Two strings (A, B) having linear densities μA = 2 × 10⁻⁴ kg/m$\mu_{A} = 2 \times 10^{-4}\text{ kg/m}$ and μB = 4 × 10⁻⁴ kg/m$\mu_{B} = 4 \times 10^{-4}\text{ kg/m}$ and lengths LA = 2.5 m$L_{A} = 2.5\text{ m}$ and LB = 1.5 m$L_{B} = 1.5\text{ m}$ respectively are joined. Free ends of A and B are tied to two rigid supports C and D, respectively creating a tension of 500 N in the wire. Two identical pulses, sent from C and D ends, take time t₁$t_{1}$ and t₂$t_{2}$ , respectively, to reach the joint. The ratio t₁/t₂$t_{1}/t_{2}$ is :

Related Formula

Core Logic

For Oxygen (O₂$O_2$) at standard temperature and pressure (S.T.P.): T = 273 K$T = 273 \text{ K}$ M = 32 g/mol = 32 × 10⁻³ kg/mol$M = 32 \text{ g/mol} = 32 \times 10^{-3} \text{ kg/mol}$ γ = 1.4$\gamma = 1.4$ R = 8.3 J K⁻¹ mol⁻¹$R = 8.3 \text{ J K}^{-1} \text{ mol}^{-1}$

Step 1: Calculate Velocity

Approximating to the closest given option yields 310 m/s$310 \text{ m/s}$.

Pattern Recognition

For diatomic gases around room temp or STP, velocities range roughly from 250$250$ to 350 m/s$350 \text{ m/s}$ depending on molar mass (N₂ ≈ 334$N_2 \approx 334$, O₂ ≈ 315$O_2 \approx 315$). Recognize 315$315$ is closest to option (1) due to standard approximations taken in exams.

Chapter Mix

Class 11 Physics: Waves Class 11 Physics: Kinetic Theory of Gases

Related Formula

Core Logic

For a closed organ pipe, the fundamental frequency (1st harmonic) is:

where L₁$L_1$ is the length of the closed pipe.

For an open organ pipe, the first overtone (2nd harmonic) is:

where L₂$L_2$ is the length of the open pipe (L₂ = 60 cm$L_2 = 60\mathrm{\,cm}$).

Step 2: Equating Frequencies

Given f₁ = f₂$f_1 = f_2$:

L₂ = 4L₁$L_2 = 4L_1$

Chapter Mix

Class 11 Physics: Waves