Ask Question
18 November, 02:27

A string of length L, fixed at both ends, is capable of vibrating at 309 Hz in its first harmonic. However, when a finger is placed at a distance ℓ from one end, the remaining length L - ℓ of the string vibrates in its first harmonic with a frequency of 463 Hz. What is the distance ℓ? Express your answer as a ratio of the length L.

+2
Answers (1)
  1. 18 November, 02:36
    0
    i = 0.3326 L

    Explanation:

    A fixed string at both ends presents a phenomenon of standing waves, two waves with the same frequency that are added together. The expression to describe these waves is

    2 L = n λ n = 1, 2, 3 ...

    The first harmonic or leather for n = 1

    Wave speed is related to wavelength and frequency

    v = λ f

    λ = v / f

    Let's replace in the first equation

    2 L = 1 (v / f₁)

    For the shortest length L = L-l

    2 (L - l) = 1 (v / f₂)

    These two equations form our equation system, let's eliminate v

    v = 2L f₁

    v = 2 (L-l) f₂

    2L f₁ = 2 (L-l) f₂

    L - l = L f₁ / f₂

    l = L - L f₁ / f₂

    l = L (1 - f₁ / f₂)

    .

    Let's calculate

    l / L = (1 - 309/463)

    i / L = 0.3326
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “A string of length L, fixed at both ends, is capable of vibrating at 309 Hz in its first harmonic. However, when a finger is placed at a ...” in 📘 Physics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers