Physics Bootcamp

Just as any mechanical wave, sound wave transports energy and momentum from the source to the detector, not by any transport of matrial, but by coupling of motion that causes the wave to form.

Unlike mechanical wave on a string, sound in air is longitudinally polarized because particles of the air vibrate along the same line as that of wave travel (see Figure 15.1.1). When sound travels through air, particles of air vibrating in the forward direction press against other particles of air creating a higher pressure than when the wave was not there, called . This gives rise to regions of compression and rarefaction of air.

As a matter of fact sound wave in all fluids are longitudinal since fluids cannot provide restoring force to a shear stress generated when a sound wave traveling in the medium. Sound waves in solids can be both longitudinal and transverse. You will study various types of stress in another chapter.

Both light and sound have physically measurable characteristics and human-perceived characteristics. For instance, frequency and intensity of sound can be measured by instruments which provide objective measures of the wave. Perception of frequency is called pitch and perception of intensity is called loudness which can be subjective.

Generally, higher frequency sound is perceived to be at higher pitch than the sound at lower frequency. But, our brain can sometimes interpret louder sound to be at a higher pitch even though it may have the same frequency. Sound of higher intensity is generally perceived as louder. But that also depends on the frequency. We Will discuss the human response in another place.

If we have a sinusoidal sound wave, it will have a single frequency \(f\) and a single wavelength \(\lambda\text{.}\) They will be related to speed \(v\) by the fundamental formula of wave motion by

This simply says that wave travels a distance equal to the wavelength in time \(1/f\text{.}\)

By analyzing the vibration of the particles of the medium, we can show that the speed of mechanical waves, including sound wave, through a medium comes from a competition between two opposite tendencies - a restoring force whose tendency is to bring the particle to equilibrium and an inertia whose tendency is to maintain the motion. In a one-dimensional system such as a string, the restoring force is provided by the tension in the string \((F_T)\) and the inertia is provided by mass per unit length of the string \((\mu )\text{.}\) The speed of mechanical wave in a string was stated in the last chapter to be

The speed of sound in air is similarly related to the properties of air. The restoring force is provided by the bulk modulus \(B\) and the inertia is provided by mass per unit volume \(\rho\text{.}\) The speed of sound in air is therefore given in terms of properties of air by the following.

The density of air is not constant. It depends on the temperature and pressure. We quote here experimental relation of dependence of speed on temperature. At 1 atm and \(0^{\circ}\text{C}\text{,}\) the speed of sound in air is found to be 331 m/s and at another temperature \(t^{\circ}\text{C}\text{,}\) the speed of sound in air at 1 atm is given by the following approximate formula.

Thus at room temperature of \(20^{\circ}\text{C}\text{,}\) the speed of sound in air is approximately \(343\text{ m/s}\text{.}\)

Speed of sound is different in different materials depending upon their bulk moduli and densities and the polarization of the wave. While we have only longitudinally polarized waves in liquids and gases, sound waves in solids can be also transverse. Table 15.1.2 gives the speed of sound in some common materials of interest.