What Beat Frequency Results from Unequal Tensions in Piano Strings?

[physics10189]

Homework Statement

In certain ranges of a piano keyboard, more
than one string is tuned to the same note to
provide greater intensity. For example, the
note at 162 Hz has two strings at this pitch.
If one string slips from its normal tension of
645 N to 516 N, what beat frequency will be
heard when the two strings are struck simul-
taneously? Answer in units of beats/s.

Homework Equations

f(beat)=f1-f2

The Attempt at a Solution

Am i using the right equation?

 

[einstein_a_go_go]

I think so...also you will need the relationship between the tension in the string and the frequency of vibration

 

[physics10189]

how would I do that because
the question is asking me beats per sec
how would i get ther relationship between the tension and the frequency

 

[Redbelly98]

That equation is indeed helpful for solving this problem. You'll need to figure out the second frequency however.

 

[Redbelly98]

how would I do that because
the question is asking me beats per sec
how would i get ther relationship between the tension and the frequency

What equation does your textbook have that involves the string tension?

 

[physics10189]

Tension=(velocity^2)*((mass)/(length))

which i have neither of the length of the string nor the mass of it.

 

[Redbelly98]

That's okay, since the mass and length do not change for the string they are not needed.

You can use that equation to figure out by what factor the velocity (and therefore the frequency) changes when the tension changes by a factor of 516/645