Rankers Physics

Waves and its Characteristics: Practice Problem & Solution

Equation of progressive wave is given by $y = 4 \sin[\pi(\frac{t}{5} - \frac{x}{9}) + \frac{\pi}{6}]$ where $y, x$ are in cm and $t$ is in seconds. Then which of the following is correct? (1988)
$v = 5 \text{ cm}$
$\lambda = 18 \text{ cm}$
$a = 0.04 \text{ cm}$
$f = 50 \text{ Hz}$

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 $y = A \sin(2\pi(\frac{t}{T} - \frac{x}{\lambda}) + \phi)$, rewrite the given equation as $y = 4 \sin[2\pi(\frac{t}{10} - \frac{x}{18}) + \frac{\pi}{6}]$. This gives $\lambda = 18 \text{ cm}$.

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