A stationary wave is represented by y = 10sin ((π x)/(4))cos (20π t) where x and y are in cm and t in second. The distance between two consecutive nodes is (a) 1 cm (b) 8 cm (c) 4 cm (d) 2 cm

Answer: (c). k = π/4 = (2π)/(λ) ⇒ λ = 8 cm. Consecutive nodes are (λ)/(2) = 4 cm apart. So the answer is (c) 4 cm.

A stationary wave is represented by y = 10sin ((π x)/(4))cos (20π t)… | MHT CET 2022 (11 Aug, Shift 2)

Q71MHT CET 2022 · 11 AUG · SHIFT 2Easy

Stationary Waves & Vibrating Strings

A stationary wave is represented by $y = 10\sin\left(\frac{\pi x}{4}\right)\cos(20\pi t)$ where $x$ and $y$ are in $\text{cm}$ and $t$ in second. The distance between two consecutive nodes is

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Answer: (c)

$k = \frac{\pi}{4} = \frac{2\pi}{\lambda} \Rightarrow \lambda = 8\text{ cm}$ .
Consecutive nodes are $\frac{\lambda}{2} = 4\text{ cm}$ apart.
So the answer is (c) 4 cm.

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