A violin string has a standard length of 32.8 cm. It sounds the musical note A(440 Hz) when pl

step 1 Hello, in this question we applied the idea that frequency is inversely proportional to length.

A violin string has a standard length of 32.8 cm. It sounds...

A violin string has a standard length of $32.8 \mathrm{~cm}$. It sounds the musical note $\mathrm{A}(440 \mathrm{~Hz})$ when played without fingering. How far from the end of the string should you place your finger to play the note $\mathrm{C}(523 \mathrm{~Hz}) ?$

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vibrating String Fundamentals

The fundamental frequency of a fixed string is determined by its length, tension, and linear density according to the relation f = (1/2L)?(T/?). This means that when the tension and mass per unit length of the string remain constant, the pitch of the note produced depends directly on the effective length of the vibrating portion of the string.

Inverse Proportionality between Frequency and Effective Length

For a vibrating string with constant tension and density, the fundamental frequency is inversely proportional to the effective length. This inverse relationship (f ? 1/L) implies that shortening the vibrating length will raise the pitch, while increasing the length will lower it.

Proportional Reasoning in Adjusting Pitch

Using the inverse proportionality between frequency and string length, one can relate two different frequencies with their corresponding effective lengths. By setting the product of the frequency and effective length constant, it is possible to determine where along the string the finger should be placed to achieve a desired change in pitch.

Please give Ace some feedback