# A Level Physics Required Practical: Investigating Stationary Waves On A String

In this article, we thoroughly explain the A Level Physics required practical Stationary Waves On A String.

We use google sheets to plot our graph and tables with our results, here is the link too view it

- Supporting Resources
- Apparatus Setup
- Overview of the experimental procedure and the goals of the investigation
- Data Analysis and Interpretation of Results

## Supporting Resources

You'll notice we made our own equipment, if you are interested in building your own then check out our other articles in this series.

## Apparatus Setup

A string is attached to a fixed point at one end. The other end has a mass attached and is hung over a pulley attached to the bench.

The mass supplies the tension in the string. You will need a top pan balance to measure the mass.

The length of the string can be adjusted by a movable bridge and can be measured using a metre ruler.

The string is vibrated by a vibration generator. You can adjust this with a signal generator and measure the frequency with an oscilloscope.

Our DIY setup didn't need the oscilloscope as we could generate an accurate frequency for our solenoid.

## Overview of the experimental procedure and the goals of the investigation

Measure the mass on the end of the string and record it.

Obtain a set of measurements of the fundamental frequency at various lengths. Recording those lengths and frequencies.

You can do this on paper however, we have provided a google spreadsheet template you can reuse with the various formulae and graphs needed.

Keep the tension fixed (same mass) but perform the experiment with different lengths of string by adjusting the movable bridge.

### Stationary Waves, Harmonics, Nodes and Antinodes

Stationary/Standing waves are formed when two waves traveling in opposite directions interfere with each other, creating points of no movement (nodes) and points of maximum movement (antinodes).

The distance between nodes is always 1/2 the wavelength.

### Finding The Fundamental Frequency

The fundamental frequency is also the 1st harmonic. You are looking for a node at each end and a central antinode. Start at a low frequency and adjust it higher until you get maximum movement in the center of the string.

### Using Harmonics

While not in the official Teacher and Technician Sheet we also found the 2nd and 3rd harmonics.

You can calculate the 1st harmonic/ fundamental frequency from the 2nd or 3rd harmonic by dividing by 2 or 3 respectively.

This is handy as the 2nd and 3rd harmonic are easier to identify by the nodes (points of the string with no movement).

The 2nd harmonic has 3 nodes and 2 antinodes.

The 3rd harmonic has 4 nodes and 3 antinodes.

### Rinse and Repeat

Obtain a second set of results by repeating the experiment to find a mean frequency.

We found the exact same set of frequencies so the mean was a little redundant in our case. We included it in the spreadsheet though for completeness.

## Data Analysis and Interpretation of Results

### Fill Out The Data

You should have your mass and a set of frequency (measured twice) and length pairs.

You can calculate Tension by multiplying the mass by 9.8 the spreadsheet will do this for you.

Scales/ top pan balance can be used to measure the mass of 1 metre of string to get its mass per unit length.

We wanted to leave this until later as a surprise to see how close our experiment predicted this from just the tension, frequencies, and lengths.

It is needed to verify wave speed via a second method, we'll leave it to you to decide what order you want to choose.

### Graphs

In the Student Sheet they tell you to plot a graph of mean 1/frequency against length. You can calculate this on paper and plot on graph paper or use our spreadsheet.

Arguably an easier graph to work with is plotting mean frequency against 1/length. We'll leave it to you to decide but we have done both methods and both are included in the spreadsheet.

Draw a line of best fit on your graph, if using the spreadsheet this is done for you.

Otherwise, draw a line that fits the trend of the scatter plot. Ignore any outliers, try to get as many points above the line as below and pass through the origin.

### Measure Gradients

Gradients are calculated for you if using our spreadsheet.

To do this by hand pick 2 points on the line of best fit and divide the change in y by the change in x.

Selecting 2 points far apart is preferable to 2 points closer together to reduce error.

- Shared Google Spreadsheet with our results, calculations and graph you can reuse
- Recap of key points and a call to action to perform the experiment and analyze the results

### Formula Used and Results

The main formula we are using is

$$f_1=\frac{1}{2l}\sqrt{\frac{T}{\mu}}$$

Where:

- $f_1$ is the fundamental frequency or 1st harmonic
- $T$ is the tension in the string
- $l$ is the length of the string
- $\mu$ is the mass per unit length of the string