If the length of a guitar string is 90 cm, and the speed of sound is 343 m/s that day, what is the 3 rd fundamental frequency of the guitar?
To find the third fundamental frequency of a guitar string, we need to use the formula:
Frequency = (n * V) / (2L)
Where:
- n represents the harmonic number (fundamental frequency is n=1, second fundamental frequency is n=2, etc.)
- V represents the speed of sound
- L represents the length of the guitar string
In this case, the length of the guitar string is given as 90 cm, which we need to convert to meters. Since 1 meter is equal to 100 centimeters, the length of the string in meters is 0.9 m.
Now, we can substitute the values into the formula:
Frequency = (3 * 343 m/s) / (2 * 0.9 m)
Simplifying the equation:
Frequency = (1029 m/s) / (1.8 m)
Frequency ≈ 571.67 Hz
Therefore, the third fundamental frequency of the guitar string is approximately 571.67 Hz.