To determine which transition would result in a shortening of the wavelength of the sound wave, we need to consider the relationship between wave speed, frequency, and wavelength. The key relationship is given by the equation:
\[ \text{Wave Speed} = \text{Frequency} \times \text{Wavelength} \]
When a sound wave transitions from one medium to another, the frequency remains constant. Therefore, a change in wave speed will result in a change in wavelength. Specifically:
- If the speed of sound increases, the wavelength increases.
- If the speed of sound decreases, the wavelength decreases.
Based on the data provided:
- Speed of sound in Air = 343 m/s
- Speed of sound in Water = 1,433 m/s
- Speed of sound in Glass = 5,640 m/s
- Speed of sound in Steel = 5,940 m/s
Now, let's analyze the transitions one by one:
-
Water to Glass: \(\text{Water (1,433 m/s)} \rightarrow \text{Glass (5,640 m/s)}\)
- Speed increases, wavelength increases.
-
Air to Glass: \(\text{Air (343 m/s)} \rightarrow \text{Glass (5,640 m/s)}\)
- Speed increases, wavelength increases.
-
Air to Steel: \(\text{Air (343 m/s)} \rightarrow \text{Steel (5,940 m/s)}\)
- Speed increases, wavelength increases.
-
Steel to Water: \(\text{Steel (5,940 m/s)} \rightarrow \text{Water (1,433 m/s)}\)
- Speed decreases, wavelength decreases.
The only transition that results in a shortening of the wavelength is Steel to Water, because the speed of sound is decreasing.
Thus, the correct answer is: steel to water.