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Answer :
Main Answer:
Sound waves can travel in a gas only if their wavelength exceeds the mean free path.
Explanation:
Sound waves propagate through the collision of gas molecules. In a gas, molecules move randomly and collide with each other frequently, resulting in a mean free path, which is the average distance a molecule can travel between collisions.
When a sound wave travels through a gas, it causes molecules to oscillate, transferring the disturbance through successive collisions.
For the wave to propagate effectively, it must have a wavelength larger than the mean free path. If the wavelength is too small compared to the mean free path, the collisions between molecules disrupt the coherent propagation of the wave, causing it to attenuate rapidly. This condition is expressed mathematically by the relationship:
[tex]\[ \lambda > \text{Mean Free Path} \][/tex]
Where \( \lambda \) is the wavelength of the sound wave. Ensuring that the wavelength is larger than the mean free path allows the wave to maintain its integrity as it travels through the gas, enabling effective transmission of sound energy.
Thus, understanding the relationship between the wavelength of sound waves and the mean free path in a gas is crucial in comprehending how sound propagates through gaseous mediums.
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Rewritten by : Jeany
Final answer:
Sound waves can travel through gases if their wavelength is larger than the mean free path, allowing them to remain coherent. The large wavelength of sound compared to light explains their ability to bend through openings like doorways. Sound's speed varies by medium, but its frequency stays the same when changing mediums.
Explanation:
Sound waves can propagate through gases when their wavelength is somewhat larger than the mean free path of the gas particles. This is because such wavelengths allow the wave to remain coherent as it passes through the gas, where the mean free path represents the average distance a molecule travels before colliding with another molecule. Waves with a wavelength much smaller than the mean free path would be scattered by these collisions, disrupting the coherent propagation of the wave.
When a wavelength is significantly larger, such as the wavelength of sound compared to the size of a doorway, the sound waves can diffract, or bend, as they pass through the opening. This is why we can hear sounds coming through a doorway even if the source is not in our direct line of sight. The bending of sound waves around obstacles is attributed to their relatively large wavelength compared to light waves, which tend to travel in straight lines through openings larger than their wavelength.
The speed of sound is also important to consider, as it varies depending on the medium. For instance, sound travels faster in liquids and solids than in gases, because these materials are less compressible and the particles are closer together. However, as sound enters a different medium, while its speed may change, the frequency generally remains the same due to the wave being a driven oscillation with the frequency of the original source.
