Introduction
In this unit, we studies mechanical waves. One of the factors that can possibly determine the speed of a wave is the linear mass density. The linear mass density is the amount of mass per unit length. It usually represented by the Greek letter µ.
In this unit, we studies mechanical waves. One of the factors that can possibly determine the speed of a wave is the linear mass density. The linear mass density is the amount of mass per unit length. It usually represented by the Greek letter µ.
Purpose
The goal of this lab is to determine the linear mass density (µ) of the string that we are given.
The goal of this lab is to determine the linear mass density (µ) of the string that we are given.
Materials
We are provided with the following lab equipments:
a meter-stick, an oscillator, a long string, a (weightless) pulley, 100g weight*2
We are provided with the following lab equipments:
a meter-stick, an oscillator, a long string, a (weightless) pulley, 100g weight*2
Lab Design
We have to come up with a efficient plan so that it can help us successfully find the linear mass density with the lab equipment we are provided with. We first came up with the only equation we learned that involves µ: v = √(Ft/µ). In order to find µ, we will have to know the other two values - wave speed and the tension of the string. Since we cannot just measure the speed of a wave, we came to the equation v=λƒ=wavelength * frequency. Since the wave speed of the same standing wave will be the same, we can set the two equations equal to each other and further derive the equation to acquire linear mass density (µ): √(Ft/µ)=λƒ --> Ft/µ=(λƒ)^2 --> µ=Ft/[(λƒ)^2]. At this point, we are able to find all the values we need using the available lab equipments and determine the linear mass density of the string.
We have to come up with a efficient plan so that it can help us successfully find the linear mass density with the lab equipment we are provided with. We first came up with the only equation we learned that involves µ: v = √(Ft/µ). In order to find µ, we will have to know the other two values - wave speed and the tension of the string. Since we cannot just measure the speed of a wave, we came to the equation v=λƒ=wavelength * frequency. Since the wave speed of the same standing wave will be the same, we can set the two equations equal to each other and further derive the equation to acquire linear mass density (µ): √(Ft/µ)=λƒ --> Ft/µ=(λƒ)^2 --> µ=Ft/[(λƒ)^2]. At this point, we are able to find all the values we need using the available lab equipments and determine the linear mass density of the string.
Procedures
- Attach one side of the string to the oscillator and the other side through the pulley and down to a hanging mass (100g*2)
- Calculate the tension on the string using Ft=mg in this case, record tension force in N
- Set the frequency (ƒ) to a certain value on the oscillator and starts to oscillate the string until it forms a standing wave, record frequency in Hz
- Measure the wavelength (λ) of the standing wave using a meter-stick, record wavelength in m
- Calculate the linear mass density using the equation we derived ( µ=Ft/[(λƒ)^2] )
- Repeat steps 1 to 5 again with different frequencies (ƒ1, ƒ2, ƒ3... )
Data Collection
We collected data using a self-created table:
We collected data using a self-created table:
We decided to set the frequencies to the values where the string can form harmonics because it is just easier to measure the wavelength.
Conclusion
Based on our data collected and the calculations, we are pretty confident to conclude that the linear mass density (µ) of the string we are given is 0.00375kg/m. The fact that the the value of µ is very small makes sense because µ=mass/length. Strings tend to be very light but very long, and the string we were using in our experiment was not an exception.
Based on our data collected and the calculations, we are pretty confident to conclude that the linear mass density (µ) of the string we are given is 0.00375kg/m. The fact that the the value of µ is very small makes sense because µ=mass/length. Strings tend to be very light but very long, and the string we were using in our experiment was not an exception.
Uncertainties...
Since we don't know the actual linear mass density, we cannot determine the percentage difference, so we don't know exactly how accurate our experiment was, but according to our calculations I think it should be pretty accurate. The only uncertainty I think we had was when we kind of decide whether or not the string is vibrating in its harmonics. It is always hard for human eyes to see exactly if the nodes are at the two ends on the string. We might have been off for a little bit, but overall I would say it was a pretty accurate experiment.
Improve the Investigation...
The other way of finding µ using the same equipments is to vary the tension on the string. We could also do several trials where we change the hanging mass to change the tension of the string and calculate µ. We could have done more trials with changes to other variables, which could have made the lab more convincing.
Since we don't know the actual linear mass density, we cannot determine the percentage difference, so we don't know exactly how accurate our experiment was, but according to our calculations I think it should be pretty accurate. The only uncertainty I think we had was when we kind of decide whether or not the string is vibrating in its harmonics. It is always hard for human eyes to see exactly if the nodes are at the two ends on the string. We might have been off for a little bit, but overall I would say it was a pretty accurate experiment.
Improve the Investigation...
The other way of finding µ using the same equipments is to vary the tension on the string. We could also do several trials where we change the hanging mass to change the tension of the string and calculate µ. We could have done more trials with changes to other variables, which could have made the lab more convincing.
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