Physics Chapter 16: Sound and Hearing

What is the main relationship described between pressure amplitude and displacement amplitude in sound waves?

How is the wave number calculated for a sound wave given the frequency and wave speed?

What factor contributes to the increase of pressure amplitude transmitted through the ossicles in the middle ear?

Which of the following best describes the impact of the bulk modulus on sound waves?

What is the maximum displacement amplitude calculated in Example 16.1?

How does the displacement amplitude in the human inner ear compare to that in air?

What is the significance of the area ratio in determining the pressure amplitude exerted on the inner ear's stapes?

What is the value of the speed of sound in the fluid of the inner ear?

Sound Wave Fundamentals

Moderate loudness sinusoidal sound waves exhibit maximum pressure variations of approximately (3.0 \times 10^{-2}) Pa.
Common frequency used for sound analysis is 1000 Hz.
Speed of sound in air is 344 m/s with a bulk modulus of (1.42 \times 10^5) Pa.

Relationships in Sound Waves

The problem highlights the relationship between displacement amplitude (A) and pressure amplitude (P_{max}).
The wave speed (v) and the frequency (f) help derive the wave number (k) using (k = \frac{2\pi f}{v}).
Calculated (k) for 1000 Hz sound wave results in approximately 18.3 rad/m.

Displacement Amplitude Calculation

The maximum displacement amplitude (A) can be calculated using the equation (A = \frac{P_{max}}{Bk}).
Plugging in values provides (A \approx 1.2 \times 10^{-8}) m, approximately one-tenth the size of a human cell.

Sensory Detection of Sound

The human ear detects pressure fluctuations rather than direct displacement, meaning sensitivity to very small changes in pressure.

Sound Wave in Human Ear

Eardrum oscillations transfer sound vibrations through the ossicles, three tiny bones in the middle ear, to the fluid in the inner ear.
The moving part of the eardrum occupies an area of about 43 mm², while the stapes (smallest ossicle) has an area of roughly 3.2 mm².

Fluid Dynamics in Inner Ear

To analyze sound waves in the fluid of the inner ear, the speed of sound is approximately 1500 m/s.
Both pressure amplitude and displacement amplitude principles are applicable in fluid sound wave transmission, similar to those in air.

Explore the concepts of sound waves and hearing through an engaging quiz based on Chapter 16. Test your understanding of amplitude, frequency, and the properties of sound in air. Use the provided data to solve problems involving sound wave characteristics.