The variation of the fundamental frequency of a stretched string with its tension was investigated - Leaving Cert Physics - Question 2 - 2017
Question 2
The variation of the fundamental frequency of a stretched string with its tension was investigated.
The length of the string and its mass per unit length were kept ... show full transcript
Worked Solution & Example Answer:The variation of the fundamental frequency of a stretched string with its tension was investigated - Leaving Cert Physics - Question 2 - 2017
Step 1
Draw a labelled diagram of the apparatus used.
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Answer
A labelled diagram should include a stretched string connected to a tuning fork or signal generator, a tension key with weights, and a bridge support. The string should be clearly marked as the main component. Indicate that the apparatus is used to measure the fundamental frequency while keeping tension and length constant.
Step 2
Show on your diagram how (i) the tension was measured.
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Indicate the use of a newton balance or pan with weights attached to the end of the string. The diagram should show weights being hung, which directly indicates the tension applied to the string.
Step 3
Show on your diagram how (ii) the length was measured.
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Mark the measuring device such as a ruler or a tape measure on the diagram, indicating where the length of the string is measured. Clearly label the points of measurement.
Step 4
How was the fundamental frequency determined?
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The fundamental frequency was determined by adjusting the tuning fork or signal generator until resonance in the string was observed. At this point, the frequency corresponding to the tension applied was recorded.
Step 5
How would a student use the measurements taken in this experiment to draw a graph showing the relationship between frequency and tension?
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The student would plot a graph of the square of the frequency (f2) against the tension (T). This relationship allows for easy visualization of how frequency varies with tension.
Step 6
Explain how the graph verifies this relationship.
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The graph will show a straight line passing through the origin, confirming a linear relationship between frequency and tension. This corroborates the theoretical understanding that the frequency is proportional to the square root of the tension applied.
Step 7
Write an expression for $\mu$ in terms of l and m.
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For a string of constant length l, the mass per unit length μ can be expressed using the slope m of the graph as: μ=4lm1
This relates mass distribution to the slope of the measured tension-frequency relationship.
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