First slide

Stationary waves

Question

For the stationary wave $y = 4 \sin (\frac{πx}{15}) \cos (96 πt)$ , the distance between a node and the next antinode is (in m)

Easy

A

7.5
B

15
C

22.5
D

30

Solution

Comparing given equation with standard equation
$y = 2 asin \frac{2 πx}{λ} \cos \frac{2 πvt}{λ}$ gives us $\frac{2 π}{λ} = \frac{π}{15} \Rightarrow λ = 30$
Distance between nearest node and antinodes = $\frac{λ}{4} = \frac{30}{4} = 7 .5$

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