Given that ∆f=75KHz and fm=10KHz
According to the Carson’s thumb rule the bandwidth
BW=2(∆f+fm )=2(75+10)=170KHz
The frequency deviation ∆f=kf Am
Then Bandwidth BW=2(kf Am+fm )
Modulation index β=∆f/fm =75/10=7.5
If the modulating frequency is double then the bandwidth
BW=2(∆f+2×fm )=2(75+2×10)=190KHz
Hence the frequency band (BW) is enhanced by (190-170)=20KHz
If the signal amplitude is doubled with normal modulating frequency then
BW=2(2kf Am+fm )
BW=2(2∆f+fm )=2(2×75+10)=320KHz
The bandwidth is enhanced by (320-170)=150KHz