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

To calculate the ratio of sound intensities, we use the formula to convert decibels to intensity:

$L = 10 \log_{10}\left(\frac{I}{I_0}\right)$ Where:

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

For customer Q (65 dB):

• The intensity at Q, $I_Q = I_0 \times 10^{65/10}$.
  For customer R (42 dB):
• The intensity at R, $I_R = I_0 \times 10^{42/10}$.
  Now calculating the ratio:

$\text{Ratio} = \frac{I_Q}{I_R} = \frac{I_0 \times 10^{65/10}}{I_0 \times 10^{42/10}} = 10^{(65-42)/10} = 10^{2.3} \approx 199.53$

When discussing perceived loudness, the use of intensity level (measured in dB) is generally more appropriate than intensity. This is because the human perception of sound is logarithmic, meaning that we perceive sound levels in terms of ratios rather than absolute values.

For example, a change of about 10 dB typically corresponds to a perceived doubling of loudness. Therefore, utilizing intensity levels aligns better with the way humans experience sound, allowing for a more accurate comparison of loudness between different sources.

Customer P, due to her age and hearing loss, is likely to experience reduced sensitivity to higher frequencies. This could make music sound muffled or less rich compared to customer R, who does not have hearing loss and can perceive a broader range of frequencies effectively.

Customer Q, having experienced hearing loss due to working in a noisy environment, may encounter difficulties at both low and high frequencies. This loss could lead to a skewed perception of the music, making it sound less balanced.

In contrast, customer R's hearing is intact, allowing for a normal perception of the music, providing a clear sound experience compared to both P and Q.