Waves and its Characteristics: Practice Problem & Solution
The wave described by $y = 0.25\sin(10\pi x - 2\pi t)$ where $x$ and $y$ are in meters and $t$ in seconds, is a wave travelling along the: (2008)
Solution Explained:
To solve this problem, we apply the core principles of Waves and its Characteristics. Understanding the underlying formula is key to arriving at the correct answer below:
Comparing with $y = A\sin(kx - \omega t)$, the negative sign indicates it travels in the +ve x direction. Amplitude $A = 0.25text{ m}$. Wave number $k = 10\pi$, so $\lambda = 2\pi/k = 0.2text{ m}$. Angular frequency $\omega = 2\pi$, so $f = \omega/(2\pi) = 1text{ Hz}$.
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