Sound Crossing from Air into Water
A student strikes a 440 Hz tuning fork and plays it into a tube. A microphone records the sound in air at 20 °C, where the speed is 343 m/s. The student finds a wavelength of about 0.78 m. The same tuning fork is then used with a hydrophone in a tank of water, where the speed of sound is 1480 m/s. A classmate predicts that the sound will have a shorter wavelength in water because water is denser and 'slows waves down.' Another predicts that the pitch will rise in water because the speed is higher. The teacher asks the group to use the relationship among speed, frequency, and wavelength to evaluate both predictions and to explain what happens to the frequency when sound crosses from air into water.
1. Calculate the wavelength in air and in water for the 440 Hz tone. Show the equation and substitution.
Read the worked answer
Use the wave relationship v = f x wavelength, so wavelength = v / f.
In air: wavelength = 343 m/s / 440 Hz = 0.78 m.
In water: wavelength = 1480 m/s / 440 Hz = 3.36 m.
The wavelength is longer in water, not shorter, because the speed is higher and the frequency stays the same. The calculation matches the measured air wavelength and predicts a much larger water wavelength.
2. Evaluate the two predictions about wavelength and pitch when the sound enters water.
Read the worked answer
The first prediction is wrong. Frequency is set by the source, the tuning fork, and stays 440 Hz when the sound crosses into water. The speed is higher in water, so wavelength = v / f must be larger: 3.36 m instead of 0.78 m. The claim that denser water slows sound is not correct here; water's stiffness has a stronger effect than its density, so sound travels faster in water than in air.
The second prediction is also wrong. Pitch is determined by frequency, and the frequency does not change at the boundary. The sound in water has the same pitch, a higher speed, and a longer wavelength. Loudness may change because of how efficiently sound transfers between media, but that is not a pitch change.
3. A classmate says a louder tap heard through a table means sound travels faster in the table. Evaluate this reasoning.
Read the worked answer
Loudness is related to amplitude and energy, not to speed. A louder tap through a table could mean more sound energy reached the ear, or that the table transmitted the vibration efficiently, but it does not by itself show that sound traveled faster. Speed depends on the medium's elastic properties and density; in general, sound travels faster in a solid than in air, but the loudness observation is not the evidence for that.
To compare speeds, measure the time for sound to travel a known distance through each material, or measure wavelength and frequency and use v = f x wavelength. Loudness alone cannot separate amplitude from speed.