Final answer:
The characteristic that both light waves and sound waves share is that they both have wavelengths and frequencies. However, sound waves require a medium to travel, whereas light waves do not and can propagate through a vacuum.
Step-by-step explanation:
The characteristic that is common to both light waves and sound waves is that they both have wavelengths and frequencies. Sound waves are mechanical and require a medium (solid, liquid, or gas) to propagate. They are longitudinal in air, meaning that their direction of propagation is parallel to the wave's oscillations. Light waves, on the other hand, are electromagnetic and do not require a medium to travel; they can propagate through a vacuum. While they can also exhibit waveform characteristics, like frequency and wavelength, they are not longitudinal waves.
Answering the student's question, the correct choice is
(b) Both require a medium for transmission. This statement is incorrect as it applies to sound waves but not to light waves, showing that both types of waves have different requirements for transmission, which is a characteristic they do not share. The other choices are also incorrect:
(a) only sound waves cannot travel through a vacuum;
(c) sound waves are longitudinal in air but light waves are not; and
(d) they propagate at different speeds in various media.