Question

On a stringed instrument, the length of a string varies inversely as the frequency of its vibrations. An 11-inch string on a violin has a frequency of 400 cycles per second. Write the equation that relates the string length, L, to its frequency, f. What would be the frequency of a 10-inch string?

Answer 1

Answer:

• f = 4400/L
• 440 cycles per second

Step-by-step explanation:

When the variation is inverse, the product of values is a constant:

  f·L = k = (400)(11) = 4400

  f = 4400/L

Then a 10-inch string will vibrate with a frequency of ...

  f = 4400/10 = 440 . . . cycles per second