Building a sound or acoustic visualizer is an easy and interesting project that can be used to create exotic images such as these:
and this 
and this
Here's how:
Taking a closer look, the visualizer is simply a piece of scrap lumber to act as a base, a laser pointer at one end and a cylinder with a flexible membrane stretched over one end at the other.
The laser shines on a small mirror attached to the membrane. When you talk into the open end of the cylinder it makes the membrane vibrate, which causes the mirror to move with the result that the laser beam is reflected through rapidly changing angles to a far wall producinging complex patterns.
A simple way to mount the laser pointer is to wrap several tight winds of stiff wire around it and screw the end of the wire onto the base. The short length of wire between the base and the pointer can be flexed up and down, left and right to aim the pointer at the mirror on the membrane. By pushing the pointer forward so that the 'on' button is under the wire loops, they will depress it to keep the laser turned on.
The cylinder should be around 5 inches in diameter. I've made them smaller and as large as 12 inches and 5 to 6 inches works the best. It can be a coffee can with both ends cut out or a straight union for a large plastic plumbing line. Any short, strong cylinder will work. The flexible membrane is made from a large 12-inch balloon. Inflating the balloon first for two hours will pre-stretch the rubber and make it easier to wrap over the end of the cylinder. After pre-stretching, deflate the balloon and cut slightly less than halfway from the fill tube to the middle of the balloon, stretch this larger piece over the end of the cylinder and secure it with tape. Even after pre-stretching the rubber is hard to get over the end of the cylinder so having a helper assist you makes things go much easier.
Using a good quality double faced tape, mount a 1/4-1/4 inch piece of mirror 1/3 of the way from the rim to the center of the membrane. And your done!
Place the sound visualizer on one end of a table and point it a a wall at least 15 feet away. Turn on the laser pointer and bend the mount so the beam reflects off the mirror to the wall. Talk into the open end of the cylinder and you'll see the laser spot move in a wide range of complex patterns, such as the following:
Each word will have a different shape. I found children enjoy saying their own names to see what they look like. Another activity they enjoy is humming into it at a constant pitch to create a perfect circle. Finding the pitch is tricky and can even be made into a game by seeing who can find it the fastest.
While talking into the sound visualizer or playing music into it is interesting, where it really comes to life is when the output of a tone generator is fed into it. By selecting the proper frequencies, beautiful, stable or slowly undulating figures can be created.
One way to do this is to load a free tone generator onto an ipad, computer of cell phone. They can be found on-line. The one I prefer is The Generator 1.3.3. Tone and Noise Generator. What's great about this one is that it has two tone generators built into it that can be played at the same time. Using one generator creates a wide range of still patterns. But, using two creates undulating patterns that can be fine tuned by adjusting the frequency of one of the generators to change the shape of the pattern and how fast is moves. The effect is impossible to explain on a static page such as this so I invite you to view the YouTube video at the bottom of this page to see how the look in motion.
The ipad with the tone generator works great for creating the sounds needed to produce interesting images, but it doesn't produce them loud enough for the visualizer to pick up. To amplify them use a small audio amplifier or a powered, amplifying speaker. Such speakers are often battery powered and available for as little as $10.
With such a setup, you can spend hours searching through hundreds of frequency combinations looking for the most interesting patterns. The best ones occur when the one of the frequencies is a fractional or whole harmonic of the other frequency. For example, if the first oscillator is at 100 Hertz, the first full harmonic would be with the second oscillator at 200 Hertz.
One thing to keep in mind is that these patterns aren't actually visualizations of sound waves. They are visualizations of the vibration of the rubber membrane and have little to do with the shape of the sound waves that made the membrane vibrate. An analogy would be a bell and a hammer. While the hammer striking the bell starts it vibrating, the bell's vibration is based on its shape and size and does not reflect anything about the motion of the hammer before it stuck the bell. In the case of the sound visualizer, the visualizer is the bell and the sound of your voice or the tone generator is the hammer.
I hope you'll give one of these sound visualizers a chance. They're a lot of fun. Here are a few more typical traces:
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