39. (a) The resonant wavelengths are given by λ =2 L/n ,where L is the length of the string and n is an integer, and the resonant frequencies are given by f = v/λ = nv/ 2 L ,whe re v is the wave speed. Suppose the lower frequency is associated with the integer n . Then, since there are no resonant frequencies between, the higher frequency is associated with n +1. That is, f 1 = nv/ 2 L is the lower frequency and f 2 =( n + 1) v/ 2 L
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