Answer the following prompt. Make sure to show all your work in answering the question. The length of a violin string varies inversely as the frequency of its vibrations. A violin string 10 inches long vibrates at a frequency of 512 cycles per second. Find the frequency of an 8-inch string. (3 points)
Let x be the frequency of an 8-inch string.
According to the inverse variation formula, we have:
length1 * frequency1 = length2 * frequency2
Substitute the given values:
10 * 512 = 8 * x
5120 = 8x
Divide both sides by 8:
x = 640
Therefore, the frequency of an 8-inch string is 640 cycles per second.