If ${n_1},{n_2},{n_3}.........$ are the frequencies of segments of a stretched string, the frequency $n$ of the string is given by
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$(i)\,\,\,\,\,{y_1} = A\,\cos \,\,2\pi \,\left( {{n_1}t\, + \,\frac{x}{{{\lambda _1}}}} \right)$
$(ii)\,\,\,\,\,{y_2} = A\,\cos \,\,2\pi \,\left( {{n_1}t\, + \,\frac{x}{{{\lambda _1}}} + \pi } \right)$
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$(iv)\,\,\,\,\,{y_4} = A\,\cos \,\,2\pi \,\left( {{n_2}t\, - \,\frac{x}{{{\lambda _2}}}} \right)$
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