If the wavelengths of sound and white light become equal, it would mean that the frequency of sound has increased significantly. However, this scenario is not physically possible because sound and light belong to different regions of the electromagnetic spectrum and have vastly different wavelengths.
Sound waves are mechanical waves that require a medium (such as air, water, or solids) to propagate. They have longer wavelengths, typically ranging from a few centimeters to several meters, depending on the frequency. On the other hand, white light consists of a spectrum of colors with different wavelengths in the range of around 400 to 700 nanometers.
If, hypothetically, the wavelengths of sound and white light were equal, it would imply that sound waves had become extremely high-frequency waves, similar to those of visible light. However, this would pose several problems:
Sensory Perception: Human ears are not designed to detect such high-frequency vibrations as light waves. Our auditory system is adapted to perceive sound waves within the audible frequency range (typically 20 Hz to 20,000 Hz). So, if sound waves reached the same wavelength as light, we would not be able to hear them.
Transmission Medium: Sound waves require a physical medium to travel, such as air or water. Light, on the other hand, can propagate through a vacuum. If sound waves were transformed into light-like waves, they would lose their ability to propagate through the air, resulting in an inability to transmit sound as we know it.
Interference: Light waves and sound waves behave differently when it comes to interference. Light waves can superimpose constructively or destructively to create interference patterns, but sound waves would not produce the same interference effects due to their longer wavelengths. So, if sound waves had the same wavelength as light, the interference patterns we observe in optics would not occur in the same way for sound.
In summary, if the wavelengths of sound and white light were equal, it would lead to significant changes in the properties and behavior of sound waves, making them incompatible with our current understanding of sound and light. Such a scenario is not observed in nature.