The wave function for a travelling wave on a taut string is in SI units sx- t-0-350msin 10- t-3- x- -4- What are the speed and direction of travel of the wave-

On comparing the given statement with #160; #160; s(x,t) = Asin (wt kx+ ϕ) The given travelling wave travels towards positive x direction.We get # ...

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Standard XII

Physics

Differential Equation of Wave

The wave func...

Question

The wave function for a travelling wave on a taut string is (in SI units) $s (x, t) = (0.350 m) sin (10 π t - 3 π x + π / 4)$ . What are the speed and direction of travel of the wave?

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Solution

On comparing the given statement with $s (x, t) = A sin (w t - k x + ϕ)$

The given travelling wave travels towards positive x direction.

We get $w = 10 π$ $k = 3 π$ $ϕ = \frac{π}{4}$

Speed of wave $v = \frac{w}{k} = \frac{10 π}{3 π} = \frac{10}{3} m / s$

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The wave function for a travelling wave on a taut string is (in SI units) s(x,t)=(0.350m)sin(10πt−3πx+π/4). What are the speed and direction of travel of the wave?

On comparing the given statement with s(x,t)=Asin(wt−kx+ϕ)The given travelling wave travels towards positive x direction.We get w=10 π k=3π ϕ=π4Speed of wave v=wk=10π3π=103 m/s

The wave function for a travelling wave on a taut string is (in SI units) $s (x, t) = (0.350 m) sin (10 π t - 3 π x + π / 4)$ . What are the speed and direction of travel of the wave?

On comparing the given statement with $s (x, t) = A sin (w t - k x + ϕ)$

The given travelling wave travels towards positive x direction.

We get $w = 10 π$ $k = 3 π$ $ϕ = \frac{π}{4}$

Speed of wave $v = \frac{w}{k} = \frac{10 π}{3 π} = \frac{10}{3} m / s$