A sound rated at 1 bel is a 10 deciBel sound a sound rated at 2 bel is a 20 deciBel sound and so forth. More commonly, the deciBel level is expressed in the smaller unit decibel (1/10-th of a Bel), abbreviated dB. And a sound which is 1000 (103) times more intense than the TOH is 3 bels. A sound which is 100 (10 2) times more intense than the TOH is 2 bels. A sound which is 10 times more intense than the TOH is 1 bel. This deciBel scale simply expresses the intensity level of any sound in terms of how many factors of 10 greater its intensity is compared to the threshold of hearing (1 x 10 -12 W/m 2). Because their is an enormous range of intensities from the threshold of hearing to the threshold of pain, a logarithmic scale - known as the decibel scale - is often used to express sound intensity. Intensities beyond this level begin to cause pain and possibly the risk of hearing loss. Sound which 100 billion times more intense than the threshold of hearing (1 x 10 -1 W/m 2) is typically detectable without pain. The range of sound intensities which a typical human can detect is enormous. While such a sound will be different for different people, the intensity associated with this sound is defined as 1.0 x 10 -12 W/m 2. The lowest amplitude vibration which most humans can hear is defined as the threshold of hearing (TOH). The human ear is sensitive enough to detect the smallest of vibrations. Because the wave energy is spreading over a surface area, intensity is often expressed in units of Watts/meter 2 and given by the equation

The sound intensity ( I) at any given location is defined as the rate at which energy passes through that location. Because the sphere is constantly expanding, the energy is becoming diluted with increasing distance from the source. Whatever energy is created by the wave at the source fills the surface area of a sphere some distance R away. As these vibrations propagate through space, they become less intense as the size of the spherical wave front expands. Power ( P) is expressed in units of Watts. The rate at which energy is put into the wave is referred to as the power of the source. A sound wave (like any wave) is often referred to as an energy-transport phenomenon. As the sound wave propagates, it creates a wave front that fills the surface area of an ever-expanding sphere. The sound waves begin at a point (or approximately a point) and then propagate through space in three dimensions. Sound waves are produced by a vibrating object - vocal chords, guitar string, or diaphragm on a speaker. This equation provides a rather accurate estimate of the speed of sound for temperatures upwards towards 50☌. For every degree Celsius above 0☌, the speed of sound increases by approximately 0.6 m/s.

Where T is the Celsius temperature of the air through which the sound wave is moving. There are a couple of equations which describe the speed ( v) - temperature ( T) relationship the following might be the easiest to remember: For a sound wave moving through air, the primary property of air which effects its speed is the temperature of the air. The speed of sound, like the speed of any wave, is dependent upon the properties of the medium through which it is moving. Thus, the distance traveled by a wave is related to the time required for it to travel that distance. The speed of any wave ( v) is defined as the distance traveled ( d) per time of travel ( t) and is described by the following equation: The more difficult problems are color-coded as blue problems. Problems range in difficulty from the very easy and straight-forward to the very difficult and complex. This set of 32 problems targets your ability to determine wave quantities such as frequency, period, wavelength, intensity and speed from verbal descriptions and diagrams of physical situations pertaining to sound waves and resonance in strings and air columns. Overview | Problem Set | Audio Guided Solutions

Speed of sound calculator physics