Question

to increase the frequency by 2 octave (s), to 4 f , by what factor would you have to increase the tension

Answer 1

Answer:

16

Explanation:

Since frequency in a stretched string f = (n/2L)√T/μ and n, L and μ are constant, f ∝ √T  where T = tension in string

Now f₂/f₁ = √T₂/√T₁

Since f₁ = f (frequency at tension T₁) and f₂ = 4f (since its frequency increases by 2 octaves to 4f at tension T₂).

So,

f₂/f₁ = √T₂/√T₁

4f/f = √T₂/√T₁

√T₂/√T₁ = 4

squaring both sides, we have

(√T₂/√T₁)² = 4²

T₂/T₁ = 16

T₂ = 16T₁

So, the tension would have to increase by a factor of 16