Iwould love to stretch a wire from our house to the shop so i can 'call' my husband in for meals. the wire could be tightened to have a tension of 240n and a m/l 'weight' of 0.05kg/l. how long would it take for my pulse wave to travel to the shop (24m) to ring a bell to indicate dinner time.

Note: I'm not sure what do you mean by "weight 0.05 kg/L". I assume it means the mass per unit of length, so it should be "0.05 kg/m".

Solution:
The fundamental frequency in a standing wave is given by

where L is the length of the string, T the tension and m its mass. If  we plug the data of the problem into the equation, we find


The wavelength of the standing wave is instead twice the length of the string:


So the speed of the wave is


And the time the pulse takes to reach the shop is the distance covered divided by the speed:

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