Beat Frequency

What do you hear when there are two sounds that have similar, but not identical, pitches?

In Activities 1 and 2, students explored the wave nature of sound. They looked at how sound is a wave and how the frequency and amplitude of that wave determine what our ears hear. In this activity, students will learn about what happens when those waves interact with each other. Though light waves are transverse waves and sound waves are longitudinal waves, the way they interact is very similar.

Like light waves, when sound waves run into each other they interact. As students learned in Activity 1, sound waves are compression waves — meaning they are made up of compressed material and relaxed material. If two waves hit each other, it will either be a relaxed part interacting with a compressed part or two compressed parts interacting with each other.

Just like with light waves, when two waves interact at the same point in the waves, the waves add together constructively and create a bigger wave. When compressions hit each other, the air (or whatever sound is traveling in) is compressed even more and relaxed even more. Because the amplitude of the wave is now bigger, your ear hears the sound as louder. The two sounds waves have interfered constructively.

If one sound wave is compressed when it hits the relaxed portion of the other wave, the two waves cancel each other out. They interfere destructively. Your ear doesn’t hear any sound at all. If you have two tuba players in two different chairs playing the same note and you are standing some distance away, you are going to hear one really loud tuba note. That’s because it’s very easy for waves of the same wavelength to interfere constructively. It’s easy to line up two waves that are the same wavelength.

But what would happen if the tubas were playing two different pitches? It wouldn’t be so easy to line up the two waves. It would be like trying to line up three-ring binder paper when one piece had holes just a little off from the other. It’s never going to work out quite right.

But what would we hear in a situation like this? If you were to take two waves of slightly different wavelengths and put them on top of each other, at some points they would line up so that you would have compressions on top of compressions, and at some points they wouldn’t. The waves are constructively interfering at some points and destructively interfering at other points. If you were to hear these waves, you would hear these types of interference as the note getting louder and softer; sometimes it’s amplified, sometimes it’s canceled out.

If one of the tuba players is a bit off key, you would hear the note but would hear it getting louder and softer. The frequency at which the note gets louder and softer is called the beat frequency. People that tune instruments such as pianos can listen for the beats to see if two notes are actually in tune.

In this experiment, students will use two tubes to create pitches and hear beat frequencies. They will put two identical tubes in two cups of water at different heights. Just like in Activity 1, the different length columns of air will cause the tubes to play slightly different notes when the air is vibrated by the students blowing across the top. Because the two notes are so close, students will be able to hear the resulting sound getting louder and softer.

Real world connections -

• Based on what you learned, why do people use earplugs to block out loud sounds?
• When musicians play instruments, they play different notes by adding or lifting fingers to the keypads. Using what was discussed in this activity, why does this change the note?

Suggestions for drawing, illustrating, presenting content in creative ways

• Have students explore different models of visualizing sound waves

Engineering and design challenges connected to the content

• Have students try and soundproof an area of the classroom using materials that could absorb sound waves.