VISUAL  PHYSICS  ONLINE

3.1   WAVES

P31 005.m

 

An experiment was conducted to investigate the relationship between the frequency f of vibration of a stretched string vibrating in its fundamental mode and the length of the string L between the two bridges. A sonometer was used for the experiment.

The string tension FT was adjusted until the vibrating string between the movable bridges gave the same note as the vibrating tuning fork. The tension was then held constant and the experimented repeated for several different tuning forks. Each time, the distance between the bridges was adjusted until the fundamental mode of vibration was setup in the string. The results were:

 

    frequency f [Hz]    125        256        320        384        512

   Length L [m]          0.790     0.390    0.312      0.263    0.193

 

The mass of the string was 9.00 g and its length was 1.10 m.

Draw a graph of the frequency (Y axis) against L (X axis).

Draw a graph of the results such that a straight-line graph is obtained.

From the straight-line graph, determine the string tension FT.

 

Outline an experiment that you could perform to investigate the relationship between the fundamental frequency f and the string tension FT.

 

Sketch the shape of the vibrating string between the two bridges for the first six harmonics.

 

REVIEW

 

 

View solution below only after you have completed the answering the question.

 

 

 

 

 

 

 

 

Solution

The frequency of the normal modes of vibration of a string fixed at both ends is

           

 

For the fundamental mode n = 1. For our frequency and length data, a plot of the graph of f against 1/L should be a straight line passing through the Origin. The slope of the line should be

        

The blue circles show the data and the red lines are the curves of best fit. The plot of f against 1/L is a straight line through the Origin, which is agreement with our theoretical prediction.

                                 

 

 

 

To investigate the relationship between the frequency f of the fundamental mode and the string tension FT it is necessary to keep the length L between the two bridges of the sonometer fixed. From the measurements of f and FT, you would plot the graph of f against FT. To test our theoretical prediction, a straight line graph is necessary. Therefore, you could plot f against  or plot f 2 against FT.