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Video: Determining the Beat Frequencies Produced by Three Sound Waves

Ed Burdette

A piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 128.3 Hz. What beat frequency is produced by the 128.3 Hz and 128.1 Hz notes? What beat frequency is produced by the 127.8 Hz and 128.3 Hz notes? What beat frequency is produced by the 127.8 Hz and 128.3 Hz notes?

03:05

Video Transcript

A piano hammer hits three strings that emit frequencies 127.8, 128.1, and 128.3 hertz. What beat frequency is produced by the 128.3 hertz and 128.1 hertz notes? What beat frequency is produced by the 127.8 hertz and 128.3 hertz notes? What beat frequency is produced by the 127.8 hertz and 128.3 hertz notes?

Let’s start by highlighting the vital information given to us in the statement. The three emitted frequencies 127.8, 128.1, and 128.3 hertz are what we’ll keep track of to establish the beat frequencies in parts one, two, and three of the question.

To start, let’s recall the relationship that establishes beat frequency. When we combine two frequencies, call them 𝑓 sub one and 𝑓 sub 2, then the magnitude of that difference, in other words the magnitude of 𝑓 sub one minus 𝑓 sub 2, is equal to the beat frequency that’s produced.

Let’s name the three given frequencies in this problem 𝑓 one, 𝑓 two, and 𝑓 three, respectively. And you want to solve for the beat frequency between each combination of 𝑓 one, 𝑓 two, and 𝑓 three.

In part one, we’re asked for the beat frequency between 𝑓 three and 𝑓 two. We’ll call that beat frequency 𝑓 sub b one, and that equals the magnitude of 𝑓 three minus 𝑓 two. When we enter the given values for those frequencies, we find a difference or a beat frequency of 0.2 hertz. If this sound was audible, then we would hear a beat once every five seconds.

In part two, we’re asked to solve for the beat frequency between 𝑓 three and 𝑓 one. We can call that frequency 𝑓 sub b two. When we enter those given values in, we find that the beat frequency between these two frequencies is 0.5 hertz. If this sound was audible, we would hear a beat once every two seconds.

Finally, we’re asked to solve for the beat frequency between 𝑓 two and 𝑓 one. We’ll call that 𝑓 sub b three. When we enter the given values for 𝑓 two and 𝑓 one, we find that this beat frequency is equal to 0.3 hertz.

These are the beat frequencies for each combination of these three frequencies.