Standing Wave in String and Organ Pipe: Practice Problem & Solution
A stationary wave is represented by $y = A \sin(100t) \cos(0.01x)$, where $y$ and $A$ are in millimetres, $t$ is in seconds and $x$ is in metres. The velocity of the wave is: (1994)
Solution Explained:
To solve this problem, we apply the core principles of Standing Wave in String and Organ Pipe. Understanding the underlying formula is key to arriving at the correct answer below:
For the constituent waves, $\omega = 100$ and $k = 0.01$. Velocity $v = \frac{\omega}{k} = \frac{100}{0.01} = 10^4 \text{ m/s}$.
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