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Vibrating String

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The following features of a bounded string system are demonstrated by the student:

1. stable waveforms will be seen only when the driving frequency is at or near one of the natural oscillating frequencies of the system;

2. the natural oscillating frequencies are given by the expression w(n) = (n*PI/L)*(T/u)^.5 where L is the length of the string T is the tension in the string, and u is the linear mass density of the string;

3. the speed of the wave is given by v = (T/u)^.5 and that for a a given tension the speed of the wave is independent of the oscillating frequency;

4. for a given tension, the wavelength of the waves is given by lambda = nL/2; the nodes are found at positions x = lambda(n)/2, lambda(n), 3 lamda(n)/2, etc and the antinodes are found at positions x = lambda(n)/4, 3 lamda(n)/4, 5 lambda(n)/4, etc; and

5. a plot of the square of the absolute value of the amplitude of vibration vs w for w near a given natural oscillating frequency will have the common shape of a resonance curve.

Experimental values for all of the parts tend to be within 5% of the values computed from the theoretical expressions.

Course Level

Introductory: P3, P13, P15

Student Handouts


Number of set-ups available:

Per lab station:

1 oscillator/BNC to banana adaptor (female)
1 frequency counter/BNC cable
1 amplifier
1 black background
4 1 kg masses
2 0.5 kg masses
1 hanger
1 piano wire stretched between 2 right angle posts
2 C-clamps
1 paper towel
2 teflon sleeves
1 magnet
banana leads
2 alligator clips
1 2 meter meterstick
2 ring stands
2 three pronged clamps
2 bar clamps

Charges apparatus

Circuit Diagrams

circuit diagram


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Site contact: largent@Dartmouth.EDU

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