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# Beat Frequency of a Sound Wave

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Source:
Author: Jerry Silver

### The Idea

When waves meet up at the same point in space, the waves add together to form a new wave. This combining of waves is called superposition. The waves add together in a process called interference. If the crests form at the same place, we have constructive interference and the combined wave is smaller. If a crest meets a trough, we have destructive interference and a smaller wave.

Sometimes when waves combine, the pattern they produce is itself a wave. We can hear the beat frequency of a sound wave most easily when two sound waves are separated by a small frequency difference.

### What You Need

• source of two tones that differ by a few Hz. Some options for this include:
• adjustable tuning fork pair with resonant cavities
• 2 matched tuning forks, one of which can be detuned by applying a small mass to the tines of one of the tuning forks
• (Polyphonic) keyboard synthesizer
• waveform generator with two channels or two waveform generators
• optional: a good pair of ears
• optional: an oscilloscope—either a physical instrument or a sound card oscilloscope

### Method

1. Play two tones at the same time that are different by only a few Hz. For instance, you can use 440 and 445 Hz. Or, you can play two notes on a keyboard separated by a step or two.
2. Listen carefully. See if you can distinguish the first tone and the second tone individually. Then, listen for a fading in and out of the overall sound. That throbbing of the basic tone is called the beat frequency. The pulsation itself has a frequency equal to the difference between each of the two individual frequencies.
3. Using the technique developed in Project 64, display the combined waves for each of the tones on the oscilloscope.
4. Measure the frequency of the overall pulsating wave pattern that envelops both waves. Compare that to the difference in frequency for each of the two individual waves.

### Expected Results

You should hear a pulsating throbbing tone that causes the combined tones to periodically grow louder and softer.

As an example, by combining a 440 Hz wave with a 445 Hz wave, you get a combined tone that gets louder and softer every five seconds, as shown in Figure 75-1. The beat frequency is the difference between the two original waves.

### Why It Works

When two waves are produced at the same location, the beat frequency equals the difference between the frequencies of the two waves.

### Other Things to Try

We can also look at the product of the two waves that exaggerates the overall pattern of the beat frequency, as shown in Figure 75-2. Many oscilloscopes display the product of the two input waveforms.

### The Point

The beat frequency is the difference between the frequencies of the two individual waves.