In an experiment to determine the speed of sound in air a student measured the length l of a column of air when it was vibrating at its fundamental frequency f. This process was repeated for six different values of f. The following data were recorded. f (Hz) 256 288 320 341 384 480 l (cm) 29.2 25.5 22.6 20.9 18.1 13.7 (i) Draw a labelled diagram of how the apparatus was arranged in this experiment. (ii) How did the student determine the length of the column of air for a particular frequency? (iii) Draw a graph to show the relationship between 1/l. (Note: the line of best fit on your graph should not go through the origin.) (iv) Use your graph to calculate the speed of sound in air. (v) Explain why the line of best fit on the graph does not go through the origin.

Leaving Cert Physics Vibration & Sound: In an experiment to determine th

In an experiment to determine the speed of sound in air a student measured the length l of a column of air when it was vibrating at its fundamental frequency f - Leaving Cert Physics - Question 4 - 2022

Question 4

In an experiment to determine the speed of sound in air a student measured the length l of a column of air when it was vibrating at its fundamental frequency f. This... show full transcript

Worked Solution & Example Answer:In an experiment to determine the speed of sound in air a student measured the length l of a column of air when it was vibrating at its fundamental frequency f - Leaving Cert Physics - Question 4 - 2022

Step 1

Draw a labelled diagram of how the apparatus was arranged in this experiment.

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Answer

The diagram should include:

A tube as the main apparatus.
A means of changing the length of the air column (e.g., a movable end).
A means of measuring length (e.g., a ruler).
A tuning fork (indicated) to produce sound. Ensure all components are properly labelled.

Step 2

How did the student determine the length of the column of air for a particular frequency?

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Answer

The student held the vibrating tuning fork over the mouth of the pipe. They changed the length of the air column until the loudest sound was heard, indicating resonance at that frequency. The length of the pipe was then measured at this point.

Step 3

Draw a graph to show the relationship between 1/l.

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Answer

The graph should plot the values of 1/l (in cm) against the corresponding frequencies (in Hz). Ensure that the axes are correctly labelled, and include a line of best fit that does not pass through the origin.

Step 4

Use your graph to calculate the speed of sound in air.

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Answer

Using the slope of the graph, the speed of sound can be calculated with the formula:

$v = f \times \text{length}$

where v is the speed of sound, f is the frequency, and length is the mean length of the air column from the graph.

Step 5

Explain why the line of best fit on the graph does not go through the origin.

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Answer

The line of best fit does not go through the origin because there is an end correction term that accounts for the effect of the wave opening at the mouth of the tube. This correction accounts for the additional length of the column of air that resonates, which is not captured by just measuring the physical length of the tube.

In an experiment to determine the speed of sound in air a student measured the length l of a column of air when it was vibrating at its fundamental frequency f - Leaving Cert Physics - Question 4 - 2022

Worked Solution & Example Answer:In an experiment to determine the speed of sound in air a student measured the length l of a column of air when it was vibrating at its fundamental frequency f - Leaving Cert Physics - Question 4 - 2022

Draw a labelled diagram of how the apparatus was arranged in this experiment.

How did the student determine the length of the column of air for a particular frequency?

Draw a graph to show the relationship between 1/l.

Use your graph to calculate the speed of sound in air.

Explain why the line of best fit on the graph does not go through the origin.

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