Standing wave wavelengths on a 12m rope secured at both ends

[pkamensky]

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


Choices are: 4m, 2.5m, 1.5m, 67cm


12-2 =10, so 1\2 would be 5 and 12-1 = 11, so 1\2 = 5.5. I am rationalizing that 67 cm is not possible.

 

[ideasrule]

I don't understand your calculations, and your answer is incorrect. Could you show your reasoning?

In order for there to be a standing wave, the rope's length must be an integer multiple of half a wavelength. If you don't see why, try drawing a diagrams of the first few harmonics, remembering that the ends of the rope must be nodes. So, which of the wavelengths satisfy this requirement?

 

[pkamensky]

I am still confused. I do not know what numbers to use from the problem into the equation.