How Do You Calculate Wave Parameters for a Transverse Sinusoidal Wave?

[Qudos]

[itex][/itex]

Homework Statement

A transverse sinusoidal wave is moving along a string in the positive direction of an x-axis with a speed of 80 m/s. At t = 0, the string particle at x = 0 has a transverse displacement of 4.2 cm from its equilibrium position and is not moving. The maximum transverse speed of the string particle at x = 0 is 18 m/s.
It asks to solve for f,λ,[itex]y_{m}[/itex],k,ω, and [itex]\phi[/itex] in the wave formula

Homework Equations

y(x, t) = [itex]y_{m}[/itex] sin(kx ± ωt + [itex]\phi[/itex])

The Attempt at a Solution

Since it says at t and x = 0 the displacement is 4.2cm and stopped moving i assumed that meant that it had reached its max displacement. I then used [itex]u_m=ωy_m[/itex]
for the max transverse speed and solved for ω, which i put into the formula
f=[itex]\frac{ω}{2\pi}[/itex] which gave me [itex]0.00367s^-1[/itex], and solving for wavelength using [itex]λ=\frac{v}{f}[/itex] gave me 21827m which doesn't seem right, I'm pretty sure I'm doing something wrong, any help would be appreciated.

thanks

Oh and btw i converted all the cm to m before calculating.

 

[Spinnor]

You wrote,

u_m=ωy_m (why can't I copy and paste your formulas intact? Oh well)

Did you mix units, the displacement was given in cm and the velocity in m/s ? We want everything in cm or m.

 

[Qudos]

Yes i converted 4.2cm to 0.042m, then divided 18m/s by 0.042m to get a very large ω value of 428.6

 

[Qudos]

Ok, i calculated again and i think i switched the denominator with the numerator in something. Seems to be more reasonable now.
Thanks

 

[rwisz]

It seems like you're on the right track, but there are a few things that need to be corrected in your solution. Firstly, it's important to note that the maximum transverse speed is given as 18 m/s, not 80 m/s. This means that your value for ω should be 18 m/s divided by the amplitude, y_m, which is 0.042 m. This gives a value of ω = 428.57 s^-1.

Next, when solving for the frequency, you should use the given speed of 80 m/s, not the value for ω that you calculated. This gives a frequency of 0.0025 s^-1.

For the wavelength, you used the correct formula, but made a mistake in converting the units. The speed, v, is given in m/s, so you don't need to convert it. The frequency, however, is given in s^-1, so you need to convert it to Hz by dividing by 1 s. This gives a wavelength of 32000 m.

Finally, for the phase angle, you can use the given initial condition of t = 0 and x = 0 to solve for ϕ. Since the wave is moving in the positive direction of the x-axis, the phase angle should be 0.

Hope this helps!