PhysicsLAB Resource Lesson
Speed of Waves Along a String

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.
 
 
Refer to the following information for the next two questions.

A ball of string is purchased at a local hardware store. According to the manufacturer, the package contains 100 yards (91.5 meters) of string and has a mass of 12 oz (341 grams).
 What is the string's linear mass density?

 If the string's tensile strength is 90 N, what is the maximum speed a pulse could travel along the string?



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.
 
 
Refer to the following information for the next question.

Suppose a second type of string has a different set of following manufacturer's specifications: 100 meters has a mass of 300 grams.
 Determine the fundamental frequency in this string when a 5-kg mass is suspended from a 1-meter vibrating section.





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