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  • In a laboratory experiment, the speed of sound in air is measured using a resonance tube. The tube is partially filled with water, and a tuning fork of known frequency is used to produce a standing

In a laboratory experiment, the speed of sound in air is measured using a resonance tube. The tube is partially filled with water, and a tuning fork of known frequency is used to produce a standing wave inside the tube. The first resonance occurs when the tube length is L_{1}=25 \mathrm{~cm}, and the second resonance occurs when the tube length is L_{2}=75 \mathrm{~cm}. The frequency of the tuning fork is f=256 \mathrm{~Hz}.

The speed of sound v in air is:

Option: 1

320 \mathrm{~m} / \mathrm{s}


Option: 2

256 \mathrm{~m} / \mathrm{s}


Option: 3

340 \mathrm{~m} / \mathrm{s}


Option: 4

350 \mathrm{~m} / \mathrm{s}


Answers (1)

best_answer

The speed of sound in air can be calculated using the formula:

v=f \cdot \lambda

where f is the frequency of the tuning fork and \lambda is the wavelength of the sound wave.

For the first resonance, the tube length L_{1} is one-fourth of the wavelength (\lambda / 4) :

L_{1}=\frac{\lambda}{4} \Longrightarrow \lambda=4 \cdot L_{1}

Similarly, for the second resonance, the tube length L_{2} is three-fourths of the wavelength: 


L_{2}=\frac{3 \lambda}{4} \Longrightarrow \lambda=\frac{4}{3} \cdot L_{2}

Equating the two expressions for \lambda :

4 \cdot L_{1}=\frac{4}{3} \cdot L_{2}
Solve for L_{1} :

L_{1}=\frac{1}{3} \cdot L_{2}

Now, substitute the values:

L_{1}=\frac{1}{3} \cdot 75 \mathrm{~cm}=25 \mathrm{~cm}

The wavelength $\lambda$ can be calculated using L_{1} :

\lambda=4 \cdot 25 \mathrm{~cm}=100 \mathrm{~cm}=1 \mathrm{~m}

Finally, calculate the speed of sound $v$ :

v=f \cdot \lambda=256 \mathrm{~Hz} \cdot 1 \mathrm{~m}=256 \mathrm{~m} / \mathrm{s}

The calculated speed of sound is approximately 256 \mathrm{~m} / \mathrm{s}

 

Posted by

jitender.kumar

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