Question

The frequency of vibration of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 440 vibrations per second. Find the frequency of a string that has 1.25 times as much tesnsion and is 1.2 times as long.

Answer 1

Answer:

  about 409.946 Hz

Step-by-step explanation:

The multiplier of frequency is (√(tension multiplier))/(length multiplier), so is ...

  (√1.25)/1.2 = (5/12)√5 ≈ 0.931695

So, the longer, tighter string will have the lower frequency of about ...

  0.931695×440 Hz ≈ 409.946 Hz