Solved: PHYSICS Question for NEET

NEET PHYSICSEasy

The wave described by $y = 0.25\sin(10\pi x - 2\pi t)$ , where $x$ and $y$ are in metres and $t$ in seconds, is a wave traveling along the:

-ve $x$ direction with frequency $1 \text{ Hz}$ .

+ve $x$ direction with frequency $\pi \text{ Hz}$ and wavelength $\lambda = 0.2 \text{ m}$ .

+ve $x$ direction with frequency $1 \text{ Hz}$ and wavelength $\lambda = 0.2 \text{ m}$ .

-ve $x$ direction with amplitude $0.25 \text{ m}$ and wavelength $\lambda = 0.2 \text{ m}$ .

Compare with standard wave equation: The given wave equation is $y = 0.25\sin(10\pi x - 2\pi t)$ . The general equation for a progressive wave is $y = A\sin(kx - \omega t)$ .
Determine Direction of Propagation: The negative sign between the $kx$ and $\omega t$ terms indicates that the wave is travelling in the positive $x$ -direction (+ve $x$ ) .
Calculate Frequency ( $f$ ): From the equation, angular frequency $\omega = 2\pi$ . Since $\omega = 2\pi f$ , we have $2\pi f = 2\pi$ , which gives $f = 1 \text{ Hz}$ .
Calculate Wavelength ( $\lambda$ ): From the equation, wave number $k = 10\pi$ . Since $k = \frac{2\pi}{\lambda}$ , we have $\frac{2\pi}{\lambda} = 10\pi$ , which gives $\lambda = \frac{2}{10} = 0.2 \text{ m}$ . Thus, the wave travels in the +ve $x$ direction with a frequency of $1 \text{ Hz}$ and wavelength of $0.2 \text{ m}$ .

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