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A string fixed at both ends has consecutive standing wave modes for which the distances between adjacent nodes are 18 cm and 16 cm respectively. The minimum possible length of the string is

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144 cm

152 cm

176 cm

200 cm

answer is A.

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Detailed Solution

$L = \frac{{mλ}_{1}}{2} and L = (m + 1) \frac{λ_{2}}{2}$

where m is no. of harmonic

$m . 36 = (m + 1) 32 \Rightarrow m = 8$

$L = 8 \times 18 = 144 cm$

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