A string fixed at both ends has a standing wave mode for which the distances between adjacent nodes is 18 cm. For the net consecutive standing wave mode distance between adjacent nodes is 16 cm. The minimum possible length of the string is

Question

A string fixed at both ends has a standing wave mode for which the distances between adjacent nodes is 18 cm. For the net consecutive standing wave mode distance between adjacent nodes is 16 cm. The minimum possible length of the string is, 144 cm, 204 cm, 288 cm, 72 cm

MARKS App · Accepted Answer

Let the vibration takes place in the nth mode So, for 1 s t case, n λ 2 = L ......(i) And for 2 n d case, n + 1 λ ′ 2 = L .....(ii) From Equations. (i) and (ii), we get n λ 2 = ( n + 1 ) λ ′ 2 ∵ λ 2 = 18 cm a n d λ ′ 2 = 16 cm ⇒ 18 n = n + 1 16 ⇒ n = 8 So, minimum possible length l = n λ 2 ⇒ l = 8 × 18 = 144 cm

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