Photo AI
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 | 9... 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?
Answer
The data were obtained by carefully setting up an experimental arrangement that included a stretched string fixed at both ends with a pulley and weights to create tension in the string. The following steps were followed:
- Setting the string: The string was arranged on a table, attached to a pulley system to allow for tension adjustment.
- Vibrating the string: The string was set to vibrate using a tuning fork placed near it to create resonant frequencies.
- Measuring length: The length of the string was adjusted and measured accurately each time a different frequency was set.
- Recording frequencies: The frequency was measured using a frequency meter for various lengths. This process was repeated for different frequencies to ensure accurate data collection.
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.
Answer
To plot the graph:
-
Inversion of Variable: Calculate the inverse of length ( rac{1}{l}) for each recorded length and arrange it in a table alongside the corresponding frequencies.
-
Plot Encoding: On graph paper, plot frequency (f) on the y-axis against rac{1}{l} on the x-axis.
-
Drawing the Line: Draw a straight line through the origin as the data tends to show a direct proportional relationship. The line can be represented by the linear equation:
where ( m ) and ( c ) can be determined from the plotted values.
Step 3
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.
Answer
One factor that affects the fundamental frequency (f) of a stretched string is tension (T) in the string. The relationship is given by the formula:
Therefore, increasing the tension in the string will lead to an increase in the fundamental frequency.
Step 4
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?
Answer
To investigate the relationship between the fundamental frequency of a stretched string and the tension:
- Setting Up the Apparatus: Use a pulley system to apply variable weights that change the tension in the string.
- Adjusting Tension: Change the mass hanging from the string to vary the tension systematically.
- Measuring Frequency: For each tension setting, record the fundamental frequency using a microphone connected to a frequency analyzer.
- Data Collection: Repeat the measurements for multiple tension values to ensure enough data for analysis and graphing.