A wave disturbance in a medium is described by y(x,,t) = 0.02cos ,left( {50,pi t + frac{pi }{2}} right)cos (10pi x), where x and y

Q: A wave disturbance in a medium is described by $y(x,\,t) = 0.02\cos \,\left( {50\,\pi t + \frac{\pi }{2}} \right)\cos (10\pi x)$, where $ x$ and $y$ are in metres and $t$ in seconds

d (d) $y = 0.02\cos (10\,\pi x)\cos \,\left( {50\,\pi \,t + \frac{\pi }{2}} \right)$ At node, amplitude $= 0$ $ \Rightarrow $ $\cos (10\pi x) = 0 \Rightarrow 10\,\pi x = \frac{\pi }{2},\frac{{3\pi }}{2}$ $ \Rightarrow \,x = \frac{1}{{20}} = 0.05 m, 0.15m …..$ At antinode, amplitude is maximum $ \Rightarrow $$\cos (10\pi x) = \pm 1 \Rightarrow x = 0,\pi ,2\pi ...$ $==> x = 0, 0.1m, 0.2m …$ Now $\lambda = 2 \times $ Distance between two nodes or antinodes = $2 \times 0.1 = 0.2 m$ and $\frac{{2\pi vt}}{\lambda } = 50\pi t$ $v = 25\lambda = 25 \times 0.2 = 5m/\sec $.

SECTION - A [PHYSICS - MCQ]

GSEB - English Medium

A wave disturbance in a medium is described by $y(x,\,t) = 0.02\cos \,\left( {50\,\pi t + \frac{\pi }{2}} \right)\cos (10\pi x)$, where $ x$ and $y$ are in metres and $t$ in seconds

AA displacement node occurs at $x = 0.15 m$
BAn antinode occurs at $x = 0.3 m$
CThe wavelength of the wave is $0.2 m$
D
All of the above.

IIT 1995, Diffcult

STD 11 Science
NEET
STD 11 - 14. waves and sound
Physics

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