antinode There are no even multiples of the fundamental harmonic There are no even multiples of the fundamental harmonic

12. 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

13. Toccata and Fugue in D minor Toccata and Fugue in D minor Toccata and Fugue in D minor Toccata and Fugue in D minor

14. Timbre In music, the characteristic sound of any instrument is referred to as the quality of sound, or the timbre, of the sound 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 The quality depends on the mixture of harmonics in the sound

15. Quality of Sound – Tuning Fork Tuning fork produces only the fundamental frequency Tuning fork produces only the fundamental frequency

16. Quality of Sound – Flute The same note played on a flute sounds differently The same note played on a flute sounds differently The second harmonic is very strong The second harmonic is very strong The fourth harmonic is close in strength to the first The fourth harmonic is close in strength to the first

17. Quality of Sound – Clarinet The fifth harmonic is very strong The fifth harmonic is very strong The first and fourth harmonics are very similar, with the third being close to them The first and fourth harmonics are very similar, with the third being close to them