A guitar string is supposed to vibrate at 247 Hz , but is measured to actually vibrate at 255 Hz

step 1 We have a guitar stream that is supposed to vibrate at 247 Hz, but instead it vibrates at 255 Hz

A guitar string is supposed to vibrate at 247 Hz , but is...

A guitar string is supposed to vibrate at 247 $\mathrm{Hz}$ , but is measured to actually vibrate at 255 $\mathrm{Hz}$ . By what percentage should the tension in the string be changed to get the frequency to the correct value?

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 Equation

This concept involves the mathematical relationship that describes the frequency of a vibrating string. The frequency is given by the formula f = (1/2L)?(T/?), where L is the length of the string, T is the tension, and ? is the linear mass density. This equation shows how the physical properties of the string, especially tension and mass per unit length, determine its vibrational frequency.

Square Law Dependency

This concept refers to the relationship between the tension in the string and its frequency; namely, that frequency is proportional to the square root of the tension. Because of this square law dependency, any change in frequency requires a proportional change in the square of the tension. This principle is crucial when adjusting the tension to achieve a desired frequency.

Percentage Change Calculation

This concept involves determining the relative change in a quantity in terms of a percentage. When adjusting a parameter such as tension to obtain a new frequency, the percentage change is computed by comparing the new tension value, derived using the appropriate ratio (in this case, that emerges from the square of the frequency ratio), to the original tension. This provides a clear metric for how much the tension must be altered.

Transcript

Please give Ace some feedback