OCR MEI
Further Mechanics Minor
Specimen
— Question 3
Exam Board
OCR MEI
Module
Further Mechanics Minor (Further Mechanics Minor)
Session
Specimen
Topic
Dimensional Analysis
3
Find the dimensions of
density and
pressure (force per unit area).
The frequency, \(f\), of the note emitted by an air horn is modelled as \(f = k s ^ { \alpha } p ^ { \beta } d ^ { \gamma }\), where
\(s\) is the length of the horn,
\(\quad p\) is the air pressure,
\(d\) is the air density,
\(k\) is a dimensionless constant.
Determine the values of \(\alpha , \beta\) and \(\gamma\).
A particular air horn emits a note at a frequency of 512 Hz and the air pressure and air density are recorded. At another time it is found that the air pressure has fallen by \(2 \%\) and the air density has risen by \(1 \%\). The length of the horn is unchanged.
Calculate the new frequency predicted by the model.