Prince Edward plans a wedding persent to princess Rosella:?

Question

an infinite set of silver bells of identical geometric
proportions. The bell with the lowest pitch is tuned to
pitch A, the next bell is tuned to A-sharp, then B,
C, C-sharp an so on to cover entire chromatic scale
of notes. Poor fella has only 1lb of silver.

How much siver should the jeveler use
for the largest bell in the set?

Answer 1

The successive notes of an equal tempered musical scale differ in frequency by a factor of 2^(1/12). A bell or tuning fork produces a frequency which is inversely proportional to the cube root of its weight. Let A lbs be the weight of the first bell. Then we solve the equation:

1 lbs = (n=0 to ∞) ∑ A/(2^(n/12))³ = 6.28521 A

So that we have A = 0.159104 lbs

Answer 2

An infinite set of geometric proportions? does that mean the largest bell is about the size of the universe? you can never make an infinite amount of anything starting with a limited amount of material, (unless you believe in the Big Bang Theory). Well since most of us do believe in that "theory", I guess you need to "Big Bang" this pound of silver and use whatever amount you might want to use from the resulting endlessly expanding amount of silver coming out of the explosion. We could call it the silver bells universe.