Fun With Standing Waves

In this video, we see a dramatic demonstration of standing waves patterns, which form when travelling waves constructively and destructively interfere as they pass through one other.

You can easily make standing waves yourself by taking a rope, fixing it on one end, and shaking the other end up and down. If you play around you’ll find that at a specific frequency of vibration, one big peak forms in the center of the rope. That’s because as one wave peak travels down the rope and reflects off the end, the next peak meets it wave at the same spot resulting in a “double wave”. This adding of wave peaks is called constructive interference. If you double your original “fundamental” frequency you’ll get two big peaks with a flat spot in the center. The big peaks (antinodes) occur where the travelling waves are in phase and constructively interfering, while the flat spot (a node) occurs where the peaks are exactly out of phase. The more standing wave peaks in the rope the higher the “harmonic.”

It’s no coincidence that the word harmonic reminds us of music— the notes played on musical instruments are standing sound waves. For example, if you blow on a clarinet the sound waves travelling back and forth inside the tube interfere with each other, creating standing waves. These result in a loud resonant sound at a specific frequency (also called, in this case, a specific pitch or note). If you change the length of the tube by closing one of the holes you’ll hear a different note because the standing wave frequencies depend on the length of the tube.

In the video, the idea is the same but the wave patterns are more complicated. The powder on top of the vibrating speaker flows much like waves in a fluid and as the waves travel along the surface they reflect off the edges, pass through other travelling powder waves, and we see interference patterns. Unlike with the rope, however, these patterns are two-dimensional and result in a variety of complex standing wave cells. Notice that a higher pitch coming from the speaker (which corresponds to a higher vibration rate) results in a larger number of standing wave cells—just like with the rope. You can also see that these patterns only form at specific frequencies. At in-between frequencies there are no standing waves.