Category: HC Verma Part 1: Waves & Optics

Problem Statement Solve the oscillation/wave problem: Two tuning forks have frequencies 512 Hz and 516 Hz. Find the beat frequency. $f_{beat}=|f_1-f_2|$ Step 1: Beat frequency $=|f_1-f_2|=|512-516|=4$ Hz. $$\boxed{f_{beat}=4\text{ Hz}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given Physical Concepts & Formulas Simple…

Problem Statement Solve the oscillation/wave problem: A source of 500 Hz moves toward a stationary observer at 30 m/s. Speed of sound = 330 m/s. Find observed frequency. Doppler: $f’=f\frac{v\pm v_o}{v\mp v_s}$; source approaching: $v-v_s$ in denominator Step 1: $f’=f\frac{v}{v-v_s}=500\times\frac{330}{330-30}=500\times\frac{330}{300}=550$ Hz. $$\boxed Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters…

Problem Statement A closed organ pipe of length 1 m. First three frequencies? $v=340$ 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 which conservation law or…

Problem Statement An open organ pipe of length 1 m resonates. Find the first three frequencies. $v=340$ 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 which…

Problem Statement An open organ pipe has length 50 cm. Find the fundamental frequency. Speed of sound = 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…

Problem Statement A closed organ pipe (one end closed) has length 50 cm. Fundamental frequency? $v_{sound}=340$ 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 which conservation…

Problem Statement Solve the oscillation/wave problem: Speed of sound in water is 1450 m/s, $\rho=1000$ kg/m$^3$. Find bulk modulus. $v=\sqrt{B/\rho}$ for liquids; $B=\rho v^2$ Step 1: $v=\sqrt{B/\rho}$; $B=\rho v^2=1000\times1450^2=2.1025\times10^9$ Pa. $$\boxed{B\approx2.10\times10^9\text{ Pa}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given Physical Concepts…

Problem Statement Intensity level of a sound is 80 dB. Find the intensity. 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…

Problem Statement If the intensity of a sound is doubled, by how many decibels does the intensity level increase? 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 A sound has intensity $10^{-6}$ W/m$^2$. Find intensity level in dB. ($I_0=10^{-12}$ W/m$^2$) 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…