The A string on a string bass is tuned to vibrate at a fundamental frequency of 59.0 Hz. If the tension in the string were increased by a factor of 4, what would be the new fundamental frequency?

To find the new fundamental frequency of the string bass when the tension in the A string is increased by a factor of 4, we can use the equation for the fundamental frequency of a vibrating string:

f = (1/2L) * √(T/μ)

where:
f is the fundamental frequency,
L is the length of the string,
T is the tension in the string, and
μ is the linear mass density of the string.

Since we are only changing the tension, we can assume that the length and linear mass density of the string remain constant. Therefore, the new fundamental frequency (f') can be expressed as:

f' = (1/2L) * √((4T)/μ)

Since the tension T is increased by a factor of 4, we can substitute 4T for T in the equation:

f' = (1/2L) * √((4 * 4T)/μ)
= (1/2L) * √(16 * T/μ)
= (1/2L) * 4 * √(T/μ)
= 2 * (1/2L) * √(T/μ)

Simplifying the expression, we find:

f' = 2 * f

Therefore, the new fundamental frequency of the string bass when the tension in the A string is increased by a factor of 4 is twice the original frequency. In this case, the new fundamental frequency would be 2 * 59.0 Hz = 118.0 Hz.