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

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The tension in a nylon guitar string affects the speed and wavelength of the waves produced. The calculated speed of the traveling waves is 141 m/s, derived from the formula v=sqrt(T/u), where T is tension and u is linear density. To find the wavelength, the relationship v=lambda(f) is noted, but frequency (f) is unknown. Guidance suggests analyzing the standing wave pattern by counting nodes and antinodes to determine the wavelength. Understanding these principles is essential for solving wave-related problems in guitar strings.
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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.
 
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bearhug said:
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.
 
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