Sensitivity and frequency response (A-level only) — AQA A-Level Physics

Sensitivity and frequency response are key specifications for any device that converts between electrical signals and sound, such as loudspeakers, microphones, and earphones. Sensitivity tells you how efficiently a device converts electrical power into sound intensity, usually quoted in decibels per watt at a distance of 1 metre. Frequency response describes how the output intensity varies with frequency across the audible range (20 Hz to 20 kHz), often shown as a graph of relative intensity against frequency.

Understanding these concepts is essential for evaluating audio equipment and for explaining why some devices sound 'better' than others. In AQA A-Level Physics, you need to interpret frequency response graphs, perform calculations involving sensitivity and the inverse square law for sound intensity, and explain the effects of resonance and non-uniform response. This topic builds on your knowledge of waves, intensity, and the decibel scale, and it connects to practical applications in music technology and acoustics.

• →Sensitivity is defined as the sound intensity level produced per unit electrical input power, typically measured in dB/W at 1 m. A higher sensitivity means the device produces more sound for the same input power.
• →Frequency response is a graph showing how the sound intensity level (or relative output) varies with frequency. A flat frequency response means all audible frequencies are reproduced equally, which is ideal for high-fidelity audio.
• →Resonances in a device cause peaks in the frequency response at specific frequencies, leading to over-emphasis of those frequencies. Dips occur where the device is less efficient at converting energy.
• →The decibel scale is logarithmic: a change of +10 dB corresponds to a tenfold increase in intensity. When combining changes (e.g., due to power and distance), you add or subtract decibels.
• →Sound intensity follows an inverse square law: I proportional to 1/r^2 for a point source radiating uniformly. This means doubling the distance reduces intensity to one quarter, a change of -6 dB.

• State that a reference tone, usually 1 kHz, is set to a fixed sound intensity level and the listener adjusts a comparison tone until the two are judged equally loud.
• Describe repeating the adjustment at many frequencies to obtain a set of points that form one equal loudness curve.
• Explain that each curve is labelled by the sound intensity level of the 1 kHz reference, measured in phons, so the curve represents one perceived loudness.
• Interpret a curve by comparing the required intensity level at a given frequency with the value at 1 kHz, noting that greater sensitivity means a lower required level.
• Use the curves to explain why low and high frequency tones need higher intensity levels than a 1 kHz tone to be perceived as equally loud at moderate levels.
• Recognise that the curves become flatter at higher levels, so the ear's relative sensitivity to frequency is less pronounced for loud sounds.
• State that the ear detects sound intensities spanning many orders of magnitude, so a linear intensity scale would be unwieldy.
• Define sound intensity level using the logarithmic relationship 10 log₁₀(I / I₀), with I₀ equal to 1 × 10⁻¹² W m⁻².
• Explain that equal ratios of intensity produce equal differences in decibels, so the scale reflects relative changes in intensity.
• Relate the logarithmic scale to perception by noting that a tenfold increase in intensity corresponds to an increase of 10 dB and is heard as a modest change in loudness.
• Use the scale to compare sounds, for example recognising that 60 dB is 10³ times the intensity of 30 dB because the difference is 30 dB.
• States that intensity is power per unit area, with area measured perpendicular to the direction of energy transfer.
• Recalls the equation I = P/A and uses consistent units, typically W m⁻².
• Applies the inverse-square relationship I = P/(4πr²) for a point source radiating uniformly in all directions.
• Explains that intensity decreases with distance because the same power is spread over an increasing spherical surface area.
• Distinguishes intensity from total power: a source may emit constant power while intensity at a detector falls with distance.
• Uses the decibel relationship qualitatively or quantitatively to link intensity ratios to loudness changes.

