Standing Waves — Organ Pipe (Worked Example)

Given

• L = 2.0 m

• v = 343 m/s

• n = 1 (open pipe)

Find

The fundamental f₁.

Principle

An open pipe also fits half wavelengths: f_n = nv/(2L).

Formula

Solution

1. Substitute: $f_1 = 343/(2 \times 2.0)$

2. Denominator: $4.0$

3. Divide: $f_1 = 85.8\ \mathrm{Hz}$

Unit check

(m/s) ÷ m = Hz. Wave speed over length is a frequency — dimensionally correct.

What this means physically

85.8 Hz — a deep bass note near F2. Cathedral organs use 8-metre pipes to reach 21 Hz — you feel those notes more than hear them.