Rankers Physics

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

A tuning fork is used to produce resonance in a glass tube. The length of the air column in this tube can be adjusted by a variable piston. At room temperature of $27^\circ\text{C}$ two successive resonances are produced at $20 \text{ cm}$ and $73 \text{ cm}$ of column length. If the frequency of the tuning fork is $320 \text{ Hz}$, the velocity of sound in air at $27^\circ\text{C}$ is: (2018)
$350 \text{ m/s}$
$339 \text{ m/s}$
$330 \text{ m/s}$
$340 \text{ m/s}$

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:

$v = 2f(L_2 - L_1) = 2 \times 320 \times (0.73 - 0.20) = 640 \times 0.53 = 339.2 \text{ m/s}$.

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