First slide

Stationary waves

Question

A wave disturbance in a medium is described by $y = 0.02 \cos (50 π t + π / 2) \cos 10 π x$ where $x, y$ are in meters and $' t'$ in second.
Which option is incorrect.

Moderate

A

A node occurs at $x = 0.15 m$
B

An antinode occurs at $x = 0.3 m$
C

The speed of wave is $5 m / \sec$
D

The wavelength is $0.3 m$

Solution

$C o m p a r i n g i t w i t h y = A \cos (w t + π / 2) \cos k x I f k x = π / 2, a n o d e o c c u r s ∴ 10 π x = π / 2 \Rightarrow x = 0.05 m H e n c e, n o d e s w i l l o c c u r a t 0.05, 0.15, 0.25 . . . . . I f k x = π, a n a n t i n o d e o c c u r s ∴ 10 π x = π \Rightarrow x = 0.1 m H e n c e, a n t i - n o d e s w i l l o c c u r a t 0.1, 0.2, 0.3 . . . . A l s o w a v e s p e e d v = w / k = \frac{50 π}{10 π} = 5 m / \sec ∴ λ = 2 π / k = 2 π / 10 π = 0.2 m$

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