You have a long string, and you oscillate one end, causing a (transverse) wave t

Question

You have a long string, and you oscillate one end, causing a (transverse) wave to propagate along it. The wave's formula is D=0.41sin(5.4x+41t) where displacement D and position x are given in meters and time t is given in seconds

Part C

What is the speed of this wave?

Express your answer using two significant figures

Part D

What is the direction this wave travels?

Part E

What is the amplitude of this wave?

Express your answer using two significant figures.

Explanation / Answer

The standard form of the wave equation is

y = a sin 2 ( vt/ - x/)

where a is the amplitude of the wave

compare it with
y = 0.41 sin (41t + 5.4x)
or
y = 0.41 sin 2( 6.525352667t + 0.859436692 x)

C)

Hence,
v/ = 6.525352667
1/ = - 0.859436692
velocity of wave = v = - 5.608127515 m/s here negative sign indicates that the given wave propogates in opposite direction as standard wave propogates

D)

as we seen in above part the wave propogates in negative x direction

E)

a = 0.41 = amplitude of the wave

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