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12 wrz 2022 · The speed of a pulse or wave on a string under tension can be found with the equation \[|v| = \sqrt{\frac{F_{T}}{\mu}} \label{16.8}\] where \(F_T\) is the tension in the string and \(µ\) is the mass per length of the string.
- 17.3: Speed of Sound
Determine the speed of sound in different media. Derive the...
- 17.3: Speed of Sound
12 wrz 2022 · Determine the speed of sound in different media. Derive the equation for the speed of sound in air. Determine the speed of sound in air for a given temperature. Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength.
For this reason, the derivation of the speed of sound in a medium depends on the medium and on the state of the medium. In general, the equation for the speed of a mechanical wave in a medium depends on the square root of the restoring force, or the elastic property, divided by the inertial property,
The speed of a wave on a string depends on the square root of the tension divided by the mass per length, the linear density. In general, the speed of a wave through a medium depends on the elastic property of the medium and the inertial property of the medium.
As an example, for water waves, v w is the speed of a surface wave; for sound, v w is the speed of sound; and for visible light, v w is the speed of light. The amplitude X is completely independent of the speed of propagation v w and depends only on the amount of energy in the wave.
Learning Objectives. By the end of this section, you will be able to: Explain the relationship between wavelength and frequency of sound. Determine the speed of sound in different media. Derive the equation for the speed of sound in air. Determine the speed of sound in air for a given temperature.
vw = f λ, v w = f λ, where vw v w is the speed of sound, f f is its frequency, and λ λ is its wavelength. The wavelength of a sound is the distance between adjacent identical parts of a wave—for example, between adjacent compressions as illustrated in Figure 2.
