Question:
For stationary wave, \(y = 12cos(\frac{πx}{10})sin(36πt)\) cm, the distance between a node and the successive antinode is
For stationary wave, \(y = 12cos(\frac{πx}{10})sin(36πt)\) cm, the distance between a node and the successive antinode is
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Read the wave number k from the cosine term; the node-to-antinode distance is a quarter of the wavelength.
Updated On: Oct 1, 2026
- \(20\) cm
- \(12\) cm
- \(10\) cm
- \(5\) cm
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The Correct Option is D
Solution and Explanation
Step 1: Understand the concept
In a stationary wave \(y = 2A\cos(kx)\sin(\omega t)\), the quantity \(k = \dfrac{2\pi}{\lambda}\). Nodes and antinodes alternate, and the distance between a node and the next antinode is \(\dfrac{\lambda}{4}\).
Step 2: Find \(k\)
Comparing with \(\cos\left(\dfrac{\pi x}{10}\right)\) gives \(k = \dfrac{\pi}{10}\ \text{cm}^{-1}\).
Step 3: Find the wavelength
\[ \lambda = \frac{2\pi}{k} = \frac{2\pi}{\pi/10} = 20\ \text{cm} \]
Step 4: Result
The node to antinode distance is \(\dfrac{20}{4} = 5\) cm, option (D). The value 10 cm is the distance between adjacent nodes, and 20 cm is the full wavelength.
Final Answer:
The distance is 5 cm. This is option (D). \[ \boxed{\text{(D) }5\ \text{cm}} \]
In a stationary wave \(y = 2A\cos(kx)\sin(\omega t)\), the quantity \(k = \dfrac{2\pi}{\lambda}\). Nodes and antinodes alternate, and the distance between a node and the next antinode is \(\dfrac{\lambda}{4}\).
Step 2: Find \(k\)
Comparing with \(\cos\left(\dfrac{\pi x}{10}\right)\) gives \(k = \dfrac{\pi}{10}\ \text{cm}^{-1}\).
Step 3: Find the wavelength
\[ \lambda = \frac{2\pi}{k} = \frac{2\pi}{\pi/10} = 20\ \text{cm} \]
Step 4: Result
The node to antinode distance is \(\dfrac{20}{4} = 5\) cm, option (D). The value 10 cm is the distance between adjacent nodes, and 20 cm is the full wavelength.
Final Answer:
The distance is 5 cm. This is option (D). \[ \boxed{\text{(D) }5\ \text{cm}} \]
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