Required Practical 1 Flashcards
(9 cards)
What is the aim of RP1?
The overall aim of the experiment is to measure how the frequency of the first harmonic is affected by changing one of the following variables:
The length of the string
The tension in the string
Strings with different values of mass per unit length
Variables
Independent variable = either length, tension, or mass per unit length
Dependent variable = frequency of the first harmonic
Control variables
If length is varied = same masses attached (tension), same string (mass per unit length)
If tension is varied = same length of the string, same string (mass per unit length)
If mass per unit length is varied = same masses attached (tension), same length of the string
Equipment resolution
Resolution of measuring equipment:
Metre ruler = 1 mm
Signal generator ~ 10 nHz
Top-pan balance = 0.005 g
Method
This method is an example of the procedure for varying the length of the string with the frequency – this is just one possible relationship that can be tested
Set up the apparatus by attaching one end of the string to the vibration generator and pass the other end over the bench pulley and attach the mass hanger
Adjust the position of the bridge so that the length L is measured from the vibration generator to the bridge using a metre ruler
Turn on the signal generator to set the string oscillating
Increase the frequency of the vibration generator until the first harmonic is observed and read the frequency that this occurs at
Repeat the procedure with different lengths
Repeat the frequency readings at least two more times and take the average of these measurements
Measure the tension in the string using T = mg
Where m is the amount of mass attached to the string and g is the gravitational field strength on Earth (9.81 N kg–1)
Measure the mass per unit length of the string μ = mass of string ÷ length of string
Simply take a known length of the string (1 m is ideal) and measure its mass on a balance
Analysing the Results
Graph
Plot a graph of the mean values of f against 1/L
Draw a line of best fit and calculate the gradient
Work out the wave speed, which will be 2 × gradient
Verify the wave speed of the travelling waves using the equation:
Velocity Equation v= root T / u
Where:
T = tension (N)
μ = mass per unit length (kg m−1)
Assess the uncertainties in the measurements of length and the frequency and carry out calculations to determine the uncertainty in the wave speed
Systematic errors
An oscilloscope can be used to verify the signal generator’s readings
The signal generator should be left for about 20 minutes to stabilise
The measurements would have a greater resolution if the length used is as large as possible, or as many half-wavelengths as possible
This means measurements should span a suitable range, for example, 20 cm intervals over at least 1.0 m
Random errors
The sharpness of resonance leads to the biggest problem in deciding when the first harmonic is achieved
This can be resolved by adjusting the frequency while looking closely at a node. This is a technique to gain the largest response
Looking at the amplitude is likely to be less reliable since the wave will be moving very fast
Safety Considerations
Use a rubber string instead of a metal wire, in case it snaps under tension
If using a metal wire, wear goggles to protect the eyes in case it snaps
Stand well away from the masses in case they fall onto the floor
Place a crash mat or any soft surface under the masses to break their fall
