There is no single owl that makes a "Tu-whit, Tu-who" call.
Male and female tawny owls have very distinctive calls, that are often heard together. The commonly heard female contact call is a shrill, "tu-whit"; the male makes a quavering "hoo" sound. William Shakespeare used this owl's song in Love's Labour's Lost (Act 5, Scene 2) as "Then nightly sings the staring owl, Tu-whit; Tu-who, a merry note, While greasy Joan doth keel the pot". But apparently Shakespeare did not realise that two "staring owls" are involved. This stereotypical call is actually a duet, with the female making the "tu-whit" sound, and the male responding "hoo". So, indeed, there is no single owl that does Tu-whit, Tu-who -- it takes two to do it! And here you have David Attenborough with the two owls, male and female: BBC