Understanding Sound Wave Speed in a Medium

The question describes a "running race" between different types of sound waves: ultrasonics, audible, and infrasonic waves, all traveling within the same medium. We need to determine which one, if any, would win this race.

Let's first understand what distinguishes these three types of sound waves. They are primarily classified based on their frequency ranges:

• Infrasonic waves: These are sound waves with frequencies generally below the range of human hearing, typically considered to be below 20 Hertz (Hz).
• Audible waves: These are the sound waves that humans can hear. Their frequencies typically range from about 20 Hz to 20,000 Hz (20 kHz).
• Ultrasonic waves: These are sound waves with frequencies generally above the range of human hearing, typically considered to be above 20 kHz.

The speed of a wave is related to its frequency ($\text{f}$) and wavelength ($\lambda$) by the formula:

$\text{v} = \text{f} \lambda$

Where $\text{v}$ is the speed of the wave.

However, a crucial property of wave propagation, including sound waves, is that the speed of the wave in a specific medium depends only on the physical properties of that medium, such as its density and elasticity (or bulk modulus for fluids/gases). It does not depend on the frequency or wavelength of the wave itself.

Consider sound traveling through air at a specific temperature and pressure. All sound waves, regardless of whether they are low frequency (infrasonic), medium frequency (audible), or high frequency (ultrasonic), will travel at the same speed in that air.

Since all three types of waves mentioned (ultrasonics, audible, and infrasonic) are sound waves and are propagating in the same medium, their speeds will be identical.

If they all start at the same time and travel the same distance in the same medium, they will arrive at the finish line simultaneously.

Therefore, in a race between ultrasonics, audible, and infrasonic waves in the same medium, none of them would be faster than the others. They would all have the same speed, resulting in a tie.

Key Concept: Speed of Sound

The speed of sound in a medium is determined by:

• The stiffness (or elasticity) of the medium. Sound travels faster in stiffer materials.
• The density of the medium. Sound generally travels slower in denser materials, assuming similar stiffness.

Examples:

• Speed of sound in solids > Speed of sound in liquids > Speed of sound in gases. This is primarily due to the differences in stiffness and intermolecular spacing.

Changes in frequency or wavelength of a sound wave only affect the relationship between frequency and wavelength ($\text{v} = \text{f} \lambda$), but not the speed $\text{v}$ itself in a given medium under constant conditions.

Analysis of Options

• Option 1: Infasonics - Incorrect, because infrasonic waves do not travel faster than other sound waves in the same medium.
• Option 2: Ultrasonics - Incorrect, because ultrasonic waves do not travel faster than other sound waves in the same medium.
• Option 3: Audible - Incorrect, because audible waves do not travel faster or slower than other sound waves in the same medium.
• Option 4: All have same speed and there is no winner or loser. - Correct, as the speed of sound depends on the medium, not the frequency of the wave.

Conclusion

Because ultrasonics, audible, and infrasonic waves are all types of sound waves and travel through the same medium, they all propagate at the same speed. Thus, in a running race, they would finish at the same time, meaning there is no distinct winner or loser based on their speed in that medium.

Revision Table: Sound Wave Properties

Additional Information: Factors Affecting Sound Speed

While the frequency of a sound wave does not affect its speed in a given medium, other factors related to the medium itself can change the speed of sound:

• Temperature: In gases, the speed of sound increases with increasing temperature.
• Humidity: In air, a slight increase in humidity can increase the speed of sound.
• Medium Type: The speed of sound is highest in solids, lower in liquids, and lowest in gases because of differences in their elasticity and density.
• Pressure: For an ideal gas, the speed of sound is independent of pressure at a constant temperature.

Understanding these factors helps explain why sound travels at different speeds in different conditions or materials, but the relative speed of different frequency sound waves in the *same* condition and medium remains constant.