The equations of motion of two waves propagating in the same direction in a medium is given by y 1- A sin - t - kx and y2-A sin - t-k x-Then amplitude of the particle in this medium isA- -2 A cos-2B- 2 A cos-2C- -2 A cos-D- 2 A cos-

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Resultant Amplitude

The equations...

Question

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

\sqrt{2} A c o s θ

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

2 A c o s θ

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

\sqrt{2} A c o s \frac{θ}{2}

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

2 A c o s \frac{θ}{2}

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

Open in App

Solution

The correct option is D $2 A c o s \frac{θ}{2}$
Resultant amplitude when waves of phase difference $θ$ , interfere is given by
$y_{0} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} (c o s θ)}$
Here $A_{1} = A_{2} = A$

$\Rightarrow y_{0} = A \sqrt{2 (1 + c o s θ)} = 2 A c o s \frac{θ}{2}$

Suggest Corrections

Similar questions

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. Equations of motion in the same direction are given by:

y_{1} = a s i n (ω t - k x)

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. Equations of two progressive waves at a certain point in a medium are given by :

y_{1} = a (sin ω t + θ_{1})

and

y_{2} = a (sin ω t + θ_{2})

.
If amplitude and time period of resultant wave formed by the superposition of these two waves are same as those of either wave, then

(θ_{1} - θ_{2})

is :

Q. Equations of two progressive waves at a certain point in a medium are given by

y_{1} = a sin (ω t + ϕ_{1})

and

y_{2} = a sin (ω t + ϕ_{2})

. If amplitude and time period of resultant wave formed by the superposition of these two waves is same as that of both the waves, then

ϕ_{1} - ϕ_{2}

is?

Join BYJU'S Learning Program

The equations of motion of two waves propagating in the same direction in a medium is given by y1=A sin(ωt−kx) and y2=A sin(ωt−kx−θ). Then amplitude of the particle in this medium is

The correct option is D 2A cosθ2Resultant amplitude when waves of phase difference θ, interfere is given by y0=√A21+A22+2A1A2(cosθ) HereA1=A2=A ⇒y0=A√2(1+cosθ)=2A cos θ2

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 correct option is D $2 A c o s \frac{θ}{2}$
Resultant amplitude when waves of phase difference $θ$ , interfere is given by
$y_{0} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} (c o s θ)}$
Here $A_{1} = A_{2} = A$

$\Rightarrow y_{0} = A \sqrt{2 (1 + c o s θ)} = 2 A c o s \frac{θ}{2}$