In an experiment to investigate the variation of the fundamental frequency $f$ of a stretched string with its length $l$, the following data were recorded. $f$/Hz $102$ $114$ $126 $141$ $165 $194$ $232$ $l$/m $0.603$ $0.553$ $0.503$ $0.453 $0.403$ $0.353$ $0.303$ $0.253 How were the data obtained? Using the data, draw a suitable graph on graph paper to show the relationship between the fundamental frequency of the stretched string and its length. The fundamental frequency of a stretched string depends on factors other than its length. Name one of these factors and give its relationship with the fundamental frequency. If you were doing an experiment to establish the relationship between the fundamental frequency of a stretched string and this other factor, how would you obtain the relevant data?

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In an experiment to investigate the variation of the fundamental frequency $f$ of a stretched string with its length $l$, the following data were recorded - Leaving Cert Physics - Question 3 - 2012

Question 3

In an experiment to investigate the variation of the fundamental frequency $f$ of a stretched string with its length $l$, the following data were recorded. $f$/Hz ... show full transcript

Worked Solution & Example Answer:In an experiment to investigate the variation of the fundamental frequency $f$ of a stretched string with its length $l$, the following data were recorded - Leaving Cert Physics - Question 3 - 2012

Step 1

How were the data obtained?

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Answer

The data were collected through the following steps:

Experiment Setup: The string was arranged showing means of changing frequency using a pulley and pan system fixed at both ends.
Vibrating the String: The string was placed on a bridge and vibrated until a standing wave was formed, indicating resonance.
Adjusting Length: The length of the string was adjusted until different frequencies were produced.
Length Measurement: The length was measured using a ruler between nodes.
Repeating Trials: The experiment was repeated with a fork of different frequencies to gather a range of data.

Step 2

Using the data, draw a suitable graph on graph paper to show the relationship between the fundamental frequency of the stretched string and its length.

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Answer

To create the graph:

Inverse Values: Calculate the inverse length ( $1/l$ ).
Plot Points: Plot the fundamental frequency ( $f$ ) on the y-axis against the inverse length ( $1/l$ ) on the x-axis.
Graph Shape: The plot should show a linear relationship, resulting in a straight line through the origin indicating that frequency increases as the inverse length decreases.

Step 3

Name one of these factors and give its relationship with the fundamental frequency.

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Answer

One factor that affects the fundamental frequency of a stretched string is the tension in the string. The relationship can be described using the formula: $f ext{ (frequency)} ext{ is directly proportional to } \\sqrt{T} \text{ (tension)},$ where $T$ is the tension in the string.

Step 4

How would you obtain the relevant data?

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Answer

To obtain the relevant data regarding the relationship between tension and frequency, the following steps should be followed:

Maintaining Fixed Length: Keep the length of the string fixed during the experiment.
Change Tension: Use weights to change or measure the tension in the string.
Measure Frequency: Use a frequency meter or tuning fork to measure the fundamental frequency while varying the tension for different trials.
Repeat Measurements: Conduct multiple trials to ensure consistent results and repeat for a range of frequencies.

In an experiment to investigate the variation of the fundamental frequency $f$ of a stretched string with its length $l$, the following data were recorded - Leaving Cert Physics - Question 3 - 2012

Worked Solution & Example Answer:In an experiment to investigate the variation of the fundamental frequency $f$ of a stretched string with its length $l$, the following data were recorded - Leaving Cert Physics - Question 3 - 2012

How were the data obtained?

Using the data, draw a suitable graph on graph paper to show the relationship between the fundamental frequency of the stretched string and its length.

Name one of these factors and give its relationship with the fundamental frequency.

How would you obtain the relevant data?

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