Question

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 degree C two successive resonances are produced at 20 cm and 73 cm column length. If the frequency of the tuning fork is 320 Hz, the velocity of sound in air at 27 degree C is

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Solution

The correct option is **B**

339 m/s

**Step 1: Given**

Length of 1st resonance, ${l}_{1}=20cm=0.2m$

Length of 2nd resonance, ${l}_{2}=73cm=0.73m$

Frequency, $f=320Hz$

Temperature = 27^{o} C

**Step 2: Formula Used:**

$V=2f\left({l}_{2}-{l}_{1}\right)$

Where $V$ velocity of sound, $f$ is frequency, ${l}_{1}$ is length of 1st resonance , and ${l}_{2}$ is length of 2nd resonance.

**Step 3: Calculation:**

Given that two successive resonance is produced, so using the formula of resonance,

$V=2f\left({l}_{2}-{l}_{1}\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}V=2\xc3\u2014320\left(0.73-0.2\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}V=640\xc3\u2014\left(0.53\right)\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}V=339.2m/s$

**As velocity of sound in air at 27 ^{o} C is 339.2 m/s. Hence option B is correct.**

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