What determines what pitch an object such as a bell or tuning fork produces when struck? I have heard that the box in the "king's chamber" of the great pyramid at Giza is tuned to 438 Hz. I know that in hand-bell choirs, the bigger the bell, the lower the tone, but I have noticed that size does not seem to be the determining factor in a bell's tone.
When an object resonates, it will have a tendency to vibrate in a characteristic way (it's normal modes) to produce sounds at its characteristic frequencies, of which there may be more than one. Theses frequencies are basically a function of the geometry of the object, as well as the mass density and 'stiffness' of the material used. For example, an empty bottle will produce a characteristic pitch when air is blown across the top (similar to a flute). The bottle's length sets up the characteristic wavelength of the pitch produced. Half-filling it with water will produce the same pitch an octave higher (ie: half the wavelength). The pitch produced is also a function of the density and velocity of air. Blowing harder (higher velocity) can produce a different (alternative) mode of oscillation with different pitch.
In the case of a tuning fork, there is usually just one characteristic pitch (normal mode), which is a function of the density of the fork material, its characteristic length, cross-sectional area, as well as its 'stiffness'. A heavier (higher density) metal will oscillate slower and have lower pitch than a tuning fork made of a lighter metal. A longer tuning fork will also produce a deeper pitch (longer wavelength), all else being equal. Using a 'stiffer' material (a material with higher Young's modulus which does not 'stretch' or 'bend' as easily) will tend to produce a higher frequency pitch.