How Does Tension Affect the Speed and Wavelength of Waves in a Guitar String?

[bearhug]

A nylon guitar string has a linear density of 9.0 g/m and is under a tension of 180.0 N. The fixed supports are L = 80.0 cm apart. The string is oscillating in the standing wave pattern shown in the figure. Calculate the speed of the traveling waves whose superposition gives this standing wave. (m/s)

The speed I calculated to be v=sqrt(T/u) = 141 m/s and I know this is right

Calculate the wavelength of the traveling waves whose superposition gives this standing wave. (m)

There are several equations I have been looking at to try and figure out the wavelength. v=lambda(f) but I don't have f.
k=2pi/lambda but I don't have k. I thought that maybe 0.8m would be considered x and use a sinusoidal equation but I still am lacking the amplitude and w. I just need some guidance on this problem.

 

[Doc Al]

The string is oscillating in the standing wave pattern shown in the figure.

You can figure out the wavelength by studying the pattern. Hint: Count the nodes/antinodes.

 

[kyle8921]

As a scientist, your calculations for the speed of the traveling waves appear to be correct. To calculate the wavelength, you can use the equation v = λf, where v is the speed of the wave, λ is the wavelength, and f is the frequency. In this case, the frequency can be calculated using the equation f = nv/2L, where n is the number of nodes in the standing wave pattern (in this case, n = 1). Plugging in the values, we get:

v = λf
141 m/s = λ(1/2)(141 m/s)/(0.8 m)
λ = 0.8 m

Therefore, the wavelength of the traveling waves is 0.8 meters. This is equal to twice the distance between the fixed supports (L = 80.0 cm = 0.8 m), which is expected for a standing wave pattern.