Standing Waves (with mechanical oscillator)
To demonstrate how frequency and tension effect standing waves on a string.
Mechanical oscillator with string
Function generator with cords
Hanger and weights
Attach a pulley to the edge of a table and place the oscillator about two meters away. Hang a 50g hanger with an 100g weight on it from the string over the pulley. The distance from the top of the pulley to the mechanical oscillator should be exactly two meters. Plug the oscillator in the function generator and start the generator. Experiment with the frequency and amplitude until you can find the fundamental standing wave. You can then just double the frequency to show that at the new frequency you will have the next standing wave and each time you add the frequency of the fundamental standing wave you will arrive at the next standing wave. With enough amplitude you should be able to easily see 6 or 7 antinodes. Set the function generator back to the fundamental frequency. Now take an additional 50g of weight and add it to the hanger. The standing wave should disappear since the tension of the string is now greater. You will have to play with the frequency and amplitude again to find the fundamental again.
Make sure that the amplitude is not to high, especially when you are at the smaller frequencies. I may however be necessary to make the amplitude larger as the frequency gets larger so that the waves can still be seen. Also when the tension is increased it is also necessary to increase the amplitude to see waves again.
The following is the basic formula for finding the frequency at which the different standing waves will occur under certain conditions.
fn = Frequency, n = number of antinodes, L = length of string, M = Mass on string, g = acceleration due to gravity, = mass per unit length of string
Using the above formula and a mass of 150 grams and a string with a mass per unit length of .47g/m. I also used a length of 2 meters for the calculations. I found that the frequency for this scenario was 14.01 hertz for the fundamental standing wave. Each standing wave after that is just the number of antinodes multiplied by that number. When the weight is increased 200 grams and everything else is the same the fundamental frequency becomes 16.15 hertz. If you use the same measurements your results should be close to those but either way the ratio from the 150g trial to the 200g trial should be about 280/323.