Equations of motion in the same direction are given by- y1 - 2a sin - t - kx y2 - 2a sin - t - kx - -The amplitude of the medium particle will be-

The correct option is A 2acosθ/2 [ The resultan ...

You visited us 13 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Wave Equation

Equations of ...

Question

Equations of motion in the same direction are given by:
$y_{1} = 2 a s i n (ω t - k x)$
$y_{2} = 2 a s i n (ω t - k x - θ)$
The amplitude of the medium particle will be:

2 a cos \frac{θ}{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\sqrt{2} a c o s θ

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 a c o s θ / 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\sqrt{2} a c o s θ / 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 a cos \frac{θ}{2}$
$\begin{matrix} T h e r e s u l tan t a m p l i t u d e i s g i v e n b y a_{R} = \sqrt{a^{2} + a^{2} + 2 \cdot a \cdot a cos θ} = \sqrt{2 a^{2} (1 + cos θ)} = 2 a cos \frac{θ}{2} (H cos θ = 2 {cos}^{2} \frac{θ}{2}) \end{matrix}$
Hence,
option $(A)$ is correct answer.

Suggest Corrections

Similar questions

Q. The equations of motion of two waves propagating in the same direction in a medium is given by

y_{1} = A s i n (ω t - k x)

and

y_{2} = A s i n (ω t - k x - θ)

.
Then amplitude of the particle in this medium is

The equations of motion of two waves propagating in the same direction is given by
$y_{1} = A s i n (ω t - k x)$
and $y_{2} = A s i n (ω t - k x - θ)$
The amplitude of the medium particle will be

Q. Three one dimensional mechanical waves in an elastic medium is given as and

y_{1} = 3 A s i n (ω t - k x)

y_{2} = A s i n (ω t - k x + π)

y_{3} = 2 A s i n (ω t + k x)

are superimposed with each other. The maximum displacement amplitude of the medium particle would be

Q. What are represented by the equation

r {sin}^{2} θ = 2 a cos θ .

Q. Statement I- Two longitudinal waves given by equations

y_{1} (x, t) = 2 a sin (ω t - k x)

and

y_{2} (x, t) = a sin (2 ω t - 2 k x)

will have equal intensity.
Statement II- Intensity of waves of given frequency in same medium is proportional to square of amplitude only.

Join BYJU'S Learning Program

Equations of motion in the same direction are given by:y1=2a sin (ωt−kx)y2=2a sin (ωt−kx−θ)The amplitude of the medium particle will be:

The correct option is A 2acosθ2TheresultantamplitudeisgivenbyaR=√a2+a2+2⋅a⋅acosθ=√2a2(1+cosθ)=2acosθ2(Hcosθ=2cos2θ2)Hence,option (A) is correct answer.

Equations of motion in the same direction are given by:
$y_{1} = 2 a s i n (ω t - k x)$
$y_{2} = 2 a s i n (ω t - k x - θ)$
The amplitude of the medium particle will be: