What is the length of a tube with specific frequencies and speed of sound?

Calculation of the Length of the Tube

Length Calculation: The length of the tube is found by using the formula for the speed of a wave which involves the fundamental frequency. We substitute the given values into the equation and find that the length of the tube is approximately 1.03 meters.

Explanation

To answer this question, we first need to understand the concept of fundamental frequency and overtones in physics. Fundamental frequency, also known as the first harmonic, is the lowest frequency in the harmonic sequence. Overtones, on the other hand, are the higher frequencies. In a tube, the first overtone, or the second harmonic, is exactly twice the fundamental frequency.

From the question, the fundamental frequency is 164 Hz and the first overtone is 328 Hz. So, that's consistent. Now, we know that the speed of a wave (v) is equal to its frequency (f) times its wavelength (λ), described as: v = f * λ. In a tube where the wave can bounce back and forth, the length of the tube is essentially half the wavelength (λ/2).

If we rearrange the equation to solve for length (L), we get L = v / (2f). Substituting the given values in, we calculate the length as L = 338 m/s / (2*164 Hz) = 1.03 m.