1. Longitudinal Standing Waves and Complex Sound Waves 17.6 and 17.7

2. 17.6 Longitudinal Standing Waves Just like stringed instruments rely on standing transverse waves on strings Wind instruments rely on standing longitudinal sound waves in tubes The waves reflect off the open ends of tubes One difference at the ends are antinodes instead of nodes

3. Formula for Tube Open at Both Ends Distance between antinodes = ½ Distance between antinodes = ½ Tube must be integer number of ½ Tube must be integer number of ½ –L = n(1/2 n ) or n = 2 L/n f n = v / n

4. Example What is the lowest frequency playable by a flute that is 0.60 m long if that air is 20 °C. f = 193.3 Hz f = 193.3 Hz

5. Tube with One Closed End Node at the closed end Antinode at the open end At fundamental frequency L = ¼ At fundamental frequency L = ¼ The 2 nd harmonic adds one more node or ½ The 2 nd harmonic adds one more node or ½ Thus the lengths are odd integer multiples of ¼ Thus the lengths are odd integer multiples of ¼

6. 17.7 Complex Sound Waves In reality most musical instruments not only produce the one fundamental frequency Most instruments produce harmonics also The wave we hear is the sum of the fundamental and the harmonics The varying amplitudes of the harmonics give each instrument its timbre

7. Complex Sound Waves

8. Practice Problems Try blowing your way through these problems 506 CQ 14 – 15, P 34 – 38 Total of 7 Problems