Two waves are represented by: x_1=Asinωt+(π)/6 and x_2=Acosωt. Then the phase difference between them is

Correct answer: (C) (π)/2. Given, x_1=Asinωt+(π)/6 and x_2=Acosωt x_1 can be written as x_1=Acos(π)/2-ωt-(π)/6 x_1=Acos(π)/3-ωt The phase difference between them =(π)/2

Q144 / 160 · AP EAMCET 2021 (20 Aug Shift 2) · Physics

Two waves are represented by: $x_{1} = A \sin (ω t + \frac{π}{6})$ and $x_{2} = A \cos ω t$ . Then the phase difference between them is

A
$\frac{π}{6}$
B
$\frac{π}{3}$
Correct answer
C
$\frac{π}{2}$
D
$π$

Solution

Given, $x_{1} = A \sin (ω t + \frac{π}{6})$ and $x_{2} = A \cos (ω t)$

$x_{1}$ can be written as $x_{1} = A \cos (\frac{π}{2} - ω t - \frac{π}{6})$

$x_{1} = A \cos (\frac{π}{3} - ω t)$

The phase difference between them $= \frac{π}{2}$

Hence, the correct answer is option: 'C'.

Relevant Questions

The equation of a transverse wave propagating along a stretched string of length 80 cm is , here ' x ' and ' y ' are in cm and the time ' t 26 May, 2025 (E)Basics of Mechanical Waves
A steel wire of length 81 cm has a mass of . If the wire is under a tension of 50 N, then the speed of transverse waves on the wire is22 May, 2025 (M)Basics of Mechanical Waves
The speed of a stationary wave represented by the equation is (In the given equation and are in metre and is in second)21 May, 2025 (E)Basics of Mechanical Waves
The speed of a wave on a string is when the tension is 120 N . The percentage increase in the tension in order to raise the wave speed by is19 May, 2024 (E)Basics of Mechanical Waves
During the propagation of a longitudinal wave, in the region of compressions and rarefactions19 May, 2023 (M)Basics of Mechanical Waves
The ratio of radii of two wires is and the density of their materials are in the ratio . If same tension is applied to both the wires then t17 May, 2023 (M)Basics of Mechanical Waves

Two waves are represented by: x1=Asinωt+π6 and x2=Acosωt. Then the phase difference between them is

Solution

Relevant Questions

Two waves are represented by: $x_{1} = A \sin (ω t + \frac{π}{6})$ and $x_{2} = A \cos ω t$ . Then the phase difference between them is