Answer:
16
Step-by-step 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