Beats

What the Activity is for

Generating and then hearing beats.

Hear, and perhaps see, how two contributions coming into and out of step can result in a third frequency that is not actually there.

What to Prepare

• a police whistle
• a computer linked to powered loudspeakers (do not try to run this experiment from your laptop speakers) and a data projector
• Audacity or another sound processor

What Happens During this Activity

Choose a single frequency, say 1000 Hz, and generate five seconds worth of sound. Play this. Silence the channel.

Choose a new channel and generate five seconds of a new single frequency, say 1010 Hz. Play this. Silence this channel.

Now zoom in to both channels so that you can see about a 0.25 second of both sounds. Use the cursor to move through the channels, looking for a point where both signals are in step – that is they're going up and down together, albeit temporarily. Now scan through the channel until you meet a point where again they're going up and down together. Use either the time axes or the software facilities to measure the duration between these two points. Then ask how many times per second these frequencies come back into step, taking care to match the development of this point to the abilities of the class. Scan through the channel to confirm this prediction. Now use the idea of superposition to predict the frequency with which you'll get more and less sound if you play both channels.

Now play both channels. Listen very carefully: you'll hear a new frequency generated as a result of the first two. This frequency is 10 Hz. You can now repeat and extend the procedure but having chosen a new pair of generated frequencies, separated either by 10 Hz or a new different separation. Explore what you hear and, if you like, what you see. You might combine both channels using the software in order to show what is arriving at the ear.

As a finale, record the police whistle into the sound analyser, and you'll find two real frequencies, and one ghost frequency that is generated as a result of the contributions of these two. The ghost frequency depends on the difference between the real frequencies as this determines how often they are in and out of step.