#### Calculating Standing Waves in an Open Tube:

# v=fλ

where v = the speed of sound,

f is the funadmental frequency, and

λ is the wavelength.

# f=v/λ

To calculate the wavelength:

# λ=2L

Where L is the length of the tube in meters.

To calculate the resonant frequencies for the length of the tube:

# f(n)=(n*v)/2L

Where n is the resonant frequency number, making f(1) the fundamental frequency

Now, a ruben’s tube has a closed end, so the calculations differ slightly from that of an open tube.

To calculate the wavelength:

# λ=4L

therefore to calculate the fundamental frequency, the formala is:

# f(1)=(1*v)/4L

Assuming that we are using propane gas (LPG) for the fuel of the ruben’s tube, v is the speed of sound in propane (248m/s). Therefore, if we know the fundamental frequency we wish to achieve. Let’s assume our fundamental is A4 (440hz), we can determine the ideal length of the Ruben’s Tube with the formula:

# L=(n*v)/f/4

# L=(1*258)/440/4

# L=0.14659m

A tube length of 0.14569m would display a single arc when A4 (440Hz) is played into the tube.