The displacement of particles in a string stretched in the x-direction is represented by y. Among the following expressions for y, those describing wave motion are:
Correct answer: A. cos kx sin ωt
- A. cos kx sin ωt
- B. k2x2 - ω2t2
- C. cos2(kx + ωt)
- D. cos (k2x2 - ω2t2)
Explanation
The correct expression for wave motion is typically of the form y(x, t) = A sin(kx - ωt) or y(x, t) = A cos(kx - ωt), where A is the amplitude, k is the wave number, and ω is the angular frequency. Option A, cos kx sin ωt, follows this form, as it is a combination of spatial and temporal sinusoidal functions, representing a wave traveling through space. Option B is a quadratic expression and not sinusoidal, which is essential for wave representation. Option C involves a squared trigonometric function, which does not describe a simple harmonic wave. Option D involves a cosine function of a quadratic expression, deviating from the linear form required for wave motion.
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About Waves
Progressive waves transfer energy through oscillations, with wavelength, frequency, amplitude and wave speed related by v = fλ; sound speed depends on the medium. Superposition produces interference and stationary waves in strings and organ pipes, while simple harmonic motion describes the oscillation itself and must be distinguished from wave propagation.
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