Three waves of equal frequency having amplitudes 10 mm , 4 mm , and 7 mm arrive at a given point with a successive phase difference of (π /2) , the amplitude of the resulting wave in mm is given by

Question

Three waves of equal frequency having amplitudes 10 mm , 4 mm , and 7 mm arrive at a given point with a successive phase difference of (π /2) , the amplitude of the resulting wave in mm is given by (A) 7 (B) 6 (C) 5 (D) 4

Tardigrade Admin · Accepted Answer

As phase difference between waves of amplitudes

10 mm

and

7 mm

is

π

, therefore, their resultant amplitude

= 10 - 7 = 3 mm

.
Now amplitudes

3 mm

and

4 mm

have a phase difference

= \frac{π}{2}

.

∴

Resultant amplitude

= 3^{2} + 4^{2} = 5 mm

Q. Three waves of equal frequency having amplitudes $10 mm$ , $4 mm$ , and $7 mm$ arrive at a given point with a successive phase difference of $\frac{π}{2}$ , the amplitude of the resulting wave in mm is given by

$7$

$6$

$5$

$4$

As phase difference between waves of amplitudes $10 mm$ and $7 mm$ is $π$ , therefore, their resultant amplitude $= 10 - 7 = 3 mm$ .
Now amplitudes $3 mm$ and $4 mm$ have a phase difference $= \frac{π}{2}$ .
$∴$ Resultant amplitude $= 3^{2} + 4^{2} = 5 mm$

Q. Three waves of equal frequency having amplitudes 10mm , 4mm , and 7mm arrive at a given point with a successive phase difference of 2π​ , the amplitude of the resulting wave in mm is given by

7

6

5

4

As phase difference between waves of amplitudes 10mm and 7mm is π , therefore, their resultant amplitude =10−7=3mm . Now amplitudes 3mm and 4mm have a phase difference =2π​ . ∴ Resultant amplitude =32+42​=5mm

Q. Three waves of equal frequency having amplitudes $10 mm$ , $4 mm$ , and $7 mm$ arrive at a given point with a successive phase difference of $\frac{π}{2}$ , the amplitude of the resulting wave in mm is given by

$7$

$6$

$5$

$4$

As phase difference between waves of amplitudes $10 mm$ and $7 mm$ is $π$ , therefore, their resultant amplitude $= 10 - 7 = 3 mm$ .
Now amplitudes $3 mm$ and $4 mm$ have a phase difference $= \frac{π}{2}$ .
$∴$ Resultant amplitude $= 3^{2} + 4^{2} = 5 mm$