Progressive Waves & Wave Equation — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Progressive Waves & Wave Equation MCQs with step-by-step solutions (21 questions). Part of Superposition of Waves. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Progressive Waves & Wave Equation · easy · theory
A progressive wave travelling through a medium transfers:
A. Energy and momentum, but not matter ✓ Correct
B. Matter along with energy
C. Matter but not energy
D. Neither energy nor matter
Solution: The particles of the medium merely oscillate about their mean positions; the disturbance, and with it energy and momentum, travels onward.
Q2 — Progressive Waves & Wave Equation · easy · theory
Sound waves travelling through air are:
A. Stationary waves
B. Transverse, with particles vibrating perpendicular to propagation
C. Electromagnetic waves
D. Longitudinal, with particles vibrating along the direction of propagation ✓ Correct
Solution: A gas has no shear elasticity, so it cannot sustain transverse waves. Sound in air propagates as compressions and rarefactions along the direction of travel.
Q3 — Progressive Waves & Wave Equation · medium · theory
The equation $y = A\sin(\omega t - kx)$ represents a wave travelling along the:
A. Positive $y$-direction
B. Negative $x$-direction
C. Positive $x$-direction ✓ Correct
D. Negative $y$-direction
Solution: A constant phase requires $\omega t - kx = $ constant, so $x$ increases as $t$ increases. The wave therefore advances along $+x$.
Q4 — Progressive Waves & Wave Equation · easy · theory
The relation between the speed $v$, frequency $n$ and wavelength $\lambda$ of a wave is:
A. $v = n^2\lambda$
B. $v = \dfrac{\lambda}{n}$
C. $v = \dfrac{n}{\lambda}$
D. $v = n\lambda$ ✓ Correct
Solution: In one period the wave advances exactly one wavelength, so $v = \dfrac{\lambda}{T} = n\lambda$.
Q5 — Progressive Waves & Wave Equation · easy · theory
The propagation constant (wave number) $k$ of a wave of wavelength $\lambda$ is:
A. $2\pi\lambda$
B. $\dfrac{2\pi}{\lambda}$ ✓ Correct
C. $\dfrac{1}{\lambda}$
D. $\dfrac{\lambda}{2\pi}$
Solution: The wave number counts the phase change per unit distance, which is $2\pi$ radian over one wavelength.
Q6 — Progressive Waves & Wave Equation · medium · theory
In a progressive wave, all the particles of the medium vibrate with:
A. Different frequencies and amplitudes
B. Different amplitudes and the same phase
C. The same phase and different frequencies
D. The same amplitude and frequency but different phases ✓ Correct
Solution: The wave carries the same disturbance to every particle, so amplitude and frequency are common; what varies from point to point is the phase, which lags progressively with distance.
Q7 — Progressive Waves & Wave Equation · medium · theory
Transverse mechanical waves can propagate through:
A. Vacuum only
B. All states of matter equally
C. Gases only
D. Solids, but not through the interior of gases ✓ Correct
Solution: A transverse wave needs a restoring force against shear. Solids possess shear elasticity; gases and liquids (in bulk) do not.
Q8 — Progressive Waves & Wave Equation · medium · theory
The speed of a mechanical wave in a given medium depends on:
A. The amplitude of the wave
B. The elastic and inertial properties of the medium ✓ Correct
C. The frequency of the wave
D. The wavelength of the wave
Solution: Wave speed is fixed by the medium, for example $v = \sqrt{\dfrac{T}{\mu}}$ on a string. Changing the source frequency changes the wavelength instead, leaving $v$ unaltered.
Q9 — Progressive Waves & Wave Equation · medium · numerical
A progressive wave is given by $y = 0.2\sin[2\pi(50t - 0.5x)]\text{ m}$. Its speed is:
A. $25\text{ m/s}$
B. $50\text{ m/s}$
C. $200\text{ m/s}$
D. $100\text{ m/s}$ ✓ Correct
Solution: Comparing with $y = A\sin(\omega t - kx)$: $\omega = 100\pi$ and $k = \pi$. So $v = \dfrac{\omega}{k} = \dfrac{100\pi}{\pi} = 100\text{ m/s}$.
Q10 — Progressive Waves & Wave Equation · easy · numerical
A wave of frequency $500\text{ Hz}$ has a wavelength of $0.6\text{ m}$. Its speed is:
A. $500\text{ m/s}$
B. $300\text{ m/s}$ ✓ Correct
C. $833\text{ m/s}$
D. $0.0012\text{ m/s}$
Solution: $v = n\lambda = 500 \times 0.6 = 300\text{ m/s}$.
Q11 — Progressive Waves & Wave Equation · easy · numerical
A tuning fork of frequency $256\text{ Hz}$ produces sound of speed $340\text{ m/s}$. The wavelength is approximately:
A. $1.33\text{ m}$ ✓ Correct
B. $0.75\text{ m}$
C. $2.66\text{ m}$
D. $87040\text{ m}$
Solution: $\lambda = \dfrac{v}{n} = \dfrac{340}{256} \approx 1.33\text{ m}$.
