A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is

For a string fixed at both ends, the resonant frequencies arevn=nv2L where n=1,2,3,…..The difference between two consecutive resonant frequencies isΔvn=vn+1-vn=(n+1)v2L-nv2L=v2Lwhich is also the lowest resonant frequency (n=1)Thus the lowest resonant frequency for the given string=420 Hz -315 Hz = 105 Hz