How does tension affect the frequency of a standing wave on a string?

In summary, the fundamental frequency of a string held under tension is affected by the tension and can be calculated using the equation v = (F/(ρ⋅A))^(1/2), where F is the tension, ρ is the density of the string, and A is the cross section area. By doubling the tension, the new fundamental frequency can be found to be 354 Hz. The derivation of this equation is not included in the conversation, but it is important to understand the meaning and application of the equation rather than just plugging in values.
  • #1
sushichan
12
1

Homework Statement


A string is held under tension, with both ends fixed, and has a fundamental frequency of 250 Hz. If the tension is doubled, what will the new frequency of the fundamental mode be?

Homework Equations



The Attempt at a Solution


I don't know how tension can affect the equation v=ƒλ. I re-read the chapter twice still couldn't find it.(Ans: 354 Hz)
 
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  • #2
Hello Sushi, welcome to PF :smile: !

Perhaps you can google "vibrating string" ?
 
  • #3
According to my physics book, the tension affects the speed of sound in the string.
A useful equation is: v = (F/(ρ⋅A))^(1/2)
where F = tension
ρ = density of string
A = cross section area of string :)
 
  • #4
Looks good to me ! Even better: it matches what one finds, e.g. here

Hey, wait a minute ! We're supposed to help folks find the answers by themselves, not just dump them on a plate !
 
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  • #5
BvU said:
Hey, wait a minute ! We're supposed to help folks find the answers by themselves, not just dump them on a plate !

I'm sorry, but my jugment was simply that revealing a, for the asker unknown, equation was a way to help him/her in solving the actual problem.
In my opinion it might be hard to know what to search for without knowing what you look for. And physics is after all about problem solving and not google-searching skills, at least it is for me.

However, I'm sorry and will do my best to avoid helping people like this in the future! :)
 
  • #6
Alettix said:
According to my physics book, the tension affects the speed of sound in the string.
A useful equation is: v = (F/(ρ⋅A))^(1/2)
where F = tension
ρ = density of string
A = cross section area of string :)
What is the derivation of it?
Simply putting values in a formula is not physics.
Although it is OP duty to ask meaning of an equation,
But interest is developed in young guys when one explains them in a proper way.
 
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  • #7
Thank you all, I know how to solve it now ^^

It's just funny I don't see this formula in the textbook.
 

FAQ: How does tension affect the frequency of a standing wave on a string?

1. What are standing waves?

Standing waves are a type of wave phenomenon that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This interference results in a pattern of nodes (points of no displacement) and antinodes (points of maximum displacement) that do not appear to move.

2. How is tension related to standing waves?

Tension is a crucial factor in the formation of standing waves. The tension of a medium, such as a string or a column of air, affects the speed at which a wave travels. When the tension is just right, the waves traveling in opposite directions will interfere constructively, resulting in a standing wave pattern.

3. Can standing waves occur in all types of mediums?

Yes, standing waves can occur in any medium where waves can propagate, such as strings, air columns, and even water. However, the specific conditions for standing wave formation may vary depending on the properties of the medium, such as tension, density, and length.

4. What is the relationship between the wavelength and the length of a standing wave?

The wavelength of a standing wave is directly related to the length of the medium in which it is formed. For example, in a string fixed at both ends, the wavelength of the standing wave will be twice the length of the string. In general, the wavelength of a standing wave is equal to twice the length of the medium.

5. How do standing waves affect sound and music?

Standing waves play a crucial role in the production of musical notes and the sound quality of instruments. In string instruments, standing waves are responsible for creating different harmonics, which produce distinct pitches. The length, tension, and material of the strings all affect the formation of standing waves and, therefore, the sound produced by the instrument.

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