Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below.

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