First slide

Stationary waves

Question

The equation of stationary wave along a stretched string is given by $y = 5 \sin \frac{πx}{3} \cos 40 πt$ , where x and y are in cm and t in second. The separation between two adjacent nodes is

Easy

A

1.5 cm
B

3 cm
C

6 cm
D

4 cm

Solution

On comparing the given equation with standard equation $y = 2 asin \frac{2 πx}{λ} \cos \frac{2 πvt}{λ} \Rightarrow \frac{2 πx}{λ} = \frac{πx}{3} \Rightarrow λ = 6$
Separation between two adjacent nodes = $\frac{λ}{2} = 3$ cm

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