2 The speed of propagation, \(c\), of a soundwave travelling in air is given by the formula \(c = k p ^ { \alpha } d ^ { \beta }\),
where

• \(p\) is the air pressure,
• \(d\) is the air density,
• \(k\) is a dimensionless constant.
  1. Use dimensional analysis to determine the values of \(\alpha\) and \(\beta\).

During a series of experiments the speed of propagation of soundwaves travelling in air is initially recorded as \(340 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). At a later time it is found that the air pressure has increased by \(1 \%\) and the air density has fallen by \(0.5 \%\).

Determine, for the later time, the speed of propagation of the soundwaves.