Question

Which of the following wavelengths will produce standing waves on a string that is 3.5 m long?

Answer 1

In a string of length L, the wavelength of the n-th harmonic of the standing wave produced in the string is given by:

$\lambda=\frac{2}{n} L$

The length of the string in this problem is L=3.5 m, therefore the wavelength of the 1st harmonic of the standing wave is:

$\lambda=\frac{2}{1} \cdot 3.5 m=7.0 m$

The wavelength of the 2nd harmonic is:

$\lambda=\frac{2}{2} \cdot 3.5 m=3.5 m$

The wavelength of the 4th harmonic is:

$\lambda=\frac{2}{4} \cdot 3.5 m=1.75 m$

It is not possible to find any integer n such that $\lambda=5 m$, therefore the correct options are A, B and D.

Answer 2

For standing waves to be produced, 
L = nλ/2, where L is the length of the string, λ is the wavelength and n a natural number.

3.5 = nλ/2
7/λ = n

Therefore, the only answers that produce whole numbers when plugged into λ are A and B.