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The square root of the tension in the string has a direct relationship with the transverse wave's speed. The speed of the wave will grow by 9, or by three times, if the tension of the rope is increased by a factor of 9.
What connection exists between the wave's tension and its speed?
The speed of the wave is doubled since it is related to the square root of the tension.
When we view a thing hanging from a cable, rope, or thread, we are observing tension forces. When an item is dragged by a rope, wire, or cable, tension forces are defined as the forces that are transmitted.
As a result, the stretched wire's frequency is inversely related to length; as length grows, the frequency decreases.
With tension, the wave's velocity along the string quickens. To be accurate, the tension must be increased four times for the velocity to rise by the same amount.
Learn more about tension refer
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