The diagram given illustrates the waveform of a note produced by vibrations in an air column of length L. If the speed of sound in air is V, derive an expression for the frequency of the notes
A.
\(\frac{V}{L}\)
B.
\(\frac{5VL}{2}\)
C.
\(\frac{5L}{4V}\)
D.
\(\frac{5V}{4L}\)
Correct answer is D
L = \(\frac{5\lambda}{4}\)
\(\lambda = \frac{4L}{5}\)
But \(\lambda = f\lambda\)
f = \(\frac{v}{\lambda} = \frac{v}{\frac{4L}{5}}\)
= \(\frac{5v}{4L}\)