Yes, time dilation can indeed affect the frequency of waves, including sound waves. When an observer is in a gravitational field or moving relative to another observer, the perceived frequency of waves, such as sound waves or light waves, can be altered due to the time dilation effect.
Let's consider the example of sound waves. Sound is a mechanical wave that travels through a medium, such as air or water. The frequency of a sound wave corresponds to the pitch of the sound we perceive. When an observer is in a gravitational field or in relative motion, the time dilation effect can cause a change in the frequency of the sound waves they perceive.
In a stronger gravitational field, where time runs slower, the perceived frequency of sound waves will decrease. This means that a higher-pitched sound would be perceived as lower-pitched by an observer in a strong gravitational field compared to an observer in a weaker gravitational field.
Similarly, when an observer is in relative motion, the relative velocity between the observer and the source of the sound can cause a change in the perceived frequency. The observer in motion will experience time dilation, and the perceived frequency of the sound waves will be altered accordingly. This effect is known as the Doppler effect, which is responsible for the change in pitch we hear when a source of sound is moving towards or away from us.
It's important to note that the effect of time dilation on the frequency of sound waves is typically quite small in everyday scenarios. However, in extreme conditions near massive objects or at very high velocities, the time dilation effect can become significant and lead to noticeable changes in frequency.
In summary, time dilation can affect the frequency of waves, including sound waves. In the presence of a gravitational field or relative motion, the perceived frequency of sound waves can be altered, potentially resulting in changes in pitch or "deeper voices" as you mentioned.