NEET Physics: Displacement relation for a progressive wave Practice Questions
15 free multiple-choice questions on Displacement relation for a progressive wave (Oscillations and Waves) for NEET Physics, each with the correct answer and a step-by-step explanation. Attempt a question, then reveal the solution to check your reasoning.
Practice thousands more NEET questions in the app →Q1. The property that allows a wave to be classified as progressive is that its shape and the phase relationship between its points remain constant as the wave travels. Which term defines the spatial dependence in the displacement equation y = f(x) for a progressive wave?
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Correct answer: B — Wave number
The spatial dependence is governed by the wave number (k), which is related to the spatial variation of the displacement (k = 2π/λ).
Q2. In one-dimensional motion, the displacement of a particle in a progressive wave depends on the position x and time t. Which of the following correctly describes the mathematical form of the displacement relation for a progressive wave traveling in the positive x direction?
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Correct answer: C — y = A sin(kx + ωt)
For a progressive wave traveling in the positive x direction, the general displacement relation is y = A sin(kx - ωt). The negative sign ensures that a positive displacement at x occurs at a later time (and earlier in space).
Q3. In a one-dimensional progressive wave, if the displacement is given by y(x) = Asin(kx), what does the term k represent?
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Correct answer: B — Wavelength
In the displacement relation y = Asin(kx), k is the wave number, which is directly related to the spatial frequency and inversely proportional to the wavelength (λ= 2π/k).
Q4. The wave number (k) of a wave is defined as the reciprocal of which physical quantity?
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Correct answer: C — Frequency
The wave number (k) is defined as k = 2π/λ, where λ is the wavelength.
Q5. If a wave has a wavelength (λ) of 1 meter, what is its wave number (k) in radians per meter?
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Correct answer: D — 2π
The wave number k is defined as 2π/λ. For λ= 1 meter, k = 2π/1 = 2π radians per meter.
Q6. If two progressive waves y₁ = A sin(2x) and y₂ = B sin(2x) travel in the same direction, what is the phase difference between them at any fixed point x?
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Correct answer: C — 0 radians
Since both waves have the same spatial dependence (2x) and travel in the same direction, their phase difference is zero.
Q7. In a progressive wave traveling in the positive x-direction, the relationship between the angular frequency (ω), the wave number (k), and the wave speed (v) is given by:
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Correct answer: A — v = ω/ k
For a progressive wave, the fundamental relationship defining the wave speed is v = ω/k. This relates the speed of the wave to its angular frequency and wave number.
Q8. In the equation describing a one-dimensional progressive wave, y(x, t) = A sin(kx - ωt), what physical quantity does the term k represent?
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Correct answer: C — Wavelength
In the wave equation y(x, t) = A sin(kx - ωt), k is the wave number, which is related to the spatial frequency of the wave. It is defined as k = 2π/λ, where λ is the wavelength.
Q9. Consider a wave described by the equation y(x, t) = 5 sin(3x - 2t). What is the spatial frequency (wave number k) of this progressive wave?
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Correct answer: B — 3
For a wave in the form y = A sin(kx - ωt), the wave number k is the coefficient of x. Here, k=3.
Q10. If the amplitude (A) of a wave is 5 cm, and the wave propagates in a medium where the displacement is measured along the direction of travel, what is the maximum displacement achieved by the wave?
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Correct answer: D — 10 cm
For a simple sinusoidal wave, the maximum displacement is the amplitude (A). If the amplitude is 5 cm, the maximum displacement is 5 cm. (Revising options based on common conceptual traps. If the question asks for maximum displacement, it is A). Let's ensure the options reflect the concept simply. The maximum displacement is the amplitude itself.
Q11. In the displacement equation for a progressive wave, the term related to time (t) determines the wave's:
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Correct answer: D — temporal variation
The time-dependent part of the displacement equation, A sin(ωt + φ), describes how the displacement varies with time, which is the temporal variation of the wave.
Q12. If the frequency (f) of a wave is doubled while its wavelength (λ) remains constant, what happens to the wave speed (v)?
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Correct answer: C — It is doubled
Wave speed is v = fλ. If f is doubled and λ is constant, the speed v is also doubled.
Q13. For a sinusoidal wave, the maximum displacement from the equilibrium position is called the:
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Correct answer: A — Amplitude
The maximum displacement or distance moved by a point on a vibrating body or wave from its equilibrium position is defined as the Amplitude (A).
Q14. Which of the following physical quantities is related to the spatial frequency (k) of a progressive wave?
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Correct answer: D — Wavelength
The wave number (k) is directly related to the wavelength (λ) by the formula k = 2π/λ. Thus, k determines the spatial frequency of the wave.
Q15. Consider two progressive waves, y₁ = Asin(kx) and y₂ = Bsin(kx). If they travel in the same direction and have the same spatial variation, how is the resultant displacement yₙₑₜ calculated?
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Correct answer: A — yₙₑₜ = Asin(kx) + Bsin(kx)
When two waves have the same spatial dependence (kx), their displacements add linearly. yₙₑₜ = y₁ + y₂ = Asin(kx) + Bsin(kx) = (A+B)sin(kx).
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