Paper 2 · Moments and Equilibrium
The fundamental frequency f of an open pipe of length L, with the speed of sound v, is given as f = v/(2L). Checking this using base units, which statement is correct?
ABoth sides reduce to s^-1, so the equation is dimensionally consistent.
BThe left side reduces to s^-1 but the right side reduces to m s^-1, so the equation is not dimensionally consistent.
CBoth sides reduce to metres, so the equation is dimensionally consistent but physically meaningless.
DThe right-hand side is dimensionless, so the equation cannot represent a frequency.
Explanation: [v]=m s^-1 and [L]=m, so [v/(2L)] = (m s^-1)/m = s^-1, which matches the units of frequency, [f]=s^-1 (Hz). The equation is dimensionally consistent.
Derived from ZIMSEC Physics Paper 2, November 2002, Q1