Question

The frequency of the standing wave when there is one loop is called the fundamental frequency of the first harmonic. In general, what statement can be made about the degree to which the frequency at each of the harmonics increases compared to the frequency at the fundamental frequency, or first harmonic?

Answer 1

One loop equals half wavelength.
If only one loop exists, it means one loop equals one string length.

using v = f$\lambda$ = 2nL .... because $\lambda$/2 = L and f = n ... fundamental frequency

Similarly for second harmonic, two loops will be formed.
Two loops equal one wavelength and two loops equal one string length. Hence
v = f$\lambda$ = 2nL ... because f = 2n ... socond harmonic and $\lambda$ = L

Hence we will see that v in all cases will be same.

As frequency will increase, the wavelength will decrease or number of loops will increase.