The velocity of sound in air is affected by change in the I. Moisture content of air II. Temperature of air III. Composition of air IV. Atmospheric pressure Choose the correct answer.
Factors Affecting Velocity of Sound in Air Explained
The velocity or speed of sound in a medium depends on the properties of that medium. For sound traveling through air, which is a gas, the speed is primarily determined by the gas's temperature, composition, and density. Let's analyze each of the given factors:
I. Moisture Content of Air
Moisture content refers to the amount of water vapor in the air, often expressed as humidity. Moist air is a mixture of dry air and water vapor. At the same temperature and pressure, water vapor is less dense than dry air (because water molecules, H\(_2\)O, have a lower molar mass than the average molar mass of dry air, which is mostly N\(_2\) and O\(_2\)). The speed of sound in a gas is given by the formula:
\( v = \sqrt{\frac{\gamma P}{\rho}} \)
where \( v \) is the speed of sound, \( \gamma \) is the adiabatic index (ratio of specific heats), \( P \) is the pressure, and \( \rho \) is the density of the gas.
Alternatively, for an ideal gas, the speed can also be expressed as:
\( v = \sqrt{\frac{\gamma R T}{M}} \)
where \( R \) is the ideal gas constant, \( T \) is the absolute temperature, and \( M \) is the molar mass of the gas.
When moisture increases, the density \( \rho \) of the air mixture decreases (at constant temperature and pressure), and the average molar mass \( M \) of the air mixture decreases. Since \( v \propto \frac{1}{\sqrt{\rho}} \) and \( v \propto \frac{1}{\sqrt{M}} \) (when considering the second formula while keeping \(\gamma\) and \(T\) constant), a decrease in density or average molar mass leads to an increase in the speed of sound. Therefore, the moisture content of air affects the velocity of sound.
II. Temperature of Air
Temperature has a significant effect on the speed of sound in air. As shown in the formula \( v = \sqrt{\frac{\gamma R T}{M}} \), the speed of sound is directly proportional to the square root of the absolute temperature \( T \). When temperature increases, the particles of the gas move faster, and the sound waves (which propagate through collisions between particles) travel more quickly. So, temperature definitely affects the velocity of sound.
III. Composition of Air
The composition of air refers to the different gases present and their proportions (e.g., Nitrogen, Oxygen, Argon, Carbon Dioxide, etc.). Different gases have different adiabatic indices (\( \gamma \)) and different molar masses (\( M \)). Since the speed of sound depends on \( \gamma \) and \( M \) (as seen in \( v = \sqrt{\frac{\gamma R T}{M}} \)), a change in the composition of air will change the values of \( \gamma \) and \( M \) for the mixture, thus affecting the speed of sound. For example, the speed of sound is different in pure Oxygen compared to pure Nitrogen. Therefore, the composition of air affects the velocity of sound.
IV. Atmospheric Pressure
The formula for the speed of sound in a gas is \( v = \sqrt{\frac{\gamma P}{\rho}} \). For an ideal gas at a constant temperature, the pressure \( P \) is directly proportional to the density \( \rho \) according to the ideal gas law (\( PV = nRT \), so \( P = \frac{n}{V}RT = \frac{m/M}{V}RT = \frac{\rho}{M}RT \), which means \( P/\rho = RT/M \)). Thus, the ratio \( \frac{P}{\rho} \) remains constant at a constant temperature, even if the pressure changes. This implies that, ideally, a change in atmospheric pressure alone (at constant temperature) does not affect the speed of sound. However, changes in pressure in the atmosphere are often accompanied by changes in temperature, and these temperature changes *do* affect the speed of sound. But considering pressure as an isolated variable at constant temperature, it does not directly affect the speed of sound in an ideal gas like air.
Summary of Factors Affecting Sound Velocity
Based on the analysis, the factors that directly affect the velocity of sound in air are:
- I. Moisture content of air
- II. Temperature of air
- III. Composition of air
Atmospheric pressure (at constant temperature) does not directly affect the velocity of sound in air.
Therefore, the correct answer includes I, II, and III.
Revision Table: Factors and Sound Speed
| Factor | Effect on Velocity of Sound in Air | Explanation |
|---|---|---|
| Moisture Content (Humidity) | Increases (at constant T, P) | Humid air is less dense and has lower average molar mass than dry air. \( v \propto 1/\sqrt{\rho} \) and \( v \propto 1/\sqrt{M} \). |
| Temperature | Increases (as T increases) | Speed is proportional to the square root of absolute temperature. \( v \propto \sqrt{T} \). |
| Composition | Changes (depends on specific gas properties) | Different gases have different adiabatic indices and molar masses, affecting \( v = \sqrt{\frac{\gamma R T}{M}} \). |
| Atmospheric Pressure | No direct effect (at constant T) | For an ideal gas, \( P/\rho \) is constant at constant temperature. \( v = \sqrt{\frac{\gamma P}{\rho}} \). |
Additional Information: Speed of Sound
The speed of sound in air at \(0^\circ\text{C}\) is approximately \(331\) meters per second (\(\text{m/s}\)). The speed increases with temperature. For every \(1^\circ\text{C}\) rise in temperature above \(0^\circ\text{C}\), the speed of sound in dry air increases by about \(0.6\) \(\text{m/s}\). A simple linear approximation for the speed of sound \( v \) in dry air in \(\text{m/s}\) as a function of temperature \( \theta \) in degrees Celsius is:
\( v \approx 331 + 0.6\theta \)
This formula highlights the significant effect of temperature on the speed of sound. The effect of humidity and composition is generally less pronounced than that of temperature under typical atmospheric conditions but is still a factor.
Important Questions from The Speed of Sound
The speed of a longitudinal wave in a solid bar is given by v = √(X/ρ), where 'ρ' is density of the medium. What is the unknown term 'X'?
At standard temperature and pressure, in which of the following media does sound propagate with the greatest speed?
Velocity of sound is maximum in:
What is the relation between the frequency f, wavelength λ, and speed v of the sound?
An object is 10.64 km below the sea level. A research team sends down a sonar signal to confirm this depth. After how long can it expect to get the echo? Take speed of sound in sea water = 1520 m/s.
