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What happens to the frequency of transverse vibration of stretched string if its tension is halved and the area of a cross-section of the string is doubled?

What happens to the frequency of transverse vibration of stretched string if its tension is halved and the area of a cross-section of the string is doubled?

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The frequency of transverse vibration of a stretched string is calculated as

where;

  • T is the tension on the string
  • μ is the mass per unit length

When the tension is halved and the area of cross section is doubled, we calculate the frequency as;

Thus, when the tension is halved and the area of cross section is doubled, the frequency increases by a factor of 1.414.

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