Question

When under equal tension, the frequency (f) of a vibrating string in a piano varies inversely with the string length. If a string is 410 mm long and vibrates at a frequency of 515 cycles per second, at about what frequency will a 705 mm string vibrate?

a) 296 cycles per second
b) 342 cycles per second
c) 429 cycles per second
d) 592 cycles per second

Answer 1

The frequency at which a 705 mm string will vibrate is approximately 342 cycles per second.

Step-by-step explanation:

When under equal tension, the frequency (f) of a vibrating string in a piano varies inversely with the string length. This means that as the string length increases, the frequency decreases, and vice versa.

To find the frequency at which a 705 mm string will vibrate, we can set up a proportion using the given values:

Frequency1 / Length1 = Frequency2 / Length2

Substituting the values into the proportion, we get:

515 cycles per second / 410 mm = Frequency2 / 705 mm

Solving for Frequency2, we find that it is approximately 342 cycles per second.