## Sound Waves

15.1 Sound Waves

### Learning Objectives

By the end of this section, you will be able to:

- Explain the difference between sound and hearing
- Describe sound as a wave
- List the equations used to model sound waves
- Describe compression and rarefactions as they relate to sound

### Sound Waves

The physical phenomenon of **sound** is a disturbance of matter that is transmitted from its source outward. **Hearing** is the perception of sound, just as seeing is the perception of visible light. On the atomic scale, sound is a disturbance of atoms that is far more ordered than their thermal motions. In many instances, sound is a periodic wave, and the atoms undergo simple harmonic motion. Thus, sound waves can induce oscillations and resonance effects.

### Models Describing Sound

Sound can be modeled as a pressure wave by considering the change in pressure from average pressure,

This equation is similar to the periodic wave equations seen in Module 14, where ΔP is the change in pressure, ΔP_{max} is the maximum change in pressure, k = 2π/λ is the wave number, ω = 2π/T= 2πf is the angular frequency, and ϕ is the initial phase.

The wave speed can be determined from v = ω/k =λ/T. Sound waves can also be modeled in terms of the displacement of the air molecules. The displacement of the air molecules can be modeled using a cosine function:

In this equation, *s* is the displacement and s_{max} is the maximum displacement.

**Discuss!**

Consider a sound wave modeled with the equation:

What is the maximum displacement, the wavelength, the frequency, and the speed of the sound wave?

A sound wave is modeled as

What is the maximum change in pressure, the wavelength, the frequency, and the speed of the sound wave?

Sound waves can be modeled as a change in pressure. Why is the change in pressure used and not the actual pressure?