$3($a$)$ The external Lecture hall wall is $3$ meters by $10$ meters in area, facing a car park at a distance of $10m$ from the line of traffic. An octave $-$band analysis at the lecture wall window gave the following.

The construction consist of a $250mm$ cavity wall containing a single glazed window. The sound reduction indices are $55dB$ for the cavity wall and $44dB$ for the window both at $1000Hz.$

$($a$)$ Calculate the Insulation needed for each frequency $[2$ marks$]$

$($b$)$ Calculate for $1000Hz$ the maximum area of window, if the necessary insulation at $1000Hz$ must be $50$ dB $[8$ marks$]$

$\backslash$table$[[$Frequency $(Hz),20-75,75-150,\backslash$table$[[150-$