1. ## Help me!

A tuning fork with a frequency of 440 Hz is held above a resonance tube that is partially filled with water. Assuming that the speed of sound in air is 342 m/s, for what three smallest heights of the air column will resonance occur? Where will the nodes and antinodes occur? (Hint: For resonance to occur, the frequency of the tuning fork must match that of the tube.)

2. Originally Posted by babygirl
A tuning fork with a frequency of 440 Hz is held above a resonance tube that is partially filled with water. Assuming that the speed of sound in air is 342 m/s, for what three smallest heights of the air column will resonance occur? Where will the nodes and antinodes occur? (Hint: For resonance to occur, the frequency of the tuning fork must match that of the tube.)
The wavelength $\displaystyle \lambda=\frac{c}{f}$ in $\displaystyle \mbox{m}$, where $\displaystyle f$ is the frequency in $\displaystyle \mbox{Hz}$ and $\displaystyle c$ is the speed of sound in $\displaystyle \mbox{m/s}$.

For a air column closed at one end and open at the other; at resonance you
have a node at the closed end and an anti-node at the open end, so the
length for the lowest resonance is a quarter wavelength, the next resonance
is three quarters of a wavelength, and the third is at one and a quarter wavelengths.

So pluging in the numbers:

$\displaystyle \lambda=342/440\approx 0.777 \mbox{m}$,

so the required lengths are $\displaystyle 0.25\lambda,\ 0.75\lambda,\ 1.25\lambda$.

RonL