• 💡When describing production, name the reference frequency and explain the listener's adjustment task rather than describing a purely instrumental measurement.
• 💡When interpreting, quote a frequency and read the corresponding intensity level from the curve, then compare it with the 1 kHz value to support the conclusion.
• 💡Use the flattening of the curves at high levels to explain why loudness perception depends less on frequency for loud sounds.
• 💡Quote the logarithmic equation and the reference intensity when explaining why the decibel scale is used.
• 💡Convert between intensity ratios and dB differences by using powers of ten, for example a 20 dB difference corresponds to an intensity ratio of 10².
• 💡Link the mathematical compression of the scale to the everyday observation that very large intensity changes are heard as moderate loudness changes.
• 💡Write the defining equation before substituting numbers so the power and perpendicular area are clearly identified.
• 💡When a question mentions a point source, check whether the inverse-square law applies before calculating.
• 💡Convert distances to metres and areas to square metres before evaluating intensity to avoid unit errors.
• 💡Link any calculated intensity ratio to the decibel scale if the question asks about loudness or hearing.
• 💡Always state the units when quoting sensitivity (dB/W at 1 m) and frequency (Hz). Marks are often awarded for correct units in definitions and calculations.
• 💡When describing a frequency response graph, comment on specific features: peaks (resonances), dips, and the overall range. Use terms like 'flat response', 'resonant peak', and 'attenuation'.
• 💡In calculations involving distance, remember the inverse square law and that a halving of distance increases intensity by a factor of 4 (+6 dB), while doubling distance reduces it by a factor of 4 (-6 dB). Show your working clearly.

• Treating an equal loudness curve as a graph of loudness against frequency; correct this by identifying the axes as sound intensity level against frequency, with each curve representing constant perceived loudness.
• Assuming that equal sound intensity level always means equal loudness; correct this by using the curves to show that equal loudness generally requires different intensity levels at different frequencies.
• Reading the phon label as a frequency or as a sound intensity level in dB; correct this by stating that the phon value is the sound intensity level of the 1 kHz reference tone for that curve.
• Treating the decibel value as directly proportional to intensity; correct this by using the logarithmic relationship and noting that equal dB differences correspond to equal intensity ratios.
• Using the wrong reference intensity or omitting I₀ when calculating sound intensity level; correct this by stating that I₀ is 1 × 10⁻¹² W m⁻².
• Assuming a 10 dB increase doubles loudness; correct this by explaining that a tenfold intensity increase of 10 dB is perceived as only a moderate loudness change, often described as roughly a doubling of perceived loudness.
• Using the total surface area of a sphere but forgetting the factor 4π, writing I = P/r²; the corrected form is I = P/(4πr²).
• Treating intensity as a vector and giving a direction; intensity is a scalar, although energy flow has a direction.
• Using the full area of a tilted surface rather than its component perpendicular to the beam; the corrected approach uses A cos θ.
• Confusing intensity with amplitude; intensity is proportional to amplitude squared for a given wave.
• Students often think that a high sensitivity means a flat frequency response. Correction: Sensitivity is a single number indicating overall loudness for a given input, while frequency response shows how that loudness varies with frequency. A device can be very sensitive but have a very uneven response.
• Students may assume that a frequency response graph is plotted on a linear frequency axis. Correction: Frequency axes are almost always logarithmic, so equal intervals represent multiplying by 10 (e.g., 10 Hz to 100 Hz is the same visual distance as 100 Hz to 1000 Hz). This affects how you interpret the shape.
• Students sometimes forget that the decibel scale is logarithmic when calculating changes. Correction: You cannot simply add or subtract intensity values; you must convert to decibels using 10 log10(I/I0) or use the fact that multiplying intensity by a factor adds 10 log10(factor) dB.

1. 1Start by revising the definitions of sensitivity and frequency response. Write them out and ensure you can state the units and typical values for common devices.
2. 2Practice interpreting frequency response graphs. Find examples online or in textbooks and describe the features (peaks, dips, range) in writing. Focus on the logarithmic frequency axis.
3. 3Work through calculations involving sensitivity, power, and distance. Use the inverse square law and decibel changes. Check your answers with a peer or teacher.
4. 4Create a set of flashcards for key terms and formulas. Test yourself on the relationships between intensity, power, distance, and decibels.
5. 5Attempt past paper questions on this topic. Mark your answers using the mark scheme and note where you lost marks, especially for explanations and graph interpretation.

• 📋Definition and explanation questions: e.g., 'Define sensitivity and explain what is meant by a flat frequency response.' Advice: Give precise definitions with units, and explain that flat means equal output across frequencies.
• 📋Graph interpretation: e.g., 'The graph shows the frequency response of a microphone. Describe and explain two features of the graph.' Advice: Identify peaks/dips, relate to resonance, and comment on the logarithmic axis.
• 📋Calculation questions: e.g., 'Calculate the sound intensity level at a given distance from a loudspeaker of known sensitivity and input power.' Advice: Use the inverse square law and decibel addition/subtraction; show all steps.
• 📋Practical application: e.g., 'Explain why a loudspeaker with a peak at 100 Hz might be unsuitable for high-fidelity music reproduction.' Advice: Link the peak to over-emphasis of bass frequencies and distortion of the original sound.