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