Which of the following vital signs is measured at the tympanic membrane?

The tympanic membrane, also known as the eardrum, is part of the auditory system and is closely associated with the body's core temperature. Measuring temperature at the tympanic membrane provides a quick and accurate reading because the ear is well-supplied with blood vessels, reflecting the core body temperature closely. This method is particularly useful in clinical settings as it allows for non-invasive and rapid assessments.

In contrast, blood pressure is measured through a sphygmomanometer and is typically taken at the arm. Heart rate is assessed by palpating arteries, often at the wrist or neck, and respiratory rate is determined by observing the rise and fall of the chest or counting breaths. These vital signs do not involve the tympanic membrane and are measured through entirely different methods. Thus, temperature is the only vital sign from the provided options that can be accurately measured at the tympanic membrane.