Understanding the Speed of Sound Waves

The speed at which sound waves travel depends on the medium through which they are passing and the physical conditions of that medium, such as temperature and pressure. The question asks us to identify the statement that is not correct regarding the speed of sound waves.

Analyzing Statements About Speed of Sound Waves

Let's examine each statement provided in the options:

Statement 1: The speed of sound waves in steel is higher than that in water.

• Sound generally travels fastest in solids, slower in liquids, and slowest in gases.
• This is because the particles in solids are much closer together and more rigidly connected than in liquids or gases, allowing vibrations (sound) to be transmitted more efficiently.
• Steel is a solid, and water is a liquid.
• Therefore, the speed of sound in steel is expected to be significantly higher than in water.
• This statement is correct.

Statement 2: The speed of sound waves in air decreases with increase in temperature.

• Air is a gas. The speed of sound in a gas is related to its temperature.
• Specifically, the speed of sound in an ideal gas is given by the formula:
• \[ v = \sqrt{\frac{\gamma R T}{M}} \]
• Where:
• \( v \) is the speed of sound
• \( \gamma \) is the adiabatic index (a constant for a given gas)
• \( R \) is the universal gas constant
• \( T \) is the absolute temperature (in Kelvin)
• \( M \) is the molar mass of the gas
• From this formula, it is clear that the speed of sound \( v \) is proportional to the square root of the absolute temperature \( T \).
• \[ v \propto \sqrt{T} \]
• This means that as temperature increases, the speed of sound in air increases.
• This statement claims the opposite – that the speed decreases with increasing temperature.
• Therefore, this statement is not correct.

Statement 3: The speed of sound waves in air increases with increase in temperature.

• As explained when analyzing statement 2, the speed of sound in air is directly proportional to the square root of the absolute temperature.
• Thus, an increase in temperature leads to an increase in the speed of sound.
• This statement is correct.

Statement 4: The speed of sound waves in water is higher than that in air.

• As mentioned earlier, sound travels faster in liquids than in gases.
• Water is a liquid, and air is a gas.
• The particles in water are closer together than in air, allowing sound vibrations to travel faster.
• Typical speed of sound in water is about 1500 m/s, while in air at room temperature it is about 343 m/s.
• Therefore, the speed of sound in water is indeed higher than in air.
• This statement is correct.

Identifying the Incorrect Statement on Speed of Sound

We have analyzed all four statements regarding the speed of sound waves. The statement that is not correct is the one claiming that the speed of sound waves in air decreases with an increase in temperature. In reality, the speed of sound in air increases with increasing temperature.

Revision Table: Speed of Sound Comparison

Additional Information about Speed of Sound

• The speed of sound is also affected by the density and elasticity of the medium. Sound travels faster in denser but more elastic media.
• For solids and liquids, the speed of sound is given by \( v = \sqrt{\frac{B}{\rho}} \), where \( B \) is the bulk modulus (a measure of resistance to compression) and \( \rho \) is the density. Solids generally have much higher bulk moduli than liquids or gases, which is why sound travels faster in them despite sometimes being denser than liquids.
• For gases, humidity in the air slightly increases the speed of sound because moist air is less dense than dry air at the same temperature and pressure, and the bulk modulus changes less significantly.
• The speed of sound is nearly independent of pressure in ideal gases because if pressure changes while keeping temperature constant, the density changes proportionally, cancelling out the effect on speed.