A standard new bass guitar scale tends to be around 35 inches long. The scale of the bass is measured by doubling the length between the nut and the 12th fret on the neck. This is done because the 12th fret is always the middle point on the “active” parts of the string (ie the parts of the string that one would touch with their finger). For the sake of the equation, we will be trying to determine the tension required in the E string (the lowest pitch string.)
35 inches in centimetres is 88.9cm. The mass per unit length of a bass string is not information that I was able to find, but by searching for a package of 4 strings online I was able to find that all 4 strings together weigh 90.7g, or ~0.0907kg (c: amazon.com). Dividing this by 0.889m gives us an ESTIMATE mass per unit length of 0.0255kg/m.
Below is the written maths done to find the tension required in the E string of a bass guitar.
If the tension on a bass guitar is too tight or too loose, the frequency will be wrong. This will produce the wrong pitch while playing the instrument, which will negatively impact the quality of the music being played. It is a common practice to purposefully alter the frequency of instruments in order to produce a new tuning (standard tuning on bass is EADG) which tends to allow the user to experiment more freely with music theory, and create interesting and engaging pieces of music.