$$\require{cancel}$$

# 17: Sound

Sound is an example of a mechanical wave, specifically, a pressure wave: Sound waves travel through the air and other media as oscillations of molecules. Normal human hearing encompasses an impressive range of frequencies from 20 Hz to 20 kHz. Sounds below 20 Hz are called infrasound, whereas those above 20 kHz are called ultrasound. Some animals, like the bat, can hear sounds in the ultrasonic range. Many of the concepts covered in Waves also have applications in the study of sound. For example, when a sound wave encounters an interface between two media with different wave speeds, reflection and transmission of the wave occur. Ultrasound has many uses in science, engineering, and medicine. Ultrasound is used for nondestructive testing in engineering, such as testing the thickness of coating on metal. In medicine, sound waves are far less destructive than X-rays and can be used to image the fetus in a mother’s womb without danger to the fetus or the mother. Later in this chapter, we discuss the Doppler effect, which can be used to determine the velocity of blood in the arteries or wind speed in weather systems.

• 17.1: Prelude to Sound
Sound is an example of a mechanical wave, specifically, a pressure wave: Sound waves travel through the air and other media as oscillations of molecules. Normal human hearing encompasses an impressive range of frequencies from 20 Hz to 20 kHz. Sounds below 20 Hz are called infrasound, whereas those above 20 kHz are called ultrasound. Some animals, like bats, can hear sounds in the ultrasonic range.
• 17.2: Sound Waves
Sound is a disturbance of matter (a pressure wave) that is transmitted from its source outward. Hearing is the perception of sound. Sound can be modeled in terms of pressure or in terms of displacement of molecules. The human ear is sensitive to frequencies between 20 Hz and 20 kHz.
• 17.3: Speed of Sound
The speed of sound depends on the medium and the state of the medium. In a fluid, because the absence of shear forces, sound waves are longitudinal. A solid can support both longitudinal and transverse sound waves. The speed of sound is the same for all frequencies and wavelengths of sound in air.
• 17.4: Sound Intensity
Intensity is the same for a sound wave as was defined for all waves, where P is the power crossing area A. The SI unit for I is watts per meter squared. Sound intensity level in units of decibels (dB) is equal to the logarithm of the ratio between the intensity heard and the threshold intensity for hearing. The perception of frequency is pitch. The perception of intensity is loudness and loudness has units of phons.
• 17.5: Normal Modes of a Standing Sound Wave
Unwanted sound can be reduced using destructive interference. Sound has the same properties of interference and resonance as defined for all waves. In air columns, the lowest-frequency resonance is called the fundamental, whereas all higher resonant frequencies are called overtones. Collectively, they are called harmonics.
• 17.6: Sources of Musical Sound
Some musical instruments can be modeled as pipes that have symmetrical boundary conditions: open/closed at both ends. Others can be modeled as pipes that have anti-symmetrical boundary conditions: closed at one end and open at the other. String instruments produce sound using a vibrating string with nodes at each end. The air around the string oscillates at the string's frequency. The relationship for the frequencies for the string is similar to the symmetrical boundary conditions of the pipe.
• 17.7: Beats
When two sound waves that differ in frequency interfere, beats are created with a beat frequency that is equal to the absolute value of the difference in the sound wave frequencies.
• 17.8: The Doppler Effect
The Doppler effect is an alteration in the observed frequency of a sound due to motion of either the source or the observer. The actual change in frequency is called the Doppler shift.
• 17.9: Shock Waves
The Mach number is the velocity of a source divided by the speed of sound. When a sound source moves faster than the speed of sound, a shock wave is produced as the sound waves interfere. A sonic boom is the intense sound that occurs as the shock wave moves along the ground. A bow wake is produced when an object moves faster than the speed of a mechanical wave in the medium, such as a boat moving through the water.
• 17.E: Sound (Exercises)
• 17.S: Sound (Summary)

Thumbnail Figure 17.1 - Hearing is an important human sense that can detect frequencies of sound, ranging between 20 Hz and 20 kHz. However, other species have very different ranges of hearing. Bats, for example, emit clicks in ultrasound, using frequencies beyond 20 kHz. They can detect nearby insects by hearing the echo of these ultrasonic clicks. Ultrasound is important in several human applications, including probing the interior structures of human bodies, Earth, and the Sun. Ultrasound is also useful in industry for nondestructive testing. (credit: modification of work by Angell Williams)