The maximum pressure amplitude `Delta p_m` that the human ear can tolerate in loud sounds is about 28 Pa (which is very much less than the normal air pressure of about `10^5` Pa). What is the displacement amplitude `s_m`for such a sound in air of density `rho= 1.21 kg//m^3`, at a frequency of 1000 Hz and a speed of 343 m/s?

Explanation

To find the displacement amplitude \( s_m \) for a sound wave given the maximum pressure amplitude \( \Delta p_m \), we can use the relationship between pressure amplitude, displacement amplitude, density of the medium, frequency, and speed of sound.

### Step-by-Step Solution:

1. **Identify the given values:**
- Maximum pressure amplitude, \( \Delta p_m = 28 \, \text{Pa} \)
- Density of air, \( \rho = 1.21 \, \text{kg/m}^3 \)
- Frequency of the sound, \( f = 1000 \, \text{Hz} \)
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