Three longest wavelengths will correspond to the three modes of vibration that has the least amount of nodes. For a standing wave on a string fixed on both ends we have the following formula:
[tex]\lambda_n=\frac{2L}{n}; n=1,2,3,4,5,...[/tex]
Where L is the length of a string and n is the number of nodes of the standing wave.
From this formula, we see that the more nodes you have the lower your wavelength is.
We need to calculate wavelengths for n=1, n=2, and n=3.
[tex]\lambda_1=\frac{2L}{1}=560$cm\\ \lambda_2=\frac{2L}{2}=280$cm\\ \lambda_3=\frac{2L}{3}=186.67$cm\\[/tex]
