Question

the diagram shows a tuning fork vibrating over an air column open at both ends. the length of the air column is one half the wavelength of the standing waves set up by the tuning force.

1. if the length of the air column is 0.762 m and the speed of sound in air is 343 m/s, what is the fundamental frequency for the air column shown in the diagram?

113 hz
225 hz
523 hz
450 hz

Explanation:

Step1: Find wavelength from column length

Given $L = \frac{\lambda}{2}$, so $\lambda = 2L$.
$\lambda = 2 \times 0.762\ \text{m} = 1.524\ \text{m}$

Step2: Calculate frequency using wave speed

Use $v = f\lambda$, rearrange to $f = \frac{v}{\lambda}$.
$f = \frac{343\ \text{m/s}}{1.524\ \text{m}} \approx 225\ \text{Hz}$

Answer:

225 Hz