GATE 2024 IN – Question 48

In the ultrasonic measurement system shown, transmitter T sends $x(t)=\cos(2\pi f_1t)$ V toward an object vibrating as $m(t)=0.5\sin(2\pi f_2t)$ V. Neglecting other phase shifts, receiver R detects $y(t)=\cos[2\pi f_1t+\beta\cos(2\pi f_2t)]$ V. Frequency sensitivity is 500 Hz/V, $f_1=40$ kHz, and $f_2=1$ kHz. The modulation index $\beta$ and frequency deviation, respectively, are