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A plane progr...

Question

A plane progressive wave is represented by the equation $Y = 0.1 s i n (200 π t - \frac{20 π x}{17})$ 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

100 Hz, 1.7 m, 170 m/s

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150 Hz, 2.4 m, 200 m/s

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80 Hz, 1.1 m, 90 m/s

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120 Hz, 1.25 m, 207 m/s

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Solution

The correct option is A 100 Hz, 1.7 m, 170 m/s
Comparing the given equation with standard equation

we get $w = 2 π n = 200 π \Rightarrow n = 100 H z$
$k = \frac{20 π}{17} \Rightarrow λ = \frac{2 π}{k} = \frac{2 π}{\frac{20 π}{7}}$ =1.7m
and $v = \frac{w}{k} = \frac{200 π}{\frac{20 π}{7}}$ =170 m/ s.

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A plane progressive wave is represented by the equation Y=0.1 sin (200π t−20π x17) 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

The correct option is A 100 Hz, 1.7 m, 170 m/sComparing the given equation with standard equation we get w=2π n=200π⇒ n=100 Hz k=20π17⇒ λ =2πk=2π20π7=1.7m and v=wk=200π20π7 =170 m/ s.

A plane progressive wave is represented by the equation $Y = 0.1 s i n (200 π t - \frac{20 π x}{17})$ 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