A stationery wave is represented by y = 12 cos ( 6 π x ) sin ( 8 π t ) , where x & y are in c m and t in second. The distance between two successive antinodes is

Question

A stationery wave is represented by y = 12 cos ( 6 π ​ x ) sin ( 8 π t ) , where x & y are in c m and t in second. The distance between two successive antinodes is

TestHub · Accepted Answer

The given equation of the stationary wave is $y = 12 cos (\frac{π}{6} x) sin (8 π t)$ .

Comparing this with the standard equation of a stationary wave $y = A cos (k x) sin (ω t)$ , we get the wave number $k = \frac{π}{6}$ .

Since $k = \frac{2 π}{λ}$ , we have:

$\frac{2 π}{λ} = \frac{π}{6}$

$λ = 12$ cm

The distance between two successive antinodes is given by $\frac{λ}{2}$ .

Distance $= \frac{12}{2} = 6$ cm.

Answer: 6 cm

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