Which of the following statements is true? The velocity of sound is:
more in summer than in winter
Understanding the Speed of Sound and Temperature
The speed at which sound travels through a medium, such as air, depends on various factors. One of the most significant factors affecting the speed of sound in a gas is its temperature. Let's explore how temperature influences the velocity of sound and how this relates to different seasons.
Effect of Temperature on Sound Velocity
For an ideal gas like air, the speed of sound (\(v\)) is related to its temperature (\(T\)) by the formula:
\(v = \sqrt{\frac{\gamma R T}{M}}\)
Where:
- \(v\) is the speed of sound
- \(\gamma\) (gamma) is the adiabatic index of the gas
- \(R\) is the ideal gas constant
- \(T\) is the absolute temperature of the gas (in Kelvin)
- \(M\) is the molar mass of the gas
From this formula, we can see that the speed of sound (\(v\)) is directly proportional to the square root of the absolute temperature (\(\sqrt{T}\)). This means that as the temperature of the air increases, the speed of sound also increases.
Temperature Differences Between Seasons
Generally, summer seasons are characterized by higher average temperatures compared to winter seasons. In summer, the air is warmer, while in winter, the air is colder.
Comparing Sound Velocity in Summer and Winter
Based on the relationship between the speed of sound and temperature:
- In summer, the air temperature is higher.
- Since the speed of sound increases with temperature, the velocity of sound will be higher in warmer air.
- Therefore, the velocity of sound is greater in summer than in winter.
Conversely, in winter, the air temperature is lower, resulting in a lower speed of sound compared to summer.
Analysis of Given Options
Let's examine each statement based on our understanding:
- The velocity of sound is: less in summer than in winter
- The velocity of sound is: same in winter and summer
- The velocity of sound is: independent of seasons
- The velocity of sound is: more in summer than in winter
Analyzing each option:
- Option 1 states the velocity is less in summer than in winter. This contradicts the fact that summer is hotter and higher temperature leads to higher speed. So, this is false.
- Option 2 states the velocity is the same in winter and summer. This is false because temperatures differ significantly between seasons, and velocity depends on temperature.
- Option 3 states the velocity is independent of seasons. This is false because seasons imply temperature changes, and the velocity of sound is highly dependent on temperature.
- Option 4 states the velocity is more in summer than in winter. This aligns perfectly with our conclusion that higher summer temperatures lead to a higher speed of sound. So, this is true.
Thus, the statement that is true is that the velocity of sound is more in summer than in winter.
Revision Table: Factors Affecting Speed of Sound
| Factor | Effect on Speed of Sound (in gases) | Explanation |
|---|---|---|
| Temperature | Increases with increasing temperature | Particles move faster at higher temperatures, transferring vibrations more quickly. \(v \propto \sqrt{T}\) |
| Medium | Varies greatly depending on density and elasticity | Sound travels fastest in solids, then liquids, then gases. Depends on how easily the medium compresses/stretches and its mass. |
| Humidity | Slightly increases with increasing humidity | Moist air is slightly less dense than dry air at the same temperature and pressure, while also being elastic. |
| Pressure (at constant temperature) | No significant effect (in ideal gases) | Pressure and density change proportionally, cancelling out the effect on speed. |
Additional Information on Sound Propagation
While temperature is a key factor affecting the speed of sound in air, it's important to remember that sound waves require a medium to travel. Sound cannot travel through a vacuum. The speed of sound is characteristic of the medium it is traveling through.
In solids and liquids, the speed of sound is generally much higher than in gases because the particles are closer together and interact more strongly, allowing vibrations to propagate faster.
For example, the speed of sound in dry air at \(20^\circ C\) (\(293.15 K\)) is approximately \(343 \, m/s\), while the speed of sound in water at the same temperature is about \(1482 \, m/s\), and in steel, it is around \(5960 \, m/s\).
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