Amplitude does not affect wave speed because amplitude is a measure of the wave energy as it oscillates. This implies that movement of the wave is separate from the movement indicated by the sleep of the wave.
By increasing the tension, the wave speed increases and hence frequency increases. Greater tension implies greater acceleration of particles, which means greater speed of particles and hence greater speed of wave.
As we know, speed = frequency * wavelength. This clearly means that speed is directly proportional to the frequency such that when frequency increases, speed also increases and vice versa.
To know more about wave's speed, refer
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