Question

The length of a violin string varies inversely as the frequency of its vibrations. A violin string 12 inches long vibrates at a frequency of 525 cycles per second. Find the frequency of an 11 -inch violin string.

Answer 1

To find the frequency of an 11-inch violin string, given a 12-inch string vibrates at 525 Hz, use the inverse relationship between length and frequency. The calculated frequency for the 11-inch string is approximately 481.25 Hz.

Step-by-step explanation:

The length of a violin string varies inversely with the frequency of its vibrations. This means that if the length of the string is shortened, the frequency increases, and vice versa. To find the frequency of an 11-inch string, given that a 12-inch string has a frequency of 525 cycles per second, we can set up a proportion.

Let f be the frequency of the 11-inch string. The relationship of length and frequency can be written as:

12 inches / 525 Hz = 11 inches /

f

Hz

Solving for f gives us:

f = (525 Hz * 11 inches) / 12 inches

f = 481.25 Hz

Therefore, the frequency of the 11-inch violin string is approximately 481.25 Hz.