Final answer:
When the tension in a string is decreased by a factor of 9, the speed of waves on the string decreases by a factor of 3.
Step-by-step explanation:
When we decrease the tension in a string by a factor of 9 but don't change the mass of the string, the speed of the waves on the string will decrease by a factor of 3. This is because the speed of waves on a string is directly proportional to the square root of the tension in the string. By decreasing the tension by a factor of 9, we effectively decrease the speed by a factor of 3.