Question

What are the three longest wavelengths for standing waves on a 280-cm-long string that is fixed at both ends? enter your answers numerically separated by commas?

Answer 1

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:
$\lambda_n=\frac{2L}{n}; n=1,2,3,4,5,...$
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.
$\lambda_1=\frac{2L}{1}=560 cm\\ \lambda_2=\frac{2L}{2}=280 cm\\ \lambda_3=\frac{2L}{3}=186.67 cm$