Waves — Previous Year Questions (Class 11 Physics)
Waves describe the propagation of disturbances through a medium. Master wave equations, interference, and diffraction for board exam success.
TL;DR: Waves describe the propagation of disturbances through a medium. Master wave equations, interference, and diffraction for board exam success.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Waves describe the propagation of disturbances through a medium. Master wave equations, interference, and diffraction for board exam success.
Waves — Previous Year Questions with Solutions
Q (2023, 2 marks): A sound wave has a frequency of 500 Hz and travels with a speed of 340 m/s in air. Calculate its wavelength.
Answer: Using the wave equation: v = fλ
where v = 340 m/s, f = 500 Hz
λ = v/f = 340/500 = 0.68 m
Final Answer: λ = 0.68 m or 68 cm
Q (2022, 5 marks): A transverse wave on a string has the equation y = 0.05 sin(4πx - 2πt) where x and y are in meters and t is in seconds. Find (i) amplitude, (ii) wavelength, (iii) frequency, (iv) wave speed.
Answer: Comparing with standard form y = A sin(kx - ωt):
A = 0.05 m
k = 4π rad/m
ω = 2π rad/s
(i) Amplitude: A = 0.05 m = 5 cm
(ii) Wavelength: λ = 2π/k = 2π/(4π) = 0.5 m = 50 cm
(iii) Frequency: f = ω/(2π) = 2π/(2π) = 1 Hz
(iv) Wave speed: v = ω/k = 2π/(4π) = 0.5 m/s
Alternative check: v = fλ = 1 × 0.5 = 0.5 m/s ✓
Final Answer: A = 0.05 m, λ = 0.5 m, f = 1 Hz, v = 0.5 m/s
Q (2023, 3 marks): Two coherent sound sources vibrate in phase. An observer is at a point 5 m from source A and 3 m from source B. If the wavelength of sound is 0.4 m, will the observer hear a loud sound (constructive interference) or soft sound (destructive interference)?
Answer: Path difference: Δx = |5 - 3| = 2 m
Wavelength: λ = 0.4 m
Number of wavelengths: Δx/λ = 2/0.4 = 5
Since Δx is an integer multiple of λ (5λ), constructive interference occurs.
The observer will hear a loud sound (maximum intensity).
Final Answer: Constructive interference; loud sound heard
Q (2021, 5 marks): Explain the principle of superposition of waves and give one example where it leads to constructive interference and one where it leads to destructive interference.
Answer: Principle of superposition: When two or more waves travel through the same medium, the net displacement at any point is the vector sum of displacements due to individual waves.
y_net = y₁ + y₂ + ...
Constructive interference example: Two sound waves with path difference = nλ (n = 0, 1, 2, ...) interfere constructively, producing maximum intensity. Example: Speakers at equal distance from a listener.
Destructive interference example: Two sound waves with path difference = (n + 1/2)λ (n = 0, 1, 2, ...) interfere destructively, producing minimum intensity. Example: Noise-cancelling headphones use waves 180° out of phase.
Final Answer: Superposition principle explained with constructive and destructive examples
Q (2022, 3 marks): A string fixed at both ends vibrates in its second harmonic. If the length of the string is 1 m, calculate the wavelength and identify how many nodes and antinodes are present.
Answer: For a string fixed at both ends, the length L = n(λ/2), where n is the harmonic number.
For second harmonic: n = 2
L = 2(λ/2) = λ
λ = L = 1 m
For the second harmonic:
- Number of nodes = n + 1 = 2 + 1 = 3 (including both fixed ends)
- Number of antinodes = n = 2
Final Answer: λ = 1 m, 3 nodes, 2 antinodes
Q (2023, 5 marks): Derive the expression for the speed of sound in a gas in terms of pressure and density. If pressure is increased at constant temperature, how does the speed change?
Answer: Speed of sound in a gas:
v = √(γP/ρ) = √(γRT/M)
where γ is adiabatic index, P is pressure, ρ is density, R is gas constant, T is temperature, M is molar mass.
Derivation uses Newton-Laplace equation for wave propagation in fluids.
At constant temperature: If pressure is increased, density also increases proportionally (ideal gas law: P = ρRT/M).
Ratio: P/ρ remains constant
Therefore, v = √(γP/ρ) remains constant.
Conclusion: Speed of sound depends on temperature, not on pressure at constant temperature.
Final Answer: v = √(γP/ρ); speed remains constant if pressure increases at constant temperature
Frequently Asked Questions
What is the difference between transverse and longitudinal waves?
Transverse waves: Particle motion is perpendicular to wave propagation direction. Examples: light, water waves, waves on strings. Longitudinal waves: Particle motion is parallel to wave propagation direction. Examples: sound waves, seismic P-waves. Transverse waves can exhibit polarization; longitudinal waves cannot.
What causes the Doppler effect in waves?
The Doppler effect occurs when the source or observer is moving relative to the medium. When moving toward the observer, the wavelength decreases and frequency increases (higher pitch for sound). When moving away, wavelength increases and frequency decreases (lower pitch). This is due to the relative motion compressing or stretching the wavefronts.
More Class 11 Physics PYQs
- Current Electricity
- Ray Optics
- Electrostatics
- Moving Charges and Magnetism
- Electromagnetic Induction
- Alternating Current
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →