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Factors affecting frequency of sound produced by a stretched string

Smile asks:

Study how the frequency of sound produced will change in each case with the following strings of length 15cms when the strings are tied between  2 ends-

  • aluminium string
  • copper string
  • cotton string
  • metallic string
  • jute string

Also study how the pitch changes when the strings are made taught and loose. Study how the frequency of sound changes with thickness of the following strings

  • cotton strings
  • copper strings

Answer:

This seems to be a homework question or a project question. Therefore I am not giving a detailed answer so as not to tamper the basic aim of assigning a project.

The frequency of sound produced by a stretched string depends on the following factors:

  1. the length of the string
  2. the linear mass density (i.e; the mass per unit length) of the string
  3. the tension in the string

When you are using strings of different materials, the factor which changes is the mass per unit length and the same is true when you are changing the thickness.

When you make the string more taut, the tension increases and vice versa.

The question is given for a constant length. Therefore the case of effect of changing length does not come into picture.

The formula showing the relationship is 

it is evident from the formula that the frequency of sound is

  • inversely proportional to the  length
  • directly proportional to the square root of tension in the string and
  • inversely proportional to the square root of linear density of the string.

on proper substitution, the formula can be recast as

and this will be more convenient for you to answer the questions.

I recommend that you try to explore by actually performing the experiments.

Refer to http://www.tutorvista.com/content/physics/physics-iii/waves/stretched-strings-vibration.php for more


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