Category: HC Verma Part 1: Waves & Optics

Problem Statement Solve the fluid mechanics problem: A sound wave in air has pressure amplitude $p_0=1.0$ Pa. Find displacement amplitude. Given: $v=330$ m/s, $\rho=1.29$ kg/m$^3$, $f=1000$ Hz. $p_0=\rho v\omega s_0=B k s_0$ Step 1: $p_0=\rho v\omega s_0$ where $s_0$ is displacement amplitude. Step 2: $\omega=2\pi\times1000=6283$ rad/s. Step 3: $s_0=p Given Information Fluid density $\rho$, velocities,…

Problem Statement Solve the kinematics problem: A sound wave in air has displacement amplitude $0.10$ mm, frequency 1 kHz. Find intensity. $\rho=1.29$ kg/m$^3$, $v=330$ m/s. $I=\frac{1}{2}\rho v\omega^2 s_0^2$ Step 1: $I=\frac{1}{2}\rho v\omega^2 s_0^2=\frac{1}{2}(1.29)(330)(2\pi\times1000)^2(10^{-4})^2$. Step 2: $=\frac{1}{2}\times1.29\times330\ Given Information Initial velocity $u$ (or $v_0$) Acceleration $a$ (constant unless stated otherwise) Time $t$ or distance $s$ as…

Problem Statement Thunder is heard 3.0 s after the lightning flash. How far away is the storm? Speed of sound = 330 m/s. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem draws on fundamental physical principles. The…

Problem Statement Solve the kinematics problem: Find the speed of sound in air at 0 C. Given: $\gamma=1.4$, $P_0=1.01\times10^5$ Pa, density of air at STP = 1.293 kg/m$^3$. Speed of sound in gas: $v=\sqrt{\gamma P/\rho}=\sqrt{\gamma RT/M}$ Step 1: $v=\sqrt{\gamma P/\rho}=\sqrt{1.4\times1.01\times10^5/1.293}$. Step 2: $=\sqrt{1.414\times10^5/1.293 Given Information Initial velocity $u$ (or $v_0$) Acceleration $a$ (constant unless stated…

Problem Statement Solve the thermodynamics problem: The speed of sound in air at 27 C. Given $v_0=332$ m/s at 0 C. $v\propto\sqrt{T_{abs}}$ Step 1: $v\propto\sqrt{T}$; $T_1=273$ K, $T_2=300$ K. Step 2: $v_2=332\sqrt{300/273}=332\times1.0482\approx348$ m/s. $$\boxed{v\approx348\text{ m/s}}$$ Given Information Temperatures, pressures, volumes, and process type as given Universal gas constant $R = 8.314\,\text{J mol}^{-1}\text{K}^{-1}$ $C_p$ and $C_v$…

Problem Statement Wave: 1000 Hz, speed 400 m/s. Two points 10 cm apart along propagation direction. Phase difference? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving…

Problem Statement Wire 1: $L=100$ cm, $f=256$ Hz. Wire 2 same material and tension, $L=200$ cm. Find $f_2$. Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving…

Problem Statement A wave pulse reflects at a fixed end. Is it inverted or upright? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful…

Problem Statement Solve the oscillation/wave problem: Solve the oscillation/wave problem: Prove: particle velocity $= -v_{wave}\cdot(\partial y/\partial x)$ for $y=A\sin(kx-\omega t)$. Particle velocity $=-(\text{wave speed})\times(\text{wave slope})$ Step 1: $\partial y/\partial t=-A\omega\cos(kx-\omega t)$; $\partial y/\partial x=Ak\cos(kx-\omega t)$ Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to…

Problem Statement String fixed at one end, free at other, fundamental $f_0$. Allowed frequencies? Given Information See problem statement for all given quantities. Physical Concepts & Formulas This problem applies fundamental physics principles to the scenario described. The solution requires identifying the relevant conservation laws and equations of motion, then solving systematically with careful attention…