When must a vessel reduce her speed according to Rule 19e?

The correct answer is that a vessel must reduce her speed if she hears a fog signal from another vessel forward of her beam. This requirement is rooted in the need to enhance safety in reduced visibility conditions, typically encountered in fog, mist, rain, or heavy seas. When a vessel hears a fog signal, it is an indication that another vessel may be in close proximity, and reducing speed helps provide more time to assess the situation and take necessary action to avoid a collision.

The rationale for this rule is to prevent accidents in situations where visibility is compromised, thus ensuring that vessels have the ability to change course or stop if necessary. Hearing a fog signal indicates potential danger ahead, prompting the need for caution.

In contrast, the other choices are not aligned with the requirements of Rule 19e. Clear visibility does not necessitate a reduction in speed; nighttime operations alone do not mandate speed reduction unless visibility conditions warrant it. Furthermore, radar malfunctions do not specifically trigger a need to reduce speed under Rule 19e, though they may affect safe navigation in general.