Help me!

• August 7th 2006, 12:02 PM
babygirl
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.)
• August 7th 2006, 01:13 PM
CaptainBlack
Quote:

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 $\lambda=\frac{c}{f}$ in $\mbox{m}$, where $f$ is the frequency in $\mbox{Hz}$ and $c$ is the speed of sound in $\mbox{m/s}$.

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:

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

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

RonL