What is the equation for relating tension to frequency?

T.In summary, the problem involves finding the correct tension for a middle C string on a piano that is flat by 15 Hz. The formula for finding the resonant frequency of a string under tension is needed, which is f=(n/2L)√(T/μ).
  • #1
gtp405
1
0
Ok this problem seems blatantly easy but for some reason I just cannot find the equation.

Homework Statement



The middle C string of a piano is supposed to vibrate at 261.6 Hz when excited in its fundamental mode. A piano tuner finds that in a piano that has a tension of 900N on this string, the frequency of the vibration is too low (flat) by 15 hz. How much must he increase the tension of the string to achieve the correct frequency?

Homework Equations



This is what I can't find.

The Attempt at a Solution



At first glance to me this problem seems extremely easy, just use a certain formula that relates tension to frequency in some way, but I've looked high and low in the book and can't seem to find it. All I really need is an equation to relate the two.

Thanks!
 
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  • #2
[tex]f=\frac{n}{2L}{\sqrt{\frac{T}{\mu}}[/tex]

gives the resonant frequencies for a string under tension
 

What are sound waves?

Sound waves are vibrations that travel through a medium, such as air or water, and can be heard by the human ear.

How are sound waves produced by a piano?

A piano produces sound waves by using hammers to strike strings that are tuned to specific frequencies. These vibrations are then amplified by the piano's soundboard and travel through the air as sound waves.

What is the frequency range of sound waves produced by a piano?

A piano's frequency range typically spans from 27.5 Hz (A0) to 4186 Hz (C8). However, the actual frequency range may vary depending on the type and quality of the piano.

How do sound waves from a piano differ from other instruments?

The sound waves produced by a piano are unique due to the complex harmonics created by multiple strings being struck at once, as well as the use of a soundboard to amplify and project the sound. This results in a rich and full tone that is distinct from other instruments.

Can sound waves from a piano be harmful?

No, sound waves from a piano are not harmful as long as they are within a safe range of volume. Prolonged exposure to loud sound waves, however, can lead to hearing damage. It is important to practice safe listening habits and take breaks when playing or listening to loud music.

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