Category: HC Verma Part 1: Waves & Optics

Problem Statement Solve the oscillation/wave problem: An observer on a train moving at 54 km/h toward a stationary whistle (880 Hz). $v_{sound}=330$ m/s. Frequency heard? Observer approaching: $f’=f(v+v_o)/v$ Step 1: $v_o=54\times1000/3600=15$ m/s. Step 2: $f’=880\times(330+15)/330=880\times345/330=920$ Hz. $$\boxed{f’=920\text{ Hz}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$,…

Problem Statement A jackhammer produces 100 dB at 1 m. Find intensity level at 10 m. 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…

Problem Statement Solve the oscillation/wave problem: A sound wave has period $2\times10^{-3}$ s. Find frequency and wavelength if $v=340$ m/s. $f=1/T$; $\lambda=v/f$ Step 1: $f=1/T=1/(2\times10^{-3})=500$ Hz. Step 2: $\lambda=v/f=340/500=0.68$ m. $$\boxed{f=500\text{ Hz},\ \lambda=0.68\text{ m}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$, phase $\phi$) as given…

Problem Statement An open pipe of length $L$ and a closed pipe of length $L/2$ are sounded. Do they have the same fundamental 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.…

Problem Statement Solve the oscillation/wave problem: Observer at rest; source of 500 Hz approaches at 20 m/s then recedes at 20 m/s. $v=340$ m/s. Both observed frequencies? $f’=fv/(v\mp v_s)$ Step 1: Approach: $f’=500\times340/(340-20)=500\times340/320=531.25$ Hz. Step 2: Recede: $f’=500\times340/(340+20)=500\times340/360=472.2$ Hz. $$\boxed{f’_{appro Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions…

Problem Statement Same wave (1000 Hz, 330 m/s). Minimum separation of two points that are out of phase ($\pi$ phase difference)? 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 Find the acoustic impedance of air. $\rho=1.29$ kg/m$^3$, $v=330$ 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 to identify which conservation law or field equation governs…

Problem Statement A 1000 Hz sound wave travels at 330 m/s. What is the minimum separation of two points that are in phase? 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 oscillation/wave problem: An open pipe of length 40 cm and a closed pipe of length 30 cm are sounded together. Find the beat frequency. $v=330$ m/s. Beats from any pair of frequencies: $f_{beat}=|f_1-f_2|$ Step 1: Open pipe fundamental: $f_o=v/(2L)=330/0.80=412.5$ Hz. Step 2: Closed pipe fundamental: $f_c=v/(4L)=330/(4\times Given Information Mass $m$ and…

Problem Statement Solve the oscillation/wave problem: A source of 300 Hz is moving toward a wall. An observer behind the source hears 2 beats per second between direct and reflected sound. $v_{sound}=330$ m/s. Find source speed. Beat between direct and reflected: $\Delta f=f_r-f_d$ Step 1: Direct frequency (observer behind): $f_d=300(v-0)/(v+v_s)=300\t Given Information Mass $m$ and…