Question
An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10\ GHz$. What is the frequency of the microwave measured by the observer?.......$GHz$ ( speed of light $= 3 \times  10^8 $ $ms^{-1}$)

Answer

Use relativistic doppler's effect as velocity of observer is not small as compared to light

$f=f_{0} \sqrt{\frac{c+v}{c+v}}$ ; $V=$ relative speed of approach

$f_{0}=10\, \mathrm{GHz}$

$\therefore f=10 \sqrt{\frac{c+\frac{c}{2}}{c-\frac{c}{2}}}=10 \sqrt{3}=17.3\, \mathrm{GHz}$

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Similar questions

Electrical resistance of certain materials, known as superconductors, changes abruptly from a nonzero value to zero as their temperature is lowered below a critical temperature $T_c(0)$. An interesting property of superconductors is that their critical temperature becomes smaller than $T_c(0)$ if they are placed in a magnetic field, i.e., the critical temperature $T_c(B)$ is a function of the magnetic field strength $B$. The dependence of $T_c(B)$ on $B$ is shown in the figure. $Image$

$1.$ In the graphs below, the resistance $\mathrm{R}$ of a superconductor is shown as a function of its temperature $\mathrm{T}$ for two different magnetic fields $\mathrm{B}_1$ (solid line) and $\mathrm{B}_2$ (dashed line). If $\mathrm{B}_2$ is larger than $\mathrm{B}_1$ which of the following graphs shows the correct variation of $\mathrm{R}$ with $\mathrm{T}$ in these fields?

MCQ $Image$

$2.$ A superconductor has $T_C(0)=100 \mathrm{~K}$. When a magnetic field of 7.5 Tesla is applied, its $\mathrm{T}_{\mathrm{c}}$ decreases to $75 \mathrm{~K}$. For this material one can definitely say that when

$(A)$ $\mathrm{B}=5$ Tesla, $\mathrm{T}_{\mathrm{c}}(\mathrm{B})=80 \mathrm{~K}$

$(B)$ $\mathrm{B}=5$ Tesla, $75 \mathrm{~K}<\mathrm{T}_{\mathrm{c}}(\mathrm{B})<100 \mathrm{~K}$

$(C)$ $\mathrm{B}=10 \mathrm{Tesla}, 75 \mathrm{~K}<\mathrm{T}_{\mathrm{c}}<100 \mathrm{~K}$

$(D)$ $\mathrm{B}=10$ Tesla, $\mathrm{T}_{\mathrm{c}}=70 \mathrm{~K}$

Give the answer question $1, 2$

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