Which one of the following statements about sound waves and human hearing is not correct?

Introduction / Context:
The physics of sound involves not only the behaviour of sound waves in media but also how the human ear and brain perceive those waves. Several important facts are commonly taught at school level: the ear responds roughly logarithmically to intensity, superposition applies to waves, and longitudinal sound waves can travel through various media. This question presents four statements about sound and hearing and asks you to identify which one is not correct. It tests your knowledge of psychoacoustics, wave superposition and propagation in different media.

Given Data / Assumptions:
• Statement A describes a logarithmic response of hearing to sound intensity. • Statement B claims ear sensitivity does not vary with frequency. • Statement C states the principle of superposition for waves. • Statement D concerns longitudinal waves in solids, liquids and gases. • We assume normal human hearing and standard wave theory.

Concept / Approach:
The loudness of a sound as perceived by the ear does not increase linearly with physical intensity; instead, it follows an approximately logarithmic relation. This is reflected in the decibel scale, which is logarithmic in intensity. The ear is also not equally sensitive to all frequencies. It is most sensitive to mid range frequencies, roughly around 2 kHz to 4 kHz, and much less sensitive to very low or very high frequencies. Therefore, a statement claiming that ear sensitivity does not vary with frequency must be incorrect. The principle of superposition is a fundamental rule for waves in linear media: the net displacement is simply the algebraic sum of individual displacements. Finally, longitudinal sound waves can propagate through solids, liquids and gases because in all these media particles can oscillate back and forth along the direction of wave travel, transmitting compressions and rarefactions.

Step-by-Step Solution:
Step 1: Evaluate statement A. It says ear response to increasing intensity is approximately logarithmic. This matches the decibel loudness scale and is correct. Step 2: Evaluate statement B. It claims that ear sensitivity does not vary with frequency, suggesting equal sensitivity at all frequencies. Step 3: Recall that audiograms of human hearing show much better sensitivity in the mid frequency range and reduced sensitivity at very low and very high frequencies. Step 4: Conclude that statement B is false, because sensitivity is highly frequency dependent. Step 5: Evaluate statement C, which restates the principle of superposition for waves in a linear medium; this is a standard and correct result of wave theory. Step 6: Evaluate statement D, noting that sound waves can indeed travel in solids, liquids and gases as longitudinal waves, making this statement correct.

Verification / Alternative check:
You can verify statement B by considering everyday experience and scientific hearing tests. Very low frequency sounds, such as below 20 hertz, are difficult or impossible to hear, and high frequency sounds above about 20 kHz are also inaudible. Even within the audible range, equal loudness contours show that the ear needs higher intensity at low and high frequencies to perceive the same loudness as at mid frequencies. This clearly demonstrates frequency dependent sensitivity. On the other hand, the use of logarithmic decibel scales for measuring sound levels supports statement A. Wave superposition is confirmed in phenomena such as interference and beats, validating statement C. Observations of sound propagation in solids as longitudinal waves, such as in ultrasound imaging of materials, confirm statement D.

Why Other Options Are Wrong:
Option A is correct because the ear compresses a wide range of intensities into a manageable range of perceived loudness, approximately logarithmic in intensity. Option C correctly expresses the superposition principle, which is fundamental to the analysis of wave interference and standing waves. Option D accurately states that longitudinal waves can propagate through solids, liquids and gases, since particles in all these media can oscillate along the direction of travel. These statements are consistent with established physical theory and experiment, so they cannot be the incorrect one asked for in the question.

Common Pitfalls:
Learners sometimes assume that because the ear can detect a wide range of frequencies, it must be equally sensitive to all of them. This is not true; the threshold of hearing and perceived loudness vary significantly with frequency. Another pitfall is misinterpreting the decibel scale as linear, when in fact it is logarithmic and reflects the logarithmic nature of hearing. Confusion about wave propagation in different media can also lead to doubts about statement D, but remember that longitudinal waves only require that particles can be compressed and rarefied along the direction of motion, which is possible in solids, liquids and gases. Keeping these distinctions clear helps correctly identify the false statement.

Final Answer:
The correct choice is The sensitivity of the human ear does not vary with the frequency of the sound., because in reality ear sensitivity depends strongly on frequency, and this statement contradicts both experimental data and everyday experience.