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Physics

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Investigation into the frequency of stationary waves on a string with length, tension and mass per unit length of the string.

Materials and equipment:

  • signal generator
  • vibration generator
  • stand
  • 100 g mass
  • 1 m length of string
  • pulley which can be clamped to the bench
  • wooden bridge higher than the pulley
  • masses on a holder
  • metre ruler

Technical information:

  • The signal generator should be adjusted in order for the frequency to stabilise.
  • The string should be tied to the stand and passed through the hole in the vibration generator.
  • The bridge should be at the same height as the hole.

Safety:

The stand could topple over and cause injury so a counterweight can be used if it is deemed unstable.

Improvements and notes:

A counterweight can be used to ensure the stand does not topple over.

An amplifier can be used to amplify the wave.

The signal generator should be left in the initial minutes to stabilise.

Method:

  • Adjust the position of the bridge so that l is 1.000 m measured using the metre ruler.
  • Increase the frequency of the signal generator from zero until the string resonates at its fundamental frequency (as indicated in the diagram with a node at each end and a central antinode).
  • Read the frequency f, on the signal generator screen.
  • Repeat the procedure with l = 0.900, 0.800, 0.700, 0.600 and 0.500 m.

Q1 Calculate 1/frequency using the frequency values provided.

      Length (m)   Frequency (Hz)    1/Frequency (Hz-1)
1 21
0.9 23
0.8 27
0.7 32
0.6 37
0.5 48

Q2 Plot a graph of 1/f against l. (Excel is preferred you can copy the graph from excel into this document). Draw the best straight line of fit though the points and find the gradient (the graph should be a straight line).

Calculations:

Speed of the travelling waves on the string is c = fλ

Where,

λ – wavelength

f – frequency

When the string is vibrating in its fundamental mode,

l = λ/2

λ = 2l where l is value of length

Hence, (Substituting the value of λ)

c = 2fl

Gradient is 1/fl

So, c is given by 2/Gradient in ms–1

Q3 Calculate the speed of the wave using the gradient of the graph?

The speed is also given by,

c = √(T/ µ)

where,

T = Tension in the string in N

and

µ = mass per unit length of the string in kg m–1.

Q4 Calculate the Mass per unit length and Tension of your set up (the tension is caused by the 100 g weight attached at the end of the string)

µ Mass per unit length is 0.65 g m–1 = ——– kg m–1

Tension (Weight) = T = ——— N

These values can then be substituted into the above equation,

c = √(T/ µ)

to find another value for c, which can be compared to the value obtained from the graph.

Q5 By substituting the values from the previous question, calculate the value of speed c?

Further questions:

Q6 Will the weight hung need to be increased or decreased to get a lower Tension (T) and to decrease the speed (c)?

Q7 If the mass of the string is increased what effect will it have on the Linear Density (µ), the speed (c) and the fundamental frequency (f1) (assuming the length is kept constant)?

Q8 Identify the major sources of uncertainty in your work and methods to overcome it?

Q9 Why is it important to repeat scientific experiments?

Chemistry

Determining the Concentration of Ethanoic Acid in Vinegar: An Application of Acid-Base Titration

Background

Imagine that you are a scientist and you have been hired by a leading Nottingham restaurant to analyse their drop in sales because of negative customer reviews. One of the biggest critics is that the salad dressings do not have their usual zing. A major component in their salad dressings is vinegar. Vinegar is a solution of ethanoic acid in water. Ethanoic acid, CH3COOH, is a weak monoprotic acid, and it is responsible for its sour taste of vinegar and the zing. The concentration of ethanoic acid in vinegar can be determined by titrating a known amount of vinegar with a standardized solution of sodium hydroxide of accurately known concentration. Acetic acid and sodium hydroxide react as shown below:

Ethanoic acid is an example of a weak acid. For a 0.2 mol/L solution of ethanoic acid only about 1% of the acid ionizes. Compare this to a strong acid like hydrochloric acid. Very close to 100% of hydrochloric acid ionizes. A few examples of strong and weak acids are shown below:

Tasks

  1. Complete the table with your observations
  2. Doing the required calculations to find the molar concentration of ethanoic acid in the sample
  3. Answer the Questions given at the end
  4. Submit the completed worksheet at the end of the lab through your NOW drop box

Chemicals and Apparatus:

  • Vinegar sample
  • Sodium hydroxide pellets
  • Deionised water
  • Phenolphthalein indicator
  • Measuring balance
  • Stirrer
  • Burette (25 cm3)
  • Burette stand and burette clamp
  • Conical flask (100 cm3)
  • Volumetric flask (250 cm3) and stopper
  • White card or white tile
  • Beakers (250 cm3)
  • burette funnel
  • Safety glasses

Suggested methods

In every case, you should present all your observations in a Neat Table. The presentation of a clearly organised record of your observations is an important skill which you will be expected to demonstrate.

Preparing sodium hydroxide

  1. Calculate the required weight of NaOH to create a 0.2 M sodium hydroxide solution (NaOH- 40 g/mol)
  2. Measure the required amount using weighing scale
  3. Mix the weighed amount with 100 ml in a beaker and stir till it dissolves using the stirrer.
  4. Put the content from the beaker into a volumetric flask (Rinse the beaker with DI water and put it into the volumetric flask)
  5. Fill up the volumetric flask to 250 ml (To the blue mark. Meniscus should be in line with blue line)
  6. Stopper the flask and invert several times to ensure a homogeneous solution. Label the flask.
  7. Rinse the burette into a waste beaker using a small amount of your sodium hydroxide solution.
  8. Place 25 cm3 of 0.2 M sodium hydroxide solution in the burette

Filling the conical flask with vinegar solution

  1. You will be provided with the diluted vinegar solution (1 in 10)
  2. Rinse the conical flask with a small amount of your vinegar solution.
  3. Fill the conical flask with to the 25 cm3 mark with diluted vinegar and add 3 drops of phenolphthalein indicator.

Performing a titration

    1. Carry out one rough and three accurate titrations. (Question 9 has the table)
    2. Calculate the concentration of ethanoic acid in the diluted vinegar solution.
    3. Calculate the percentage (w/v) of ethanoic acid in the vinegar.

Questions relating to the experiment

  1. Calculate the grams of NaOH required to create a 250 cm-3 of 0.2 mol solution of NaOH? (NaOH – 40 g/mol)
  2. Outline the correct procedure of transferring the NaOH solution from the beaker to the volumetric flask?
  3. What will happen to the concentration of the NaOH solution if it is diluted with excess water?
  4. Give two errors that might occur when obtaining the burette readings?
  5. Why is phenolphthalein used in this titration?
  6. What do you observe at the end of the titration?
  7. If this experiment was conducted using hydrochloric acid as the titrant and NaOH was placed in the conical flask with the Phenolphthalein indicator. What will be observed during the titration?
  8. Explain why it is important to conduct multiple titrations instead of doing the experiment only once?

Titration Results

Initial volume (burette) Final volume (burette) Total volume (Final – Initial)
Rough Titration 0 11.3
Titration 1 0 11.5
Titration 2 11.5 22.7
Titration 3 0 11.6
Average total volume

Calculate the concentration of ethanoic acid in the vinegar sample?

Number of moles = concentration * volume

Concentration = number of moles/volume