Standing waves in a coffee cup

Demonstration no.: 92
Purpose: To demonstrate standing waves in a coffe cup and the influence of the handle on the frequency.
Summary: If you strike the side of a coffee cup across from the position of the handle, the cup will vibrate with a specific frequency. If you strike the cup 45 degrees from that position, the cup will vibrate with another frequency
Keywords: Damped oscillations, harmonic motion, sound, resonance, standing waves, oscillations, transversal waves.

Description:

If you strike the side of a coffee cup with a spoon, the cup will start vibrating. The vibrations are so small that you cannot see them with the naked eye, but the opening of the cup actually vibrates so that its shape changes between a circular and an elliptic shape. This is a standing wave around the circumference of the cup.

Though the vibrations are too small to see, you can hear them. The vibrating cup makes the surrounding air oscillate, thus creating sound. You can then hear the cup "sing" with the same frequency as the vibrations.

If the cup is completely symmetric, the cup will "sing" with the same frequency independent of which side the cup is struck. This, however, is not the case if the cup has a handle.

Two different modes of oscillation can be excited in a coffee cup dependent on where the cup is struck.

The handle of the cup has an effect on the oscillations of the cup. When the cup vibrates, the standing wave around the edge of the opening will have four nodes and four anti-nodes (in the fundamental mode).

If the cup is struck opposite to the handle, the handle will coincide with an anti-node. Since the handle is an extra weight to move, this will slow the oscillation. If the handle coincides with a node, the oscillation is not affected.

With a pen a standing wave in a coffee cup is excited.

Notice that you can strike the cup several places. If the cup is struck opposite the handle or 90 degrees to each side, you excite one oscillation. If the cup is instead struck 45 degrees to each side, another mode of oscillation is excited.

To visualize the oscillations in the cup, it is possible to take pictures using a special technique called holographic interferometry. This has for instance been done by two American scientists, who have supplied the following pictures to Fysikbasen:

Pictures of standing waves in a cup recorded with holographic interferometry. In one picture, the handle coincides with a node of the wave; in the other with an anti-node. By courtesy of Dr. Andrew Morrison and Dr. Thomas D. Rossing of the Northern Illinois University, USA.

Another picture recorded with holographic interferometry. In this picture, the handle coincides with a node. By courtesy of Dr. Andrew Morrison and Dr. Thomas D. Rossing of the Northern Illinois University, USA.

Equipment and materials:

Coffee cup

References:

Link to demonstration in database at Oberlin College.
Link to demonstration in database at Georgia Institute of Technology.
Article on this experiment at the Society of Amateur Scientists.
Link to demonstration in database at University of Maryland.

PIRA DCS: 3D40.00 (Oscillations and waves: Instruments)

Updated: 19 August 2007

If you have comments, corrections or suggestions regarding this demonstration,
please us at FYSIKBASEN.DK.