JEE Advanced_2016_S1 ( Physics 2016 Q-8 ) - Competishun – Live JEE & NEET Courses and Exam Prep

JEE Advanced 2016

Paper-1 2016

Multiple correct answers - Select all that apply

Question

Two loudspeakers M and N are located 20 m apart and emit sound at frequencies 118 Hz an 121 Hz , respectively. A car is initially at a point $\mathrm{P}, 1800 \mathrm{~m}$ away from the midpoint Q of the line MN and moves towards Q constantly at $60 \mathrm{~km} / \mathrm{hr}$ along the perpendicular bisector of MN. It crosses $Q$ and eventually reaches a point $R, 1800 \mathrm{~m}$ away from $Q$, Let $v(t)$ represent the beat frequency measured by a person sitting in the car at time $t$. Let $v_p, v_Q$ and $v_B$ be the beat frequencies measured at locations P, Q and R, respectively. The speed of sound in air is $330 \mathrm{~ms}^{-1}$. Which of the following statement(s) is (are) true regarding the sound heard by the person?

Select ALL correct options:

The plot below represents schematically the variation of beat frequency with time

$v_p+v_R=2 v_0$

The rate of change in beat frequency is maximum when the car passes through Q

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

⚠ Partially correct. Some answers are missing.

Solution

$ \begin{array}{lll} f_{1 P}=f_1\left(\frac{v+v_0}{v}\right) \quad \& & f_{2 P}=f_2\left(\frac{v+v_0}{v}\right) \\ \& & f_{1 Q}=f_1\left(\frac{v-v_0}{v}\right) & \& \\ & f_{2 Q}=f_2\left(\frac{v-v_0}{v}\right) \end{array} $
So,
$ \begin{aligned} & v_p=f_{2 P}-f_{1 P} \\ & v_R=f_{2 R}-f_{1 R} \\ & v_P+v_R=\left(f_{2 P}+f_{2 R}\right)-\left(f_{1 P}+f_{1 R}\right) \\ & =f_2(2)-f_1(2) \\ & =2\left(f_2-f_1\right) \\ & =2 v_Q \\ & v_P+v_R=2 v_Q \end{aligned} $

Question Tags

JEE Advance

Physics

Easy

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