First slide

Stationary waves

Question

The equation of a stationary wave is $y = 0 .8 \cos (\frac{πx}{20}) \sin 200 πt$ , where x is in cm and t is in sec. The separation between consecutive nodes will be

Easy

A

20 cm
B

10 cm
C

40 cm
D

30 cm

Solution

On comparing the given equation with standard equation $y = 2 a \sin \frac{2 πx}{λ} \cos \frac{2 πvt}{λ}]$
We get $\frac{2 π}{λ} = \frac{π}{20} \Rightarrow λ = 40$
Separation between two consecutive nodes = $\frac{λ}{2} = \frac{40}{2} = 20 cm$

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