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)
Responses
409.6 cycles per second
409.6 cycles per second
512 cycles per second
512 cycles per second
640 cycles per second
640 cycles per second
612 cycles per second
640 cycles per second
Explanation:
Let L1 be the original length (10 inches) and F1 be the original frequency (512 cycles per second). Let L2 be the new length (8 inches) and F2 be the new frequency (which we are trying to find).
According to the inverse variation relationship:
L1 * F1 = L2 * F2
10 * 512 = 8 * F2
F2 = 10 * 512 / 8
F2 = 640 cycles per second
Therefore, the frequency of an 8-inch string is 640 cycles per second.