Two transfersal sinusoidal wave

[dado]

Homework Statement

Two transfersal sinusoidal wave of amplitude 0.5 cm and 8 cm wavelength traveling in opposite
directions along the wire. Wave speed in the wire is 1.2 m / s. Write the equation of these two transfersal wave equation and find the resultant wave. Draw the shape of wire at time t = 0, 1, 2, ... s.

Homework Equations

s=A+sin(wt-kx)

The Attempt at a Solution

I did this
s1= 0,5*sin(30*pi*t - (pi*x)/4)
s2= 0,5*sin(30*pi*t + (pi*x)/4 + phi)
phi is an angle.

Did I wrote those equations right or not?

 

[ehild]

It is correct except the mistype in the first equation (+ instead of *).

The question to draw the shape at integer t values is weird (why?).

 

[dado]

thanks. How to find resultant wave if I don't know "phi"?

 

[ehild]

I think the problem meant phi=0, it would have been given otherwise.

ehild

 

[rwisz]

Your equations are not quite correct. The correct equation for a transversal sinusoidal wave is s(x,t) = A*sin(kx - wt), where A is the amplitude, k is the wave number (2π/λ), x is the position, and t is the time.

For the first wave, with an amplitude of 0.5 cm and a wavelength of 8 cm, the equation would be s1(x,t) = 0.5*sin(2πx/8 - 2πt), and for the second wave with an amplitude of 8 cm and a wavelength of 8 cm, the equation would be s2(x,t) = 8*sin(2πx/8 + 2πt).

To find the resultant wave, we can add the two equations together: s(x,t) = s1(x,t) + s2(x,t) = 0.5*sin(2πx/8 - 2πt) + 8*sin(2πx/8 + 2πt).

To draw the shape of the wire at different times, we can plug in different values for t and plot the resulting function. For example, at t=0, we have s(x,0) = 0.5*sin(2πx/8) + 8*sin(2πx/8) = 8.5*sin(2πx/8), which would look like a single wave with an amplitude of 8.5 cm. At t=0.5 s, we have s(x,0.5) = 0.5*sin(2πx/8 - π) + 8*sin(2πx/8 + π) = -0.5*sin(2πx/8) - 8*sin(2πx/8) = -8.5*sin(2πx/8), which would look like the same wave but with the opposite direction of motion.