Question

A string vibrates with a frequency 200 Hz. Its length is doubled and its tension is altered until it begins to vibrate with frequency 300 Hz. What is the ratio of the new tension to the original tension?

Answer 1

Let v₁ and v₂ be the frequencies in the two cases and L₁ ,L₂ and T₁ ,T₂ be respectively the corresponding lengths of the string and tensions under which it is vibrating.

(For the same string, μ in both the cases remains same)

Thus, the new tension is 9 times the original tension