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

Question

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

in progress 0
Nem 5 years 2021-07-30T07:46:25+00:00 1 Answers 91 views 0

Answers ( )

  1. thanhha
    1
    2021-07-30T07:47:46+00:00
    Reply

    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

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )