A tuning fork (380 Hz) is held over an open air column. Determine the following...

Question

A tuning fork (380 Hz) is held over an open-air column. Resonance first occurs (first harmonic) when the column is 44.0 cm long. What is the speed of the sound in the air at this time?

Please include a detailed and understandable answer for a Grade 11. Thanks :)

Answer 1

Because we are dealing with an open air tube, for the first (fundamental) harmonic we will have

L = 1/2 λ

here L - length of the air column,

λ - wavelength.

The connection between the frequency f, speed of sound v and wavelength λ is given by the formula

v = fλ.

Combining 2 formulas for speed of sound we will get

v = 2fL.

Putting the values, we will finally have

v = 2 · 380 Hz · 0.44 m = 334.4 m/s

If we follow the rules of error handling, the answer should be 334 m/s. Your teacher maybe wants 333.4 m/s.