When dogs bark, they are communicating. They might be communicating with their owners, with a stranger, or with another dog. Sophia Yin's experiment showed that dogs have different barks for different situations. In each situation, the dog is trying to communicate something different.
In general, higher-pitch sounds are more friendly sounding to humans than lower-pitch, or deeper, sounds. That's why people often ta to babies in high-pitch "baby talk" voices. Harsher sounds are simply not as nice as sweet sounds.
Look again at your answers to the first two questions above. Why might the "doorbell bark" be harsher and deeper than the "play bark"?