Q12 — Progressive Waves & Wave Equation · medium · numerical
A wave is represented by $y = 0.05\sin(20\pi t - 0.5\pi x)\text{ m}$. Its speed is:
A. $40\text{ m/s}$ ✓ Correct
B. $20\text{ m/s}$
C. $0.025\text{ m/s}$
D. $10\text{ m/s}$
Solution: $v = \dfrac{\omega}{k} = \dfrac{20\pi}{0.5\pi} = 40\text{ m/s}$.
Q13 — Progressive Waves & Wave Equation · easy · numerical
A wave of wavelength $2\text{ m}$ has a frequency of $170\text{ Hz}$. Its speed is:
A. $0.012\text{ m/s}$
B. $340\text{ m/s}$ ✓ Correct
C. $170\text{ m/s}$
D. $85\text{ m/s}$
Solution: $v = n\lambda = 170 \times 2 = 340\text{ m/s}$ — the speed of sound in air at ordinary temperature.
Q14 — Progressive Waves & Wave Equation · medium · numerical
The wave number of a wave of wavelength $0.5\text{ m}$ is:
A. $0.5\pi\text{ rad/m}$
B. $\pi\text{ rad/m}$
C. $2\pi\text{ rad/m}$
D. $4\pi\text{ rad/m}$ ✓ Correct
Solution: $k = \dfrac{2\pi}{\lambda} = \dfrac{2\pi}{0.5} = 4\pi \approx 12.57\text{ rad/m}$.
Q15 — Progressive Waves & Wave Equation · easy · numerical
The angular frequency of a wave of frequency $100\text{ Hz}$ is approximately:
A. $100\text{ rad/s}$
B. $1256\text{ rad/s}$
C. $314\text{ rad/s}$
D. $628\text{ rad/s}$ ✓ Correct
Solution: $\omega = 2\pi n = 2\pi \times 100 \approx 628\text{ rad/s}$.
Q16 — Progressive Waves & Wave Equation · medium · numerical
Two points on a progressive wave are separated by a path difference of $\dfrac{\lambda}{4}$. The phase difference between them is:
A. $\pi\text{ rad}$
B. $2\pi\text{ rad}$
C. $\dfrac{\pi}{4}\text{ rad}$
D. $\dfrac{\pi}{2}\text{ rad}$ ✓ Correct
Solution: $\Delta\phi = \dfrac{2\pi}{\lambda}\Delta x = \dfrac{2\pi}{\lambda} \times \dfrac{\lambda}{4} = \dfrac{\pi}{2}$.
Q17 — Progressive Waves & Wave Equation · medium · numerical
Two points on a wave of wavelength $0.8\text{ m}$ are $0.2\text{ m}$ apart. Their phase difference is:
A. $\pi\text{ rad}$
B. $\dfrac{\pi}{2}\text{ rad}$ ✓ Correct
C. $\dfrac{3\pi}{2}\text{ rad}$
D. $\dfrac{\pi}{4}\text{ rad}$
Solution: $\Delta\phi = \dfrac{2\pi}{0.8} \times 0.2 = \dfrac{\pi}{2}\text{ rad}$.
Q18 — Progressive Waves & Wave Equation · medium · numerical
A particle in a progressive wave has amplitude $0.02\text{ m}$ and angular frequency $100\text{ rad/s}$. Its maximum particle speed is:
A. $200\text{ m/s}$
B. $2\text{ m/s}$ ✓ Correct
C. $0.2\text{ m/s}$
D. $5000\text{ m/s}$
Solution: The particle executes S.H.M., so $v_{\max} = A\omega = 0.02 \times 100 = 2\text{ m/s}$.
Q19 — Progressive Waves & Wave Equation · hard · numerical
A wave is given by $y = 3\sin(4t - 0.02x)$, with $y$ and $x$ in centimetre and $t$ in second. Its speed is:
A. $2\text{ m/s}$ ✓ Correct
B. $200\text{ m/s}$
C. $0.08\text{ m/s}$
D. $4\text{ m/s}$
Solution: $v = \dfrac{\omega}{k} = \dfrac{4}{0.02} = 200\text{ cm/s} = 2\text{ m/s}$.
Q20 — Progressive Waves & Wave Equation · medium · numerical
A sound wave has a period of $0.02\text{ s}$ and travels at $340\text{ m/s}$. Its wavelength is:
A. $0.68\text{ m}$
B. $3.4\text{ m}$
C. $17\text{ m}$
D. $6.8\text{ m}$ ✓ Correct
Solution: $n = \dfrac{1}{T} = 50\text{ Hz}$, so $\lambda = \dfrac{v}{n} = \dfrac{340}{50} = 6.8\text{ m}$.
Q21 — Progressive Waves & Wave Equation · medium · numerical
Two points on a progressive wave $1\text{ m}$ apart differ in phase by $\pi\text{ radian}$. The wavelength of the wave is:
A. $0.5\text{ m}$
B. $1\text{ m}$
C. $4\text{ m}$
D. $2\text{ m}$ ✓ Correct
Solution: A phase difference of $\pi$ corresponds to a path difference of $\dfrac{\lambda}{2}$, so $\dfrac{\lambda}{2} = 1\text{ m}$ and $\lambda = 2\text{ m}$.