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The wavelength of waves travelling with the same speed would  decrease if the frequency of the waves increases. This is because,  speed of a wave is the product of the dista â¦ nce of the wavelength  times the frequency of the wave.
Keep in mind, it is a property of the wave medium, so we have to do something to the string to alter the wave speed. From earlier discussions, we know that tightening the string increases the wave speed.