Lab 4: Strings

• Standing Waves• Modes• Slinky Experiments

1. Frequency of Modes2. Pulse on Slinky

• Experiments with String– Computer as Driver Control1. Finding the Fundamental Mode2. Higher Modes3. The “Plucking Game”4. Changing the Length of the String5. Changing the Tension on the String6. Changing the Mass Per Unit Length of the String

String Oscillations onMusical 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

Waves

Speed of a wave

f

Tv

Frequency of a wave

v

f

v

Waves propagate in space– characteristic length of a wave = wavelength

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

Displacement

Standing Waves (1)

• Build up (superposition) of traveling waves– Driving wave & reflected

wave

driving wave

reflected wave

N N N N NA A A A

N: nodeA: antinode

Standing Waves (2)standing wave

4

Tt

43T

t

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

0t

42T

t

Fixed-End String

xL0

A

Third mode(Second Overtone)

?3 ?

First mode(Fundamental)

L2 1

Second mode(First Overtone)

L2

Data Table

String experiments with ƒ1 = 45 Hz case:

Picture mode #, nMeasured ƒ

(Hz)

n · measured ƒ1

(Hz)# of nodes

1 45 1 · 45 = 45 2

2 2 · 45 = 90

3 135

Superposition

Coexistence of two modes= Superposition (red)

Demo http://www.surendranath.org/Applets/Waves/Harmonics/HarmonicsApplet.html

0t21T

t