Category: HC Verma Part 1: Waves & Optics

Problem Statement Solve the oscillation/wave problem: Two forks at 300 Hz and 304 Hz. Find beat frequency and time between beats. $f_{beat}=|f_1-f_2|$; $T_{beat}=1/f_{beat}$ Step 1: $f_{beat}=304-300=4$ Hz. Step 2: Time between beats $T=1/f_{beat}=0.25$ s. $$\boxed{f_{beat}=4\text{ Hz},\ T=0.25\text{ s}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$,…

Problem Statement Solve the oscillation/wave problem: A 400 Hz source and observer are stationary. Wind blows from source toward observer at 20 m/s. $v=340$ m/s. Frequency heard? Wind affects speed not frequency when both source and observer are stationary Step 1: Wind carries sound in its direction; effective speed of sound toward observer $=340+20=36 Given…

Problem Statement Open pipe 50 cm. First overtone frequency? $v=340$ 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 field equation governs the…

Problem Statement A closed organ pipe 25 cm long. What is its first overtone frequency? $v=340$ 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…

Problem Statement Two sounds have intensities $I_1=10^{-4}$ W/m$^2$ and $I_2=10^{-8}$ W/m$^2$. What is the difference in dB? 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 A jet flies at 1200 m/s. Speed of sound = 330 m/s. Find the Mach number and the half-angle of the Mach cone. 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…

Problem Statement Solve the oscillation/wave problem: A tuning fork of 480 Hz resonates with air columns of 34 cm and 69 cm (open pipe). Find speed of sound. Open pipe resonances separated by $\lambda/2$ Step 1: For open pipe, consecutive resonances differ by $\lambda/2$: $\lambda/2=69-34=35$ cm; $\lambda=70$ cm. Step 2: $v=f\lambda=480\times0.70=336$ Given Information Mass $m$…

Problem Statement A sound source gives 60 dB at 1 m. What is the intensity level at 100 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…

Problem Statement Solve the oscillation/wave problem: An open pipe of length 60 cm resonates in 2nd harmonic. Find node and antinode positions. $v=330$ m/s. Open pipe: pressure nodes at ends; displacement antinodes at ends Step 1: 2nd harmonic of open pipe: $L=\lambda$; $\lambda=0.60$ m; $f_2=v/\lambda=550$ Hz. Step 2: Nodes at $\lambda/2=30$ cm from e Given…

Problem Statement From problems 33 and 34: What is the change in frequency as the train passes? 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…