AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Required practical 1: Investigation into the variation of the frequency of…
Full specification wording
Principle of superposition of waves and formation of stationary waves: Required practical 1: Investigation into the variation of the frequency of stationary waves on a string with length, tension and mass per unit length of the string.
In this required practical, a stretched string is driven by a vibration generator connected to a signal generator.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 7 of 7
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
In this required practical, a stretched string is driven by a vibration generator connected to a signal generator. A stationary wave forms when the driving frequency matches a harmonic of the string. For fixed ends, L = nλₙ/2 and v = fₙλₙ, so fₙ = (n/2L)√(T/μ). You investigate how fₙ varies with length L, tension T and mass per unit length μ. Vary one independent variable at a time, keep others constant, and identify the resonant frequency by observing the largest-amplitude stationary wave with clear nodes and antinodes. Plot fₙ against 1/L, against √T and against 1/√μ to obtain straight-line relationships. Assess uncertainty in frequency, length, tension and μ, and evaluate whether the string behaves ideally.
What earns the marks
- Set up a stretched string with a vibration generator near one end and a fixed support or pulley at the other, adjusting tension using hanging masses.
- Keep the harmonic number n constant, usually n = 1, while varying the independent variable so that comparisons are valid.
- For the length investigation, measure the vibrating length L between the fixed end and the vibration generator, and determine the resonant frequency for each L.
- For the tension investigation, calculate T from the hanging mass using T = mg, and measure the resonant frequency for each tension while keeping L and μ constant.
- For the mass per unit length investigation, use strings of different material or thickness, determine μ by weighing a measured length, and measure the resonant frequency while keeping L and T constant.
- Identify resonance by the formation of a stable stationary wave with clearly defined nodes and antinodes and maximum amplitude.
- Process data graphically: fₙ against 1/L, fₙ against √T and fₙ against 1/√μ should each give a straight line through the origin if the theory holds.
- Assess uncertainties in frequency, length, tension and μ, and comment on sources of error such as the mass of the string, friction at the pulley and the finite width of nodes.
Common mistakes and how to put them right
Changing more than one variable at once.
Put it right: Control all but the independent variable so that any trend can be attributed to that variable.
Measuring the total string length rather than the vibrating length between the fixed end and the vibration generator.
Put it right: Measure the length that actually contains the stationary wave.
Using the mass in grams directly to find tension.
Put it right: Convert to kilograms and use T = mg with g in m s⁻².
Assuming the string is massless or that μ is negligible.
Put it right: Measure μ by weighing a known length and to consider its effect on tension and wave speed.
Exam tips
- State clearly which variable is independent, which is dependent and which are controlled in each part of the investigation.
- Record repeated readings of resonant frequency and take a mean to reduce random uncertainty.
- Plot a graph rather than relying on a single pair of values, and use the gradient or straight-line form to test the predicted relationship.
- Describe how you judged resonance, for example by maximum amplitude and the clearest node pattern, so the method is reproducible.
Try the lesson
The start of the Principle of superposition of waves and formation of stationary waves: Required practical 1: Investigation into the variation of the frequency of stationary waves on a string with length, tension and mass per unit length of the string. lesson, made from checked teaching notes for this specification point.
Have a go first
In Required practical 1, a student investigates how the resonant frequency of the first harmonic on a stretched string varies with its length. Which quantity is the dependent variable in this investigation?
Listen
In this required practical, a stretched string is driven by a vibration generator connected to a signal generator. A stationary wave forms when the driving frequency matches a harmonic of the string. For fixed ends, L = nλₙ/2 and v = fₙλₙ, so fₙ = (n/2L)√(T/μ). You investigate how fₙ varies with length L, tension T and mass per unit length μ. Vary one independent variable at a time, keep others constant, and identify the resonant frequency by observing the largest-amplitude stationary wave with clear nodes and antinodes. Plot fₙ against 1/L, against √T and against 1/√μ to obtain straight-line relationships. Assess uncertainty in frequency, length, tension and μ, and evaluate whether the string behaves ideally. A strong answer earns marks for these points. Set up a stretched string with a vibration generator near one end and a fixed support or pulley at the other, adjusting tension using hanging masses. Keep the harmonic number n constant, usually n = 1, while varying the independent variable so that comparisons are valid. For the length investigation, measure the vibrating length L between the fixed end and the vibration generator, and determine the resonant frequency for each L. For the tension investigation, calculate T from the hanging mass using T = mg, and measure the resonant frequency for each tension while keeping L and μ constant. A common slip: Changing more than one variable at once. Instead, control all but the independent variable so that any trend can be attributed to that variable. Exam tip: State clearly which variable is independent, which is dependent and which are controlled in each part of the investigation.
Key words
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Resonant frequency
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Vibrating length
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Mass per unit length
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Graphical analysis
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See every definition
- Resonant frequency
- The driving frequency that matches a harmonic of the string, identified by observing the largest-amplitude stationary wave with clear nodes and antinodes.
- Vibrating length
- The length L between the fixed end and the vibration generator, which actually contains the stationary wave.
- Mass per unit length
- A quantity determined by weighing a measured length of string, used when strings of different material or thickness are investigated.
- Graphical analysis
- Plotting fₙ against 1/L, against √T and against 1/√μ to obtain straight-line relationships through the origin if the theory holds.
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