(a) Describe an experiment to show how the frequency of the note emitted by a vibrating string depends on the tension in the string. (SSCE 1994)
Dependency of Frequency on Tension
Aim: To describe an experiment to show how frequency depends on the tension in the string.
Apparatus: Turning fork, string, scale pan, weight hangers, pegs, weight, frictionless pulley sound box.
Assumptions: The length of the string remains constant throughout the experiment. The string used is of uniform thickness and must not be changed to ensure that the mass per unit length is constant throughout the experiment.
Method: The length of string is tied to the stake at one fixed end (F) while a known mass is added to the other end. The string is supported at points A and B with pegs to avoid sagging. This creates a tension in the string and this tension is equal to the weight of the attached mass. Set a tuning fork of known frequency into vibration. Also pluck the string in the middle and tune it in unison with the fork. Record the load in the scale pan and the corresponding frequency of the fork. Repeat the procedure other higher weights of up to three or four and using different tuning forks three or four more times.
Conclusion: The graph of the frequency against the square root of the weight (tension) produces a straight line that passes through the origin as shown in the graph below. Therefore, frequency is directly proportional to the square root of tension.
Dependency of Frequency on Tension (Some explanations): This means that with a higher tension, the frequency will also be higher. From the last graph, if we double the tension, then the frequency is quadrupled.