WAEC Physics 2010 Paper

Concept:The frequency of a stationary wave in an air pipe is inversely proportional to the length of the air column when the speed of sound is fixed.Explanation:For a given air pipe, the wavelength $\lambda$ of the stationary wave is directly proportional to the length $L$ of the air column.Thus, $\lambda \propto L$.Let $v$ be the speed of sound in air; it remains constant at a fixed temperature.The relation between frequency $f$, speed $v$, and wavelength $\lambda$ is:$$f = \frac{v}{\lambda}$$Since $v$ is constant and $\lambda \propto L$, we get:$$f \propto \frac{1}{L}$$As the length $L$ decreases, the reciprocal $\frac{1}{L}$ increases.Therefore, the frequency $f$ increases.Answer:B. increases