A sound wave travels from air into water. How does its frequency, speed, and wavelength change as it crosses the boundary?
Its frequency increases, speed remains the same, and wavelength decreases
Its frequency decreases, speed decreases, and wavelength increases
Its frequency remains constant, speed decreases, and wavelength decreases
Its frequency remains constant, speed increases, and wavelength increases
Its frequency remains constant, speed increases, and wavelength increases
Correct Answer: Its frequency remains constant, speed increases, and wavelength increases
Step 1: Frequency Behavior Across Boundaries
When a wave travels from one medium to another (in this case, from air into water), the frequency of the wave depends solely on the source producing it. Therefore, frequency (f) remains constant when crossing the boundary between two media.
Step 2: Speed of Sound in Different Media
Sound is a mechanical wave that requires a medium to travel. The speed of sound depends on the bulk modulus (rigidity/compressibility) and density of the medium. Water is much less compressible (denser and more rigid) than air, which allows mechanical disturbances to propagate faster.
Hence, the speed of sound (v) increases when moving from air into water.
Step 3: Relationship Between Speed, Frequency, and Wavelength
The speed of a wave is related to its frequency and wavelength by the wave equation:
Since frequency () is constant, speed () is directly proportional to wavelength ():
Since the speed () increases as the sound wave enters water, the wavelength () must also increase to maintain the constant frequency.
Conclusion:
As the sound wave crosses from air into water, its frequency remains constant, its speed increases, and its wavelength increases.
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