Answer :

When a string is fixed at two ends then the equation for a wave on the sting is given by,

for a node y = 0, for which

For the string of length l, let one the position of one end be x = 0, then the position of other end will be x = L, therefore,

and the frequency

The frequencies for different values of n are called harmonics, for e.g. n =1 is called the first harmonic, n = 2 is the second harmonic and so on. Theses harmonics correspond to the number of loops for the vibrations. Thus the frequencies corresponding 1 loop, 2 loops, 3 loops and 4 loops are

respectively.

Hence these frequencies are in the ratio 1:2:3:4.

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