The document shows work to solve for the frequency (f) and speed (c) given the equations C=f(2x12x10-3) and (f+2)(2x10x10-3)=f(2x12x10-3). It is determined that f=10Hz and c=0.24m/s. Logs and properties of logs are also listed.

2. PA04 June 07 Q.3(c) C=f(2 x 12 x 10 -3 ) C=(f+2)(2 x 10 x 10 -3 ) (f+2)(2 x 10 x 10 -3 )=f(2 x 12 x 10 -3 ) 20(f+2)=24f 20f+40=24f 4f=40 f=10Hz F=10 c=10(2x12x10 -3 ) c=0.24ms -1

3. Logs...yippee (synoptic June 06 Q.5B) Laws Log|ab|=log|a|+log|b| Log|a n |=nlog|a| Log|a/b|=log|a|-log|b| Log|1/a|=-log|a| Log1=0 Ln(e)=1 I=kv n Ln|I|=ln|kv n | Ln|I|=ln|k|+ln|v n | Ln|I|=ln|k|+nln|v| ln|v| Ln|I| Y=mx+c ln|k| dy/dx=n