Question

Two waves are given as y₁ = 30 sin(20t + 20) and y₂ = 10 sin(40t + 10). The ratio of the angular frequency of y₁ to y₂ is:
1. 2 : 1
2. 1 : 2
3. 3 : 1
4. 1 : 3

Answer 1

Correct Answer - Option 2 : 1 : 2

CONCEPT:

Wave motion:

• The type of disturbance that travels through a medium due to repeated vibrations of the particles of the medium about their mean positions is called wave motion.

Angular frequency:

• It is defined as the angular displacement covered in unit time.

If the wave motion is given as,

⇒ y = a sin(ωt + ϕ)

Then y = displacement at time t, a = amplitude, ω = angular frequency, and ϕ = phase

CALCULATION:

• The equation for the first wave is given as,

⇒ y1 = 30 sin(20t + 10)     ----(1)

• So the angular frequency for this wave is given as,

⇒ ω1 = 20     -----(2)

• The equation for the second wave is given as,

⇒ y2 = 10 sin(40t + 20)     ----(3)

• So the angular frequency for this wave is given as,

⇒ ω2 = 40     ----(2)

By equation 2 and equation 3,

\(\Rightarrow \frac{\omega_1}{\omega_2}=\frac{20}{40}\)

\(\Rightarrow \frac{\omega_1}{\omega_2}=\frac{1}{2}\)

• Hence, option 2 is correct.