The speed of a wave pulse traveling along a string or wire is determined by knowing its mass per unit length and its tension.

 

 

In this formula, the ratio ^mass/_length is read "mass per unit length" and represents the linear mass density of the string. This quantity is measured in kilograms/meter.

 

Tension is the force conducted along the string and is measured in newtons, N. The maximum tension that a string can withstand is called its tensile strength.

 

The formula given above tells us that the "tighter" the string (that is, the greater the tension placed on the string) the faster the waves will travel down its length. It also tells us that the "lighter" the string, that is, the smaller its ^mass/_length ratio, the faster the waves will travel down its length.

 

 

When a wave is traveling along a tightly-drawn string, the tension in the string can be produced by passing it over a massless, frictionless pulley and hanging a counterweight from its end.

 

 

 

This would produce a tension, T, equal to the weight of the hanging mass, Mg, where "g" represents the acceleration due to gravity, 9.81 m/sec².

 

The ratio ^mass/_length in our formula only applies to the vibrating string and has nothing to do with the mass of the counterweight.

 

Before continuing with the next example in which we calculate the wave speed in this scenario, you will need to be familiar with resonance and the string's fundamental frequency.