I don\'t know how to even begin this problem if anyone could help! A mass m hang

Question

I don't know how to even begin this problem if anyone could help! A mass m hangs on a string that is connected to the ceiling. You pluck the string just above the mass, and a wave pulse travels up to the ceiling, reflects off the ceiling, and travels back to the mass. Calculate the fraction that the round-trip time will be decreased, if the mass m is increased by a factor of 2.07. (Assume that the string does not stretch in either case and the contribution of the mass of the string to the tension is negligible.)

Explanation / Answer

The speed of the wave is proportional to the square root of the tension (e.g. see link). If the the mass m is increased by a factor of2.07, the weight and therefore tension, is increased by 2.07 So the speed increases by v2.07 = 1.43. Therefore the time changes by a factor 1/1.43 = 0.699 The wording in the question is ambiguous. They may want 1.338 or 0.747. as the final answer. I would write: "The time is reduced by a factor 1.43, making it 0.699 smaller.

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