AQA · A-Level · Physics
Course version: 7408 · Version from Sept 2016
Examples of these effects in mechanical systems and situations involving…
Full specification wording
Forced vibrations and resonance (A-level only): Examples of these effects in mechanical systems and situations involving stationary waves.
Resonance and damping appear in many mechanical systems and in stationary-wave situations.
Checked against the AQA 7408 specification (opens in a new tab) on .
- Point 3 of 3
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Resonance and damping appear in many mechanical systems and in stationary-wave situations. A child on a swing pushed at the natural frequency builds a large amplitude; friction and air resistance damp it. A car suspension oscillates after a bump, and shock absorbers add damping to reduce the sharpness of resonance and settle the ride. A building or bridge can resonate when driven near a natural frequency, so dampers may be fitted. In stationary waves, resonance occurs when a system supports a standing-wave pattern at particular frequencies. A string fixed at both ends resonates when its length fits a whole number of half-wavelengths, and a tube can resonate at frequencies set by its boundary conditions. Damping broadens the response, so the resonant frequencies are less sharply defined and the stationary-wave amplitude is reduced.
What earns the marks
- A mechanical example must identify the driver, the oscillating system, and the natural frequency that is matched or approached.
- Damping in a mechanical system removes energy from the oscillations, often as thermal energy, so amplitudes decay or steady-state amplitudes are reduced.
- In stationary waves on a string fixed at both ends, resonance occurs at frequencies where the string length equals a whole number of half-wavelengths.
- In tubes, the resonant frequencies depend on whether the ends are open or closed, because the boundary conditions determine the allowed stationary-wave patterns.
- Damping broadens each resonance, so the stationary-wave response is less sharply tuned to a single driving frequency.
- A suitable comparison is a lightly damped and heavily damped system driven through the same frequency range, noting the change in peak height and width.
Common mistakes and how to put them right
Describing a stationary wave as travelling along the string.
Put it right by stating that the wave appears to stand still because incident and reflected waves superpose.
Ignoring boundary conditions in tubes.
Put it right by identifying nodes and antinodes at closed and open ends before choosing the resonant frequencies.
Claiming damping changes the natural frequency dramatically.
Put it right by explaining that damping mainly reduces and broadens the resonance peak.
Using a mechanical example without naming the driver.
Put it right by stating what supplies the periodic driving force, such as a motor or a vibrating support.
Exam tips
- For each example, state the driver, the oscillating object, and why the driving frequency is near a natural frequency.
- When discussing stationary waves, sketch the mode shape and mark nodes and antinodes before doing any calculation.
- Use the same axes for comparing damped and undamped cases so the change in peak height and width is visible.
- Keep explanations of damping tied to energy removal rather than to vague ideas of friction slowing everything down.
Try the lesson
The start of the Forced vibrations and resonance (A-level only): Examples of these effects in mechanical systems and situations involving stationary waves. lesson, made from checked teaching notes for this specification point.
Have a go first
Which of the following describes a situation where resonance produces a stationary wave in a mechanical system?
Listen
Resonance and damping appear in many mechanical systems and in stationary-wave situations. A child on a swing pushed at the natural frequency builds a large amplitude; friction and air resistance damp it. A car suspension oscillates after a bump, and shock absorbers add damping to reduce the sharpness of resonance and settle the ride. A building or bridge can resonate when driven near a natural frequency, so dampers may be fitted. In stationary waves, resonance occurs when a system supports a standing-wave pattern at particular frequencies. A string fixed at both ends resonates when its length fits a whole number of half-wavelengths, and a tube can resonate at frequencies set by its boundary conditions. Damping broadens the response, so the resonant frequencies are less sharply defined and the stationary-wave amplitude is reduced. A strong answer earns marks for these points. A mechanical example must identify the driver, the oscillating system, and the natural frequency that is matched or approached. Damping in a mechanical system removes energy from the oscillations, often as thermal energy, so amplitudes decay or steady-state amplitudes are reduced. In stationary waves on a string fixed at both ends, resonance occurs at frequencies where the string length equals a whole number of half-wavelengths. In tubes, the resonant frequencies depend on whether the ends are open or closed, because the boundary conditions determine the allowed stationary-wave patterns. A common slip: Describing a stationary wave as travelling along the string. Instead, stating that the wave appears to stand still because incident and reflected waves superpose. Exam tip: For each example, state the driver, the oscillating object, and why the driving frequency is near a natural frequency.
Key words
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Resonance in mechanical systems
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Damping and energy dissipation
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Stationary waves and boundary conditions
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Sharpness of resonance in practical contexts
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See every definition
- Resonance in mechanical systems
- A mechanical example must identify the driver, the oscillating system, and the natural frequency that is matched or approached.
- Damping and energy dissipation
- Damping in a mechanical system removes energy from the oscillations, often as thermal energy, so amplitudes decay or steady-state amplitudes are reduced.
- Stationary waves and boundary conditions
- In tubes, the resonant frequencies depend on whether the ends are open or closed, because the boundary conditions determine the allowed stationary-wave patterns.
- Sharpness of resonance in practical contexts
- Damping broadens each resonance, so the stationary-wave response is less sharply tuned to a single driving frequency.
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