Speed of sound, factors affecting speed (medium, temperature)

Definition of Speed of Sound

1. The speed of sound refers to the rate at which sound waves propagate through a medium.
2. It depends on the elastic properties and density of the medium.
3. The formula to calculate the speed of sound is v = √(B/ρ), where B is the bulk modulus and ρ is the density.
4. In air, the speed of sound is approximately 343 m/s at room temperature (20°C).

Factors Affecting the Speed of Sound

1. Medium

1. The speed of sound varies across solids, liquids, and gases.
2. Sound travels fastest in solids due to high elasticity and slowest in gases because of low particle density.
3. Examples: Speed in steel is about 5000 m/s, in water about 1482 m/s, and in air about 343 m/s.

2. Temperature

1. The speed of sound in a gas increases with an increase in temperature.
2. The relationship is given by v ∝ √T, where T is the absolute temperature (Kelvin).
3. For air, the speed of sound increases by approximately 0.6 m/s per degree Celsius increase in temperature.

3. Density and Elasticity

1. A higher density of the medium generally reduces the speed of sound, provided elasticity remains constant.
2. However, a higher elastic modulus increases the speed of sound, as particles return to their equilibrium position faster.

4. Humidity

1. The speed of sound in air increases with higher humidity levels.
2. Water vapor reduces the density of air, allowing sound to travel faster.
3. Dry air transmits sound slower than humid air under the same temperature conditions.

Properties and Applications

1. The speed of sound is critical in fields like acoustics, aviation, and meteorology.
2. Understanding sound speed helps in designing sonar systems and calculating distances underwater.
3. Supersonic speeds refer to objects traveling faster than the speed of sound in the surrounding medium.
4. In gases, the speed of sound depends on the type of gas, as given by v = √(γRT/M), where γ is the adiabatic constant, R is the universal gas constant, T is the temperature, and M is the molar mass.

Experimental Observations

1. In solids, both longitudinal and transverse waves exist, but the speed of longitudinal waves is typically higher.
2. In liquids, only longitudinal waves propagate, as liquids lack rigidity to support transverse waves.
3. In gases, sound travels as pressure variations, relying on molecular collisions.
4. For air, the speed of sound is lower at higher altitudes due to lower temperature and density.

Interesting Facts

1. The speed of sound in helium is nearly 965 m/s, much higher than in air, causing the “high-pitched voice” effect.
2. The Mach number quantifies the ratio of an object's speed to the speed of sound in the medium.
3. Sonic booms occur when an object travels faster than the speed of sound, causing a shock wave.
4. The speed of sound was first measured accurately by Isaac Newton, although his initial calculation underestimated the value due to neglecting temperature effects.