Question

Minimum frequency with which a iron rod of length '3l' fixed at one end can resonate with a free iron rod of length '4l' is: [Velocity of wave in iron is v₀]

• A. $\frac{v_{0}}{4\mathcal{l}}$
• B. $\frac{v_{0}}{12\mathcal{l}}$
• C. $\frac{v_{0}}{8\mathcal{l}}$
• D. $\frac{v_{0}}{24\mathcal{l}}$

Answer 1

Answer: (A)

$\frac{v_{0}}{4\mathcal{l}}$

Answer 2

Frequency of rod fixed at one end

= (2n₁ – 1) $\frac{v_{0}}{4 \times 3\mathcal{l}}$

Frequency of free rod = $\frac{n_{2}v_{0}}{2 \times 4\mathcal{l}}$

For resonance :

(2n₁ – 1) $\frac{v_{0}}{4 \times 3\mathcal{l}}$= $\frac{n_{2}v_{0}}{4\mathcal{l \times}2}$

Ž $\frac{2n_{1} - 1}{3}$= $\frac{n_{2}}{2}$

\ Minimum frequency

= (2 × 2 – 1) × $\frac{v_{0}}{4 \times 3\mathcal{l}}$= $\frac{v_{0}}{4\mathcal{l}}$