First slide

Stationary waves

Question

A sonometer wire has a length of 114 cm between two fixed ends, where should two bridges be placed to divide the wire into three segments whole fundamental frequencies are in the ratio $1 : 3 : 4$ ?

Moderate

A

72 cm, 96 cm
B

80 cm, 96 cm
C

100 cm, 96 cm
D

78 cm, 100 cm

Solution

$I n c a s e o f a g i v e n w i r e u n d e r c o n s \tan t t e n s i o n F u n d a m e n t a l f r e q u e n c y o f v i b r a t i o n f \propto \frac{1}{l} ∴ l_{1} : l_{2} : l_{3} = \frac{1}{1} : \frac{1}{3} : \frac{1}{4} = 12 : 4 : 3 l_{1} = \frac{12}{19} \times 114 \Rightarrow l_{1} = 72 c m l_{2} = 24 c m l_{3} = 18 c m ∴ F i r s t b r i d g e i s t o b e p l a c e d 72 c m f r o m o n e e n d . S e c o n d b r i d g e i s t o b e p l a c e d 72 + 24 = 96 c m f r o m o n e e n d$

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