PhysicsLAB: Frequency of Vibrating Strings

Wave speed is dependent upon the medium through which the wave is traveling. By changing a medium you can change the wave speed. Usually any change in velocity will be balanced by an equivalent change in the wavelength - this phenomena is called refraction.

Our "string medium" can be altered by changing the tension under which it is placed. Since our apparatus regulates each string's fundamental wavelength, the greater the tension, the faster the wave travels, and therefore the higher the frequency of that string.

The new speed of the wave depends on not only the tension but the mass per unit length of the string; a quantity referred to as its linear mass density. The mathematical relationship of wave speed, tension, and linear mass density is:

In this lab you will be tuning five strings (of different linear density) to the same pitch(frequency). Since the strings have the same fundamental wavelength, this means that waves traveling along each string must have the same wave speed. By measuring the tension and linear density of each string we will be able to determine the velocity of the waves along each string. Then by measuring fundamental wavelength we can determine the frequency at which the string is vibrating.

Before you begin, open the spreadsheet entitled 1-WaveTensionLab.xls in your period folder and resave it as LastnameLastname-WavetensionLab.xls so that you can immediately begin recording and saving your data.

What is the name of your file?

What is the number of your apparatus?

Refer to the following information for the next question.

Recording values to determine the mass/length of each string

Our first step is to determine the mass per unit length of each vibrating string. To do this, you will mass and measure the length of five equivalent "sample strings." Record your results here and in your EXCEL spreadsheet.

On the data tab, what is the slope of the line of best fit for your graph of Mass/Length vs Pound Rating?

Refer to the following information for the next two questions.

Procedure to obtain values of common frequencies

An apparatus should be setup at your station that resembles the above diagram.
Hang two 200-gram masses off of the 1st string (the 30-lb test, or the “heaviest string). Each lab group should have several masses with paper clips connected to them to help suspend the masses from the end of each string.
Starting with a 200-gram mass on the 2nd string 20-lb test), continue to add mass (washers) until the two frequencies (notes) are the same.

Hint: To help hear the sound better bite on one end of a wooden stick while the other end is touching the apparatus.

Starting with a 100-gram mass on the 3rd string (15-lb test), continue to add mass (washers) until all three play the same note (have the same frequency).
Starting with a 50-gram mass on the 4th string (8-lb test), continue to add mass (washers) until all five strings have the same frequency.

Once your group feels that all five strings have the "same" frequency, measure the distance between the fixed ends of each string. Then carefully remove the hanging masses from each string and measure their total mass in grams. Record your values in the table below and also in your EXCEL spreadsheet.

Average the lengths of the five vibrating strings and record its value in your EXCEL spreadsheet. Since the length of a loop equals ½l, you can now calculate the wavelength of the waves traveling through each string.

What is the average length (in cm) of your vibrating fishing lines?

What was the average wavelength (in meters) of the waves traveling through the fishing lines on your apparatus?

Refer to the following information for the next seven questions.

Analysis and Conclusions

On the graph tab, what is the slope of your line of best fit for the graph String Tension vs Linear Mass Density?

What is this line's y-axis intercept?

What was the speed of the waves (in m/sec) traveling through the fishing lines on your apparatus?

Based on your slope, what was the common frequency (in hertz) of your five strings?

Based only on the data for the 50-lb test string, what was the desired frequency (in hertz) that you were trying to match in the other four strings?

What is the percent error between the frequency based on the 50-lb test string and the common frequency based on your line's slope?

An octave represents a doubling of the frequency, how much mass would need to be added to increase the frequency of the 50-lb test string by an octave?