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Equation of a progressive wave
Appears in
Concepts tested here
- Particle velocity and wave velocity
- Wave number and angular frequency
All Questions
2013 NEET 1 question
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A wave travelling in the +ve x-direction having displacement along y-direction as 1 m, wavelength $2\pi$ m and frequency of $\frac{1}{\pi}$ Hz is represented by:$k = \frac{2\pi}{\lambda} = \frac{2\pi}{2\pi} = 1$ and $\omega = 2\pi f = (2\pi)\left(\frac{1}{\pi}\right) = 2$
$y = \sin(kx - \omega t) = \sin(x - 2t)$
2012 AIPMT-MAINS 1 question
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The equation of a simple harmonic wave is given by $y = 3\sin\frac{\pi}{2}(50t - x)$ where x and y are in metres and t is in seconds. The ratio of maximum particle velocity to the wave velocity isComparing with $y = A\sin(\omega t - kx)$: $A = 3$ m, $\omega = 25\pi$ rad/s, $k = \frac{\pi}{2}$ $m^{-1}$
Maximum particle velocity: $v_{max} = A\omega$
Wave velocity: $v_w = \frac{\omega}{k}$
$\frac{v_{max}}{v_w} = \frac{A\omega}{\omega/k} = Ak = 3\times\frac{\pi}{2} = \frac{3}{2}\pi$