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Use the wave equation to find the speed of a wave given by y(x, t) = (2. 00 mm)[(20 m−1)x − (4. 0 s−1)t] 0. 5

Sagot :

The speed of the wave whose wave equation :

y(x,t) =[tex](2.00 mm)[(20 m^{-1} )x - (4.0 s^{-1} ) t]^{0.5}[/tex]  is 0.20 m/s

speed = 0.20 m/s

What is the speed of wave?

The wave equation is a linear second-order partial differential equation which describes the propagation of oscillations at a fixed speed in some quantity y.

The wave equation is given by:

y(x,t) =[tex](2.00 mm)[(20 m^{-1} )x - (4.0 s^{-1} ) t]^{0.5}[/tex] .......................(1)

As we know that the standard form of wave equation is of the form is

On Comparing it with equation (1)

we have,

angular number, k=20

and, angular frequency, ω=4.0 rad/s.

Thus, the speed of the wave is

v=[tex]\frac{\omega}{K}[/tex]

=[tex]\frac{(4.0 rad/s) }{(20 m^{-1}) }[/tex]

=0.20 m/s

The speed of the wave of the wave equation

y(x,t) =[tex](2.00 mm)[(20 m^{-1} )x - (4.0 s^{-1} ) t]^{0.5}[/tex]  is 0.20 m/s

Learn more above wave equation here:

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