Laws of Transverse Vibrations of a String: Sonometer

1. Law of length: the fundamental frequency of vibration of a string (fixed at both ends) is inversely proportional to the length of the string provided its tension and its mass per unit length remain the same.

v α 1/L if F and µ are constant.

2. Law of tension; the fundamental frequency of a string is proportional to the square root of its tension provided its length and the mass per unit length remain the same.

v α √(F) if L and µ are constant.

3. Law of mass: The fundamental frequency of a string is inversely proportional to the square root of the linear mass density, i.e., mass per unit length provided the length and the tension remain the same.

v α 1/ √(µ) if L and F are constant.