Just divide the wavelength by the wave period,
and you've got the wave speed.
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Average speed during a period of time =(distance traveled during the time) divided by (length of the time period)
One commonly used formula for waves is: speed (of the wave) = frequency x wavelength If you know any two of these pieces of information, you can calculate the third one.
Just divide the speed by the frequency. Since SI units are used, the wavelength will be in meters.
I believe that the speed will remain constant, and the new wavelength will be half of the original wavelength. Speed = (frequency) x (wavelength). This depends on the method used to increase the frequency. If the tension on the string is increased while maintaining the same length (like tuning up a guitar string), then the speed will increase, rather than the wavelength.
You can use a graph to calculate speed.