First slide

Travelling wave

Question

A plane progressive wave is represented by the equation
$y = 0 .1 \sin (200 πt - \frac{20 πx}{17})$ where y is displacement in m, t in second and x is distance from a fixed origin in meter. The frequency, wavelength and speed of the wave respectively are

Moderate

A

100 Hz, 1.7 m, 170 m/s
B

150 Hz, 2.4 m, 200 m/s
C

80 Hz, 1.1 m, 90 m/s`
D

120 Hz, 1.25 m, 207 m/s

Solution

Comparing the given equation with standard equation
We get $ω = 2 πn = 200 π \Rightarrow$ n = 100 Hz
$k = \frac{20 π}{17} \Rightarrow λ = \frac{2 π}{k} = \frac{2 π}{20 π / 17} = 1 .7 m$
and $v = \frac{ω}{k} = \frac{200 π}{20 π / 17} = 170 m / s .$

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