Question

In: Physics

I am doing an experiment recording the speed of sound. I am using an open-ended cardboard...

I am doing an experiment recording the speed of sound. I am using an open-ended cardboard tube that is 76.2cm (30") and the temperature in my room is 75 degrees or 23.89 celsius.

What is my speed of sound (using the speed of sound expression with explanation please)?

Given the length of my tube, what are my first five wavelengths that my tube should resonate (using the standing sound wave formula)?

What are my five wavenumbers (k) of the above (reciprocal).

What should my first five resonance frequencies (predicted) be? If i understand this correctly, I do this using the theoretical speed of sound calculated above together with the five resonance wavelengths also determined above.

Expert Solution

Expression for velocity of sound at a given temperature T Kelvin is

is the adiabatic constant R is the universal gas constant and M is the molecular mass of gas

Experiment is conducted at 23.89 C=(273+23.89) K=296.89 K

For air, adiabatic constant is 1.4 and molecular mass is about 0.02895 kg/mol

Putting the values,

For an open tube of length L, the resonance wavelengths are given by

n is an integer and n=1,2,3,4,....

Hence, the first five resonant wavelengths are given for n=1,2,3,4,5 viz-

The wave-numbers are just the reciprocals of above viz-

The first resonant frequency should be,

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