Rankers Physics

Standing Wave in String and Organ Pipe: Practice Problem & Solution

A wave in a string has an amplitude of $2text{ cm}$. The wave travels in the +ve direction of x axis with a speed of $128text{ m/sec}$ and it is noted that 5 complete waves fit in $4text{ m}$ length of the string. The equation describing the wave is (2009)
$y = (0.02)text{ m}\sin(15.7x - 2010t)$
$y = (0.02)text{ m}\sin(15.7x + 2010t)$
$y = (0.02)text{ m}\sin(7.85x - 1005t)$
$y = (0.02)text{ m}\sin(7.85x + 1005t)$

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:

Amplitude $A = 2text{ cm} = 0.02text{ m}$. Wavelength $\lambda = 4/5 = 0.8text{ m}$. Wave number $k = 2\pi/0.8 \approx 7.85text{ m}^{-1}$. Angular frequency $\omega = vk = 128 \times 7.85 \approx 1005text{ rad/s}$. For +ve x-direction, $y = A\sin(kx - \omega t) = 0.02\sin(7.85x - 1005t)$.

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