Category: HC Verma Part 1: Waves & Optics

Problem Statement Solve the oscillation/wave problem: A closed pipe resonates at $L_1=17$ cm and $L_2=51$ cm for a 500 Hz fork. Find speed of sound and end correction. $v=f\lambda$; $e=\lambda/4-L_1$ Step 1: $\lambda/2=51-17=34$ cm; $\lambda=68$ cm; $v=500\times0.68=340$ m/s. Step 2: $e=\lambda/4-L_1=17-17=0$ cm. If $\lambda/4=17$ cm, then $e=0$. $$\bo Given Information Mass $m$ and spring constant…

Problem Statement Same train (600 Hz, 20 m/s) after passing the station. Frequency now? 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…

Problem Statement If the amplitude of a sound wave is doubled, how does the intensity change? 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 A train whistle (600 Hz) moves at 72 km/h toward a station. Observer at station. $v_{sound}=330$ m/s. Find 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…

Problem Statement Solve the oscillation/wave problem: A pipe closed at one end gives resonances at 75 Hz, 225 Hz, 375 Hz. Find speed of sound if pipe length is 1.1 m. Closed pipe: $f_1=v/(4L)$ Step 1: These are 1st, 3rd, 5th harmonics of a closed pipe (odd multiples of 75 Hz). Step 2: $f_1=75$ Hz;…

Problem Statement Solve the oscillation/wave problem: A tuning fork of 256 Hz produces 3 beats per second with a sonometer wire. When the wire is slightly tightened, the beat frequency increases. Find the initial wire frequency. Beat frequency $=|f_1-f_2|$; tightening increases $f$; if beats increase, frequencies diverging Step 1: Beats = $|f_{fork}-f_ Given Information Mass…

Problem Statement Solve the oscillation/wave problem: A source of 400 Hz and an observer both move toward each other at 20 m/s each. $v_{sound}=340$ m/s. Find the observed frequency. Both approaching: $f’=f(v+v_o)/(v-v_s)$ Step 1: $f’=f\frac{v+v_o}{v-v_s}=400\times\frac{340+20}{340-20}=400\times\frac{360}{320}=450$ Hz. $$\boxed{f’=450\text{ Hz}}$$ Given Information Mass $m$ and spring constant $k$ (or equivalent), or wave parameters Initial conditions (amplitude $A$,…

Problem Statement A closed organ pipe resonates at 220 Hz fundamental. Find 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 to identify which conservation law or…

Problem Statement An open organ pipe should resonate at 440 Hz. Find the required 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 to identify which conservation…

Problem Statement Solve the oscillation/wave problem: A 512 Hz tuning fork resonates with a closed air column at 16.0 cm and 48.0 cm. Find speed of sound. Consecutive resonances: separation $=\lambda/2$; $v=f\lambda$ Step 1: Consecutive resonances in closed pipe differ by $\lambda/2$: $\lambda/2=48.0-16.0=32.0$ cm; $\lambda=0.64$ m. Step 2: $v=f\lambda Given Information Mass $m$ and spring…