Vidaara.orgClass 11 · Physics
CodeVID-P11-14-SSW-01
Superposition & Standing Waves — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
The principle of superposition gives the resultant displacement as the:
- A.product of displacements
- B.vector sum of displacements
- C.difference of speeds
- D.ratio of amplitudes
2.
At a node of a standing wave, the displacement is:
- A.maximum
- B.zero
- C.half the amplitude
- D.infinite
3.
An open pipe produces:
- A.only odd harmonics
- B.only even harmonics
- C.all harmonics
- D.no harmonics
4.
At a rigid boundary, a reflected wave undergoes a phase change of:
- A.$0$
- B.$\frac{\pi}{2}$
- C.$\pi$
- D.$2\pi$
5.
For a string fixed at both ends, the first overtone is the:
- A.fundamental
- B.second harmonic
- C.third harmonic
- D.fifth harmonic
Section B — Short Answer (2 marks)
3 × 2 = 6 marks
6.
State the conditions for constructive and destructive interference in terms of path difference.
7.
An open pipe of length 0.5 m sounds in air ($v=340$ m/s). Find its fundamental frequency.
8.
How does a standing wave differ from a progressive wave in energy transport?
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
9.
Compare the fundamental frequencies and harmonics of an open pipe and a closed pipe of equal length.
10.
A string fixed at both ends, 0.8 m long, carries a wave at 160 m/s. Find the first three harmonic frequencies.
Section D — Long Answer (5 marks)
1 × 5 = 5 marks
11.
Explain the formation of standing waves on a string fixed at both ends. Derive the expression for the allowed frequencies and define harmonics and overtones.
Answer Key
Section A — Multiple Choice Questions
- (B) vector sum of displacements
- (B) zero
- (C) all harmonics
- (C) $\pi$
- (B) second harmonic
Section B — Short Answer (2 marks)
- Constructive: $\Delta x=n\lambda$. Destructive: $\Delta x=(2n+1)\frac{\lambda}{2}$.
- $f_1=\frac{v}{2L}=\frac{340}{2\times0.5}=340\ \text{Hz}$.
- A progressive wave carries energy along the medium; a standing wave does not transport net energy — it stays confined between the boundaries.
Section C — Short Answer (3 marks)
- Open: $f_1=\frac{v}{2L}$, all harmonics ($f, 2f, 3f,\dots$). Closed: $f_1=\frac{v}{4L}$ (half of open), only odd harmonics ($f, 3f, 5f,\dots$).
- $f_1=\frac{v}{2L}=\frac{160}{1.6}=100\ \text{Hz}$; $f_2=200\ \text{Hz}$; $f_3=300\ \text{Hz}$.
Section D — Long Answer (5 marks)
- Incident and reflected waves superpose to give $y=2A\sin(kx)\cos(\omega t)$, a pattern with fixed nodes and antinodes. Both ends being nodes requires $L=\frac{n\lambda}{2}$, so $\lambda=\frac{2L}{n}$ and $f_n=\frac{v}{\lambda}=\frac{n}{2L}\sqrt{\frac{T}{\mu}}$. The $n=1$ mode is the fundamental (first harmonic); $nf_1$ are harmonics; frequencies above the fundamental are overtones (first overtone $=$ second harmonic).
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