# How Loudness of Sound is Related to the Amplitude of the Vibration that Produces the Sound

Sound is a form of energy that is produced by vibrating objects. It travels through a medium, such as air or water, as a wave. The sound wave has some characteristics, such as frequency, wavelength, speed and amplitude, that determine how we perceive the sound.

## Frequency and Pitch

The frequency of a sound wave is the number of oscillations or vibrations per second. It is measured in hertz (Hz). The frequency of a sound wave determines its pitch, which is how high or low the sound is. High-frequency sounds have high pitches, while low-frequency sounds have low pitches. For example, a bird’s chirp has a high frequency and a high pitch, while a lion’s roar has a low frequency and a low pitch.

## Wavelength and Speed

The wavelength of a sound wave is the distance between two consecutive crests or troughs of the wave. It is measured in meters (m). The wavelength of a sound wave is inversely proportional to its frequency. That means, higher the frequency, shorter the wavelength, and vice versa. For example, a sound wave with a frequency of 1000 Hz has a wavelength of 0.34 m in air, while a sound wave with a frequency of 100 Hz has a wavelength of 3.4 m in air.

The speed of a sound wave is the distance travelled by the wave in one second. It is measured in meters per second (m/s). The speed of a sound wave depends on the medium through which it travels. Sound waves travel faster in solids than in liquids, and faster in liquids than in gases. For example, the speed of sound in air is about 340 m/s, while the speed of sound in water is about 1500 m/s.

## Amplitude and Loudness

The amplitude of a sound wave is the maximum displacement or distance moved by the particles of the medium from their mean position when the sound wave passes through them. It is measured in meters (m). The amplitude of a sound wave determines its loudness, which is how loud or soft the sound is. Higher the amplitude, louder the sound, and vice versa. For example, if we strike a drum softly, it produces a soft sound with low amplitude, while if we strike it hard, it produces a loud sound with high amplitude.

The loudness of a sound is also measured by its intensity, which is the amount of energy carried by the sound wave per unit area per unit time. It is measured in watts per square meter (W/m2). The intensity of a sound wave is directly proportional to the square of its amplitude. That means, if we increase the amplitude by three times, the intensity increases by nine times.

The loudness of a sound is expressed in decibels (dB), which is a logarithmic scale that compares the intensity of a sound to a reference intensity. The reference intensity for human hearing is 10-12 W/m2, which is the threshold of hearing. A sound with an intensity of 10-12 W/m2 has 0 dB loudness. A sound with an intensity of 10-6 W/m2 has 60 dB loudness. A sound with an intensity of 10-3 W/m2 has 90 dB loudness.

The human ear can hear sounds with frequencies ranging from 20 Hz to 20 kHz and loudness ranging from 0 dB to 120 dB. Sounds above 120 dB can cause pain and damage to the ear.

## Summary

• Sound is produced by vibrating objects and travels as a wave through a medium.
• The frequency of a sound wave determines its pitch, which is how high or low the sound is.
• The wavelength of a sound wave determines its speed, which depends on the medium through which it travels.
• The amplitude of a sound wave determines its loudness, which is how loud or soft the sound is.
• The loudness of a sound is also measured by its intensity, which depends on the square of its amplitude.
• The loudness of a sound is expressed in decibels, which compare the intensity of a sound to a reference intensity.