Options given are a 440cps b 880cps c 550 cps d 2200 cps and answer for it is (c)

Frequency change of a violin string when shortened by one fifth

There are different factors that affect the frequency of a violin string including its tension, length, and thickness. When the length of the string is changed, it affects the frequency of the vibration that produces the sound.

Calculating the frequency change

To determine the frequency change of a violin string when shortened by one fifth, we need to use the formula:

f2 = f1 * (L1/L2)

Where:
- f1 is the original frequency of the string
- L1 is the original length of the string
- L2 is the new length of the string
- f2 is the new frequency of the string

If the string is shortened by one fifth, its new length will be 4/5 of the original length. Therefore:

L2 = (4/5) * L1

Substituting this value in the formula, we get:

f2 = f1 * (L1 / (4/5) * L1)

f2 = f1 * (5/4)

f2 = 1.25 * f1

Interpreting the result

The result of the calculation shows that when the violin string is shortened by one fifth, its frequency increases by 25%. Therefore, if the original frequency of the string is 440 cps, its new frequency will be:

f2 = 1.25 * 440

f2 = 550 cps

This means that the sound produced by the string will be higher in pitch and frequency. The change in frequency can also affect the tone and quality of the sound produced by the violin.