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. (1 point)
Let's denote the length of the violin string as L and the frequency of its vibrations as f.
According to the given information, the relationship can be represented as:
L ∝ 1/f
This can be written as:
L = k/f
where k is the constant of proportionality.
Using the values from the first scenario:
10 = k/512
k = 10 * 512
k = 5120
Now, we can use the constant of proportionality to find the frequency of an 8-inch string:
8 = 5120/f
f = 5120/8
f = 640 cycles per second
Therefore, the frequency of an 8-inch string would be 640 cycles per second.