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For a stationary wave y = 10 sin ((pi...

For a stationary wave
` y = 10 sin ((pi x)/15) cos (48 pi t) ` cm, the distance between a node and the nearest antinode is

A

15 cm

B

`7.5` cm

C

30 cm

D

60 cm

Text Solution

Verified by Experts

The correct Answer is:
B
`y = 10 sin ((pi x)/15) cos (48 pi t) cm`
Comparing with the standard equation of a stationary
wave, `y = 2A sin ((2 pi x)/lambda) cos ( 2 pi n t) `, we get
` :. (2 pi x)/lambda = (pi x)/15 :. lambda = 30 ` cm
` :. ` Distance between node and an antinode ` = lambda/4 = 7.5` cm
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