To determine which transition will result in a shortening of the wavelength of the sound wave, we need to consider the relationship between speed, frequency, and wavelength. The formula for this relationship is:
\[ \text{Speed} = \text{Frequency} \times \text{Wavelength} \]
When sound transitions from a medium with a lower speed to a medium with a higher speed, the wavelength increases. Conversely, when sound moves from a medium with a higher speed to a medium with a lower speed, the wavelength decreases.
Let's analyze the transitions based on the speeds given in the table:
-
Air to Steel:
- Speed of sound in air = 343 m/s
- Speed of sound in steel = 5,940 m/s
- Wavelength increases (sound travels faster).
-
Air to Glass:
- Speed of sound in air = 343 m/s
- Speed of sound in glass = 5,640 m/s
- Wavelength increases (sound travels faster).
-
Steel to Water:
- Speed of sound in steel = 5,940 m/s
- Speed of sound in water = 1,433 m/s
- Wavelength decreases (sound travels slower).
-
Water to Glass:
- Speed of sound in water = 1,433 m/s
- Speed of sound in glass = 5,640 m/s
- Wavelength increases (sound travels faster).
Based on this analysis, the transition that would result in a shortening of the wavelength is:
Steel to Water.