A popular party trick just got turned inside out. Fill a row of wine glasses with water to different levels, rub your finger around the rim and – hey presto! – you have a glass harp. Now it seems an empty wine glass submerged in liquid plays just as well.
The pitch, or frequency, at which the glass resonates depends on how much the liquid inside pushes back as you play.Daniel Quinn of Stanford University, California, and Brian Rosenberg, then a grad student at Princeton, realised that this should work when the liquid pushes into the glass from outside as well.
The pair ran a few experiments and found that the ordinary glass harp and the “inverted” glass harp were essentially the same, mathematically. “That’s one of the things we were surprised about,” Quinn says. “One is really just a mirror image of the other.”
They went on to write a universal rule for glass harps, modelling them as a cylinder and a metal rod that displaces or holds liquid. If the rod is smaller than the glass, it goes inside it; if it’s larger, it’s a liquid-filled pot encircling it. If the rod has a radius of 0 – in other words, it’s not there – you have an ordinary glass harp (see the picture above).
But modelling wasn’t enough – the pair also wanted to try playing their newly invented instrument. It turns out that a single wine glass in a tub of water makes an eerie, theremin-like sound, and the pitch changes as the glass moves up and down.
“You can control the depth yourself, so you only need one glass to perform a variety of pitches,” Quinn says. It was easy to play, too – after just a few minutes’ practice they could play the children’s song Mary Had a Little Lamb.
Journal reference: Physical Review E, DOI: 10.1103/PhysRevE.92.021003