Standing Waves: 2m, 1m, 4m, 1.5m, 67cm - Which Doesn't Fit?

[jan2905]

If two of the wavelengths of standing waves on a 12m rope secured at both ends are 2m and 1m, which of the following COULD NOT be a standing wave wavelength on the same rope with the same tension?

4m, 2.5m, 1.5m, or 67cm.


2L/n=lamda



I said 2.5m because this does not give an natural number solution to the formula. Is this correct?

 

[LowlyPion]

Correct. It would not be a fundamental evenly divisible into the length.

 

[thomate1]

Yes, that is correct. According to the formula for standing wave wavelength, the value of the wavelength should be a natural number, which means it should be a whole number greater than 0. 2.5m is not a natural number, so it cannot be a standing wave wavelength on the same rope with the same tension.