### 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?

Letβs 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 weβll keep track of to establish the beat frequencies in parts one, two, and three
of the question.

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

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

In part one, weβre asked for the beat frequency between π three and π two. Weβll call that beat frequency π sub b one, and that equals the magnitude of π three
minus π 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, weβre asked to solve for the beat frequency between π three and π one. We can call that frequency π 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, weβre asked to solve for the beat frequency between π two and π one. Weβll call that π sub b three. When we enter the given values for π two and π 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.