Question

Microwaves from a transmitter are directed normally towards a plane reflector. A detector moves normal to the reflector and travels a distance of $0.14m$ to observe $15$ successive maxima. The frequency of the transmitter is $(c=3\times {10}^{8}m/s)$

• A. $3\times {10}^{10}Hz$
• B. $2\times {10}^{10}Hz$
• C. $1.5\times {10}^{10}Hz$
• D. $3.5\times {10}^{10}Hz$

Answer 1

The correct option is C $1.5\times {10}^{10}Hz$

The detector receives direct as well as reflected waves.So interference occurs at the detector
Distance moved between two consecutive positions of maxima $=\frac{\lambda }{2}$
Distance between $15$ consecutive positions of maxima$=0.14m$
$\Rightarrow 7\left(\frac{\lambda }{2}\right)=0.14$
$\lambda =0.02m$
This gives us, $f=\frac{c}{\lambda }f=\frac{3\times {10}^8}{0.02}=1.5\times {10}^{10}Hz$