What Beat Frequency Results from Unequal Tensions in Piano Strings?

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Homework Help Overview

The problem involves understanding the beat frequency produced by two piano strings tuned to the same note but under different tensions. Specifically, it examines the scenario where one string's tension decreases, affecting its frequency and resulting in a beat frequency when struck simultaneously with the other string.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the relationship between string tension and frequency, questioning how to derive the second frequency needed to calculate the beat frequency. There are inquiries about the relevant equations and the necessary parameters for solving the problem.

Discussion Status

Some participants have provided guidance on using the tension-frequency relationship, while others express uncertainty about how to apply it without specific values for mass and length. The discussion is ongoing, with multiple interpretations and approaches being explored.

Contextual Notes

Participants note the absence of specific values for the mass and length of the strings, which are relevant to the tension-frequency relationship. There is an emphasis on understanding how changes in tension affect frequency without needing to know these parameters explicitly.

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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?
 
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I think so...also you will need the relationship between the tension in the string and the frequency of vibration
 
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
 
That equation is indeed helpful for solving this problem. You'll need to figure out the second frequency however.
 
physics10189 said:
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?
 
Tension=(velocity^2)*((mass)/(length))

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

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