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Q.

A standing wave y = A sin $(\frac{20 πx}{3})$ cos (1000 $πt$ ) is set up a taut string, where x and y are in metre. The distance between two successive points oscillating with the amplitude $\frac{A}{2}$ can be equal to

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a

10 cm

b

2.5 cm

c

5 cm

d

4 cm

answer is A, B.

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Detailed Solution

$A_{x} = A \sin (\frac{20 πx}{3})$

Question Image

⇒ x =0 is a node

$A_{x} = \frac{A}{2}$

At $\frac{20 π}{3} x = \frac{π}{6}$ , $\frac{5 π}{6}$ , $\frac{7 π}{6}$

or x = $\frac{1}{40} m, \frac{1}{8} m, \frac{7}{40} m = 2.5 c m, 12.5 c m, 17.5 c m$

Therefore , $x_{2} - x_{1} = 10 c m, x_{3} - x_{2} = 5 c m$

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A standing wave y = A sin 20πx3 cos (1000πt) is set up a taut string, where x and y are in metre. The distance between two successive points oscillating with the amplitude A2 can be equal to