Final answer:
In 1916 North Carolina, a fiddle would be the most common instrument found in someone's home because it was portable, loud enough for gatherings, and integral to Appalachian folk music.
Step-by-step explanation:
Traveling with Cecil Sharp in 1916 through the backwoods of North Carolina, the instrument you would be most likely to find in someone's home would be a fiddle. At the time, folk music in rural areas often relied on instruments that were portable and loud enough to be heard during gatherings like barn dances. The fiddle, along with other instruments such as the banjo and guitar, were popular due to their portability and volume. Large, expensive instruments like the piano were less common in these settings. The fiddle not only fits into this category but was also a staple in Appalachian music, which Cecil Sharp was interested in documenting.
Considering the cultural context and technological limitations of the era, the fiddle was an ideal choice for musicians. Its versatility allowed for both melodic and rhythmic playing, which made it suitable for various types of dances and social gatherings. Other instruments like the mandolin and dulcimer, although present, were less dominant in such settings due to their quieter sound.