Vibrating String

A 1.5m length of string driven at one end and fixed at the other shows standing waves for various driving frequencies.

What it shows

vibrating string

The fundamental is the most dramatically visible state (usually around 15Hz). It's possible to show up to 8 nodes clearly--bearing in mind the amplitude of the antinodes in the higher states will decrease due to the elasticity of the string. For best visibility the string is coated liberally with fluorescent chalk and illuminated with a blacklight.

vibrating string vibrating string

Setting it up

The entire apparatus fits on a single mobile cart. Since precision is the key to making this demo work well, proper setup requires some time to complete.

vibrating string

One side of the bench or table holds the fixed end of the string, and the Pasco Mechanical Vibrator. The string is tied in a loop, and the loop goes on the vertical rod.

On the other side of the bench is the mass and pulley that make this a constant tension system. Align the clamp bases so that the string is square to the table. The first vertical rod should line up with the V of the pulley, which will be offset from the second vertical rod by the clamps used. The pulley should also be square and plumb so the string doesn't rub or fall off. Loosen and align the clamps by eye, looking down the string from the pulley side.

Below the loop of string on the first vertical rod, a right angle clamp holds a rod which fits the hole in the base of the Mechanical Vibrator (shaker). The angle of the clamp and the position of then base allow for adjustment of the driven point on the string. There is generally a four inch section of the string between the vertical rod and the alligator clip on the shaker. The point of the string that is shaken acts sort of like a node, more so does the point where the string goes over the pulley. The shaker has an amplitude, it's a lot less than the amplitude of the string at resonance.

A mass hanging on the other side of the pulley keeps tension on the string, usually 200 or 500 g. The string is fairly elastic, and will stretch. Check the length of string with the weight attached. It should be long enough to get over the pulley, and not so long that the weight hits the floor. Note: While adjusting the length of the string, make sure the alligator clip from the Mechanical Vibrator is not holding the string. Remove the alligator clip from the string before making any and all adjustments of the string. The shaker is hardy, but can be damaged by sudden off-axis forces on a lever arm, for example, if the string slips the pulley and the weight falls.
Only when the demo is in place and ready to be tested or used; attach the shaker's alligator clip to the string.
Remove the clip from the string before moving the cart after the demo is used.

vibrating strings vibrating strings


Vertical polarization of the string can be shown by using your fingers as a filter.

vibrating strings vibrating strings