Vidaara.orgClass 11 · Physics
CodeVID-P11-14-CH-01
Waves — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- 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.
Section A — Multiple Choice Questions
6 × 1 = 6 marks
1.
Sound in air is a:
- A.transverse wave
- B.longitudinal wave
- C.electromagnetic wave
- D.matter wave
2.
The wave relation connecting speed, frequency and wavelength is:
- A.$v=\frac{f}{\lambda}$
- B.$v=f\lambda$
- C.$v=\frac{\lambda}{f^2}$
- D.$v=f^2\lambda$
3.
The speed of a transverse wave on a string is:
- A.$\sqrt{T\mu}$
- B.$\sqrt{\frac{T}{\mu}}$
- C.$\frac{T}{\mu}$
- D.$T\mu$
4.
A pipe closed at one end produces:
- A.all harmonics
- B.only odd harmonics
- C.only even harmonics
- D.no harmonics
5.
The beat frequency of two notes $f_1$ and $f_2$ is:
- A.$f_1+f_2$
- B.$|f_1-f_2|$
- C.$f_1 f_2$
- D.$\frac{f_1}{f_2}$
6.
When a source approaches a stationary observer, the observed frequency:
- A.decreases
- B.increases
- C.stays the same
- D.is zero
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
7.
Distinguish between transverse and longitudinal waves.
8.
State the principle of superposition of waves.
9.
Two forks of 340 Hz and 346 Hz sound together. Find the beat frequency.
10.
Why is the Doppler effect for sound not symmetric in source and observer motion?
Section C — Short Answer (3 marks)
2 × 3 = 6 marks
11.
A string fixed at both ends is 1 m long with wave speed 120 m/s. Find the first three harmonic frequencies.
12.
A 480 Hz source approaches a stationary observer at 20 m/s ($v=340$ m/s). Find the observed frequency.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
13.
Explain the formation of standing waves and derive the frequencies of the normal modes of a string fixed at both ends. Define harmonics and overtones.
14.
State the Doppler effect for sound and derive the expression for the observed frequency when a source moves towards a stationary observer. Give one real application.
Answer Key
Section A — Multiple Choice Questions
- (B) longitudinal wave
- (B) $v=f\lambda$
- (B) $\sqrt{\frac{T}{\mu}}$
- (B) only odd harmonics
- (B) $|f_1-f_2|$
- (B) increases
Section B — Short Answer (2 marks)
- Transverse: particle vibration perpendicular to propagation (crests/troughs). Longitudinal: vibration parallel to propagation (compressions/rarefactions).
- When waves overlap, the resultant displacement at any point is the vector sum of the displacements due to the individual waves.
- Beat frequency $=|346-340|=6\ \text{Hz}$.
- Because sound travels in a medium (air) that provides a preferred reference frame, so moving the source (changes wavelength) differs from moving the observer (changes the rate of meeting wavefronts).
Section C — Short Answer (3 marks)
- $f_1=\frac{v}{2L}=\frac{120}{2}=60\ \text{Hz}$; $f_2=120\ \text{Hz}$; $f_3=180\ \text{Hz}$.
- $f'=480\left(\frac{340}{340-20}\right)=480\times\frac{340}{320}=510\ \text{Hz}$.
Section D — Long Answer (5 marks)
- An incident wave and its reflection superpose to give $y=2A\sin(kx)\cos(\omega t)$ with fixed nodes/antinodes. Both ends being nodes gives $L=\frac{n\lambda}{2}$, so $f_n=\frac{n}{2L}\sqrt{\frac{T}{\mu}}$. $n=1$ is the fundamental (first harmonic); $nf_1$ are harmonics; the frequencies above the fundamental are overtones (first overtone $=$ second harmonic).
- Relative motion changes observed frequency: $f'=f\left(\frac{v\pm v_o}{v\mp v_s}\right)$. For a source approaching at $v_s$, in time $T$ it advances $v_s T$, compressing the wavelength to $\lambda'=\frac{v-v_s}{f}$, so $f'=\frac{v}{\lambda'}=f\frac{v}{v-v_s}>f$ (pitch rises). Application: traffic radar speed guns (also medical ultrasound, sonar, astronomical red shift).
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