String vibration calculator to calculate natural frequency of a string vibrating laterally under a tension T with both ends fixed. String vibration formula is given below the calculator.

String Vibration Calculator:

Natural frequency of string under tension
Parameter Value
Tension [T]
Beam length [L]
Uniform load per unit length [w]

Note: Use dot "." as decimal separator.


Parameter Value
First natural frequency [f1] --- Hz
Second natural frequency [f2] ---
Third natural frequency [f3] ---

String Vibration Formula:

Natural frequency of a string under a tension T with both ends fixed and a uniform load w per unit length including own weight  [f]
$$f=\frac { { K }_{ n } }{ 2\pi } \sqrt { \frac { Tg }{ w{ l }^{ 2 } } } $$

Symbol Parameter
Kn A constant where n refers to the mode of vibration.
Mode 1 - Kn = π
Mode 2 - Kn = 2π
Mode 3 - Kn = 3π
T Tension
l Length of the string
w Uniform load