When a string is divided into three segments of length l₁, l₂ and l₃ the fundamental

When a string is divided into three segments of length l₁, l₂ and l₃ the fundamental frequencies of these three segments are v₁, v₂ and v₃ respectively. The original fundamental frequency (v) of the string is

Options

(a) √v = √v₁ + √v₂ + √v₃
(b) v = v₁ + v₂ + v₃
(c) 1/v = 1/v₁ + 1/v₂ + 1/v₃
(d) 1/ √v = 1/ √v₁ + 1/ √v₂ + 1/ √v₃

Correct Answer:

1/v = 1/v₁ + 1/v₂ + 1/v₃

Explanation:

Fundamental frequency is given by v = 1/ 2l √(T / µ)
⇒ v ∞ 1/ l ⇒ P ∞ 1 / v Since, P divided into l₁, l₂ and l₃ segments.
Here, l = l₁ + l₂ + l₃
So, 1/v = 1/v₁ + 1/v₂ + 1/v₃

admin:

Related Questions

  1. A tuning fork frequency 512 Hz is vibrated with a sonometer wire and 6 beats per second
  2. A body of mass 3 kg is under a constant force which cause a displacement
  3. A concave mirror of focal length f₁ is placed at a distance d from a convex lens
  4. A series L-C-R circuit contains inductance 5 mH, capacitance 2 μF and resistance
  5. A proton beam enters a magnetic field of 10⁻⁴ Wb/m² normally. If the specific charge