1. Lab 4: Strings Standing Waves Modes Slinky Experiments 1.Frequency of Modes 2.Pulse on Slinky Experiments with String –Computer as Driver Control 1.Finding the Fundamental Mode 2.Higher Modes 3.The “Plucking Game” 4.Changing the Length of the String 5.Changing the Tension on the String 6.Changing the Mass Per Unit Length of the String

2. String Oscillations on Musical Instruments Stringed musical instruments –Can produce a single tone steadily (e.g. A @ 440 Hz) –String oscillation for a single tone Complex But periodic (e.g. 440 Hz) Can a single string produce sounds at different pitches? –How? –At what frequencies? How does the string oscillation look like? –Can they occur simultaneously? How does the string oscillation look like? How does the tone sound like? Demo http://www.surendranath.org/Applets/Waves/Harmonics/HarmonicsApplet.html

3. Waves Speed of a waveFrequency of a wave v Waves propagate in space – characteristic length of a wave = wavelength

4. Pulse on a String traveling pulse Waves on a string:transverse waves Transverse wave: displacement of medium perpendicular to the direction of propagation T :Tension on the string M/ ℓ :Mass per unit length of the string  :Density of the string (= M/ ℓ ) Note:and Demo http://phet.colorado.edu/simulations/stringwave/stringWave.swf

5. Superposition “If the medium is subject to 2 or more disturbances at the same time, the net effect is to add these disturbances algebraically (with a sense of direction)” Displacement

6. Standing Waves (1) Build up (superposition) of traveling waves –Driving wave & reflected wave driving wave reflected wave NNNNN AAAA N: node A: antinode

7. Standing Waves (2) standing wave When the standing wave forms, all nodes become clear and sharp – stationary points stand out and elsewhere blurred above ~20Hz.

8. Fixed-End String x L 0 A Third mode (Second Overtone) ? First mode (Fundamental) Second mode (First Overtone)

9. Fixed-End String First mode Third mode ? Second mode

10. Data Table String experiments with ƒ 1 = 45 Hz case: Picturemode #, n Measured ƒ (Hz) n · measured ƒ 1 (Hz) # of nodes 1451 · 45 = 452 22 · 45 = 90 3135

11. Superposition Coexistence of two modes = Superposition (red) Demo http://www.surendranath.org/Applets/Waves/Harmonics/HarmonicsApplet.html