We have observed that an increase in the tension of a string causes an increase in the velocity that waves travel on the string.  In this activity we will examine the precise relationship between tension (T) the force applied to the string, the wave speed (v_w) and the linear mass density of the string (µ = m/L which is measured in kg/m). 

 

We will stretch a string across two “bridges”, creating two fixed ends, and then allow the remaining string to hang over a supporting bar with different increments of mass generating its tension. This will allow us to increase tension in the string by the addition of mass, while keeping a constant wavelength. This will cause the velocity to change with the frequency of the string like a guitar with its tuning pegs.

 

 

A microphone will be placed next to the string and when plucked the frequency of the note will be displayed on a scale using a frequency analyzer. Notice that several frequencies are observed, the must discernible and lowest frequency represents the fundamental - seen as a dark red line with green/yellow highlights. The other frequencies represent higher harmonics (or overtones). You can notice that they are evenly spaced in frequency as predicted by our model of standing waves.

 

 

 

Measuring the length of the vibrating string allows us to calculate the wavelength. Then by focusing on the fundamental frequency (which has only one loop) and using our model for fixed-fixed standing waves we can determine the wave speed along the string.

Complete the following table by measuring calculating the required values for string one.

 

 

Record below the length of the second vibrating string segment - the light string.

 

Complete the following table by measuring calculating the required values for string two.

 

 

Samples of each of these fishing lines will now be provided to you so that you can measure their mass and length. This information will allow you to determine the linear mass density for each type of string used in the experiment.