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Amit Saxena Grade: upto college level
        A wave travelling on a string at a speed of 10 m s-1 causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave? (b) If the displacement of a particle is 1.5 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant?
3 years ago

Answers : (1)

Aditi Chauhan
askIITians Faculty
396 Points
										Sol. Wave speed = v = 10 m/sec

Time period = T = 20 ms = 20 * 10–3 = 2 * 10–2 sec
a) wave length, λ = vT = 10 * 2 * 10–2 = 0.2 m = 20 cm
b) wave length, λ = 20 cm
∴ phase diffn = (2π/λ) x = (2π / 20) * 10 = π rad
y1 = a sin (ωt – kx) ⇒ 1.5 = a sin (ωt – kx)
So, the displacement of the particle at a distance x = 10 cm.

[∅ = 2πx/λ = 2π * 10/20 = π] os goven by
Y2 = a sin (ωt – kx + π) ⇒ -a sin (ωt – kx) = -1.5 mm
∴ displacement = -1.5 mm
3 years ago
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