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

Question

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:

Accepted Answer

1. **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 $y = A\sin(kx - \omega t)$.
2. **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 $x$) .
3. **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 $f = 1 	ext{ Hz}$ .
4. **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 $\lambda = \frac{2}{10} = 0.2 	ext{ m}$ .
Thus, the wave travels in the +ve $x$ direction with a frequency of $1 	ext{ Hz}$ and wavelength of $0.2 	ext{ m}$.

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