Three customers, P, Q and R, are sitting in a café listening to music from a loudspeaker - AQA - A-Level Physics - Question 2 - 2019 - Paper 5

The sound intensity levels for customers Q and R are given as 65 dB and 42 dB, respectively. To find the sound intensities, we can use the formula: $I = I_0 \times 10^{L/10}$ Where:

• $I_0 = 10^{-12} \text{ W m}^{-2}$ (reference intensity)
• $L$ is the sound level in decibels.

Calculating for customer Q: $I_Q = 10^{-12} \times 10^{65/10} = 10^{-12} \times 10^{6.5} \approx 3.16 \times 10^{-6} \text{ W m}^2$

Calculating for customer R: $I_R = 10^{-12} \times 10^{42/10} = 10^{-12} \times 10^{4.2} \approx 1.58 \times 10^{-8} \text{ W m}^2$

Now, we can find the ratio: $\text{Ratio} = \frac{I_Q}{I_R} = \frac{3.16 \times 10^{-6}}{1.58 \times 10^{-8}} \approx 200.0$

Thus, the ratio of the sound intensity at the position of Q to that at the position of R is approximately 200.

In discussing the comparison of perceived loudness, it is essential to recognize that the human ear perceives sound logarithmically rather than linearly. Hence, using sound intensity levels (in decibels) is more appropriate for comparisons.

Decibels are based on a logarithmic scale which matches the response of human hearing. This allows us to represent large variations in intensity levels on a manageable scale. On the other hand, sound intensity (W/m²) is a linear measurement, which does not capture the logarithmic nature of sound perception effectively.

Therefore, when comparing how P and Q perceive sound in relation to R, it is more effective to use intensity levels, as they correlate better with our hearing sensitivity and provide a clearer representation of perceived loudness differences.

Customers P and Q have hearing impairments that affect their perception of the music being played compared to customer R who has no hearing loss.

Customer P, being 80 years old, likely experiences age-related hearing loss, which may affect her sensitivity to higher frequencies and overall volume perception. As a result, she may find certain aspects of music less audible or distinguishable.

Customer Q, exposed to a noisy environment, may have specific frequency ranges that are less perceivable, distorting his overall sound experience. This may cause him to favor lower frequencies while struggling with higher ones.

In contrast, Customer R, who has no hearing loss, enjoys a full range of frequencies and can perceive the music as intended. Thus, P and Q have altered perceptions, often lacking clarity and volume compared to R.