# Beat frequency for hanging bar between two wires with added offset weight

## Homework Statement

A uniform 165 N bar is supported horizontally by two identical wires A and B. A small 185 N cube of lead is placed 3/4 of the way from A to B. The wires are each o.75 m long and have a mass of 5.50 g. If both of them are simultaneously plucked at the center, what is the frequency of the beats that they will produce when vibrating in their fundamental?

## Homework Equations

fundamental frequency = (1/2L) * √(F/μ).
where L is the length of the wire, (μ) is the mass per unit length, F is the tension in the wire
f(beat) = f1-f2.

## The Attempt at a Solution

I tried to calculate the frequency of each wire A and B.
I let frequency1 be the frequency of the wire with the block closer to it, so wire B.

frequency1=(1/(2*0.75m))*√(F1)/(0.0055kg/0.75m)
frequency1=7.785*√F1

frequency2=7.785*√F2, as L and μ are the same for both wires.

This is where I got stuck. I tried to calculate the tensions:

F1= (1/2)*(165N) + (3/4)*185 = 221.25N
F2= (1/2)*(165N) + (1/4)*185 = 128.75N

I'm not sure if the tension due to the block would be distributed in the way I did.
When i put these tensions into the equation i get a large number, but i know that beats don't occur at frequency differences greater than 10-15 Hz.

Thank you.

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I have not checked your numerical answers all the way through but I do get the tension to be the same as yours.
I cant see anything wrong with your method.
I got the beat freq1uency to be 28Hz.
I will double check my numbers and correc this if it is wrong !!!

It is 28 Hz. I was a bit confused when i got this answer because my teacher said you don't hear beats at frequency differences greater than 15 Hz. Thanks for your help

Beat frequency is a frequency in its own right!!! It is the difference between the 2 frequencies and if that is an audio frequency you will hear it.
Do you play a musical instrument? Beat frequencies are used to tune instruments.

Sorry what i meant was you don't hear the individual beats and that it merges into dissonance or consonance. I should have just gone through with the 28 Hz. Thank you though, now i understand beat frequencies do occur at greater values. And no i don't play any instruments but my prof demonstrated tuning a guitar.

I know what you mean.... low beat frequencies sound like a 'throb' rather than a 'note'
Your prof probably got to produce slow throbs as he tuned his guitar!!!
But the beat frequency can sound (is!!!) a genuine note in its own right.