Introduction
While studying waves and their properties such as speed, we came across the variable µ, which represented linear density, a component in determining a wave's speed.
Purpose
To calculate the linear mass density of the string we received.
Materials
While studying waves and their properties such as speed, we came across the variable µ, which represented linear density, a component in determining a wave's speed.
Purpose
To calculate the linear mass density of the string we received.
Materials
- String
- Meterstick
- Oscillator
- Pulley
- 100g weights
Design
In order to find the linear mass density, we need to know two variables, wave speed and tension in order to plug them into the equation on the right and solve for linear density. Going into the two variables, the first of which being speed, we can calculate this by finding the wavelength and frequency of the wave and multiplying them with each other, like so: v=λƒ. |
Procedures
- Set up your oscillator on one side and a pulley on the other side and add a string in the oscillator and on the pulley with a mass of 100g on the end of the hanging string
- Use the mass and force of gravity to calculate the force of tension exerted on the string
- Set frequency and wait until a standing wave is created. Write down the frequency and measure the wavelength of the standing wave.
- Calculate your linear mass density using the variables you collected and the equation above
- Repeat steps 1-4 for different frequencies and record the data
Data
Mass |
Tension |
Frequency |
Wavelength |
Standing Wave |
0.2 kg |
2 N |
11 Hz |
2.1 m |
1st harmonic |
0.2 kg |
2 N |
22 Hz |
1.05 m |
2nd harmonic |
0.2 kg |
2 N |
33 Hz |
0.7 m |
3rd harmonic |
Calculations