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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.
Answer
To draw the apparatus, include the following components:
- A string (stretched between a bridge and a tuning fork).
- A tuning fork or signal generator to produce sound.
- A paper rider or additional device to indicate resonance.
- A newton balance/pan where weights are placed to measure tension.
- Label each component clearly, particularly focusing on the tension measurement area and an indication of where the length of the string is measured.
Step 2
Show on your diagram how (i) the tension and (ii) the length were measured.
Answer
(i) The tension was measured using a newton balance attached to the string, which allows for different weights to be added accurately. (ii) The length of the string was indicated by markings on a meter rule affixed alongside the string, from the fixed point to the point where the string is held taut.
Step 3
How was the fundamental frequency determined?
Answer
The fundamental frequency was determined by adjusting the tuning fork or signal generator slightly and listening for resonance. The tuning fork was matched to the natural frequency of the string, often observed as a peak in amplitude. The adjustment continued until a clear tone was noted, indicating resonance.
Step 4
How would a student use the measurements taken in this experiment to draw a graph showing the relationship between frequency and tension?
Answer
A student would plot the measured frequency values (f) on the y-axis against the square root of the tension values () on the x-axis. This allows for a clear visualization of how frequency varies with tension.
Step 5
Explain how the graph verifies this relationship.
Answer
The resulting graph yields a straight line passing through the origin, demonstrating that frequency is directly proportional to the square root of tension. This linear relationship signifies that an increase in tension leads to an increase in the fundamental frequency of the string.
Step 6
Write an expression for μ in terms of l and m.
Answer
For a string of constant length ( l ), the mass per unit length ( \mu ) can be expressed as:
[ \mu = \frac{T}{4 \pi^2 f^2} ]
Given the slope ( m ) of the graph,
[ \mu = \frac{1}{4 m} \text{ (if not subject of equation)} ]
This incorporates the slope derived from the plotted values.