Category: HC Verma Part 1: Waves & Optics

Problem Statement Solve the work-energy problem: A loudspeaker produces 60 dB at 2 m distance. Find acoustic power output. $I_0=10^{-12}$ W/m$^2$. $I=P/(4\pi r^2)$; $I=I_0\times10^{\beta/10}$ Step 1: $I=I_0\times10^{60/10}=10^{-12}\times10^6=10^{-6}$ W/m$^2$. Step 2: $P=I\times4\pi r^2=10^{-6}\times4\pi\times4=5.03\times10^{-5}$ W. $$\boxed{P\appr Given Information Mass $m$, velocity $v$, height $h$, or other given quantities Any forces doing work (conservative or non-conservative) as specified…

Problem Statement A fork of 440 Hz resonates with a closed pipe at its 3rd harmonic. Find pipe length. $v=330$ 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 key is…

Problem Statement Solve the thermodynamics problem: An open organ pipe resonates at 256 Hz at 0 C. Find its frequency at 20 C. $v_0=332$ m/s. $f\propto v\propto\sqrt{T_{abs}}$ for fixed length pipe Step 1: $f\propto v\propto\sqrt{T}$; $f_{20}=256\times\sqrt{293/273}=256\times1.036\approx265$ Hz. $$\boxed{f_{20}\approx265\text{ Hz}}$$ Given Information Temperatures, pressures, volumes, and process type as given Universal gas constant $R = 8.314\,\text{J…

Problem Statement A man shouts and hears echo after 4 s from a cliff. Speed of sound = 330 m/s. Distance to cliff? 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 Two sources each of 70 dB. Combined intensity level? 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 key is to identify which conservation law or field equation governs the…

Problem Statement Solve the Newton’s Laws / mechanics problem: Newton’s formula gives $v=\sqrt{P/\rho}$ for air. At STP: $P=10^5$ Pa, $\rho=1.293$ kg/m$^3$. Result vs Laplace correction? Laplace: sound is adiabatic, so $v=\sqrt{\gamma P/\rho}$ Step 1: Newton: $v_N=\sqrt{10^5/1.293}=\sqrt{77342}\approx278$ m/s. (Incorrect — isothermal) Step 2: Laplace: $v_L=\sqr Given Information Mass(es), forces, angles, and coefficients of friction as given…

Problem Statement An open pipe produces frequencies 800 Hz, 1000 Hz, 1200 Hz (consecutive). Find pipe length. $v=340$ 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 key is to identify…

Problem Statement Solve the oscillation/wave problem: A wall reflects sound from a 500 Hz source moving toward it at 10 m/s. $v=330$ m/s. Find the frequency of reflected sound heard by the source. Double Doppler: wall first as observer, then as source; source becomes observer Step 1: Wall receives: $f_{wall}=500\times330/(330-10)=500\times330/320=515.6 Given Information Mass $m$ and…

Problem Statement Source 600 Hz and observer both move away from each other at 15 m/s each. $v=330$ m/s. Observed frequency? 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 key is…

Problem Statement An open pipe of length 30 cm resonates at its fundamental. A closed pipe of what length resonates at the same frequency? 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.…