Question

A violin string vibrates at 294 Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a standing wave.)

Answer 1

Concepts and reason

The concept used to solve this problem is the fundamental frequency of a vibrating string.

Use the concept of frequency of vibrating frequency to calculate the frequency of a violin string.

Fundamentals

The fundamental frequency is the lowest frequency in a resonating system.

Expression for the fundamental frequency of vibrating string is given below:

Here, the frequency of the string is , velocity of wave on string is , and the length of the string is .

Expression for the fundamental frequency of vibrating string is given below:

When the finger is placed on the string, only two-third of the string vibrates as a standing wave.

Since the velocity of the wave on string is constant, therefore,

Here, the frequency of the string when unfingered is , the length of the vibrating string when unfingered is , the frequency of the string when fingered is , and the length of the vibrating string when fingered is .

Rearrange the above equation to get .

Expression for the frequency when the string is fingered is given below:

Substitute for , for , and for .

Ans:

The frequency of vibration when the string is fingered one-third of its length from the end is .