The equation of displacement of two waves are given as - y1-10 sin 3 - t-3 - y2- 5 sin 3 - t-3cos 3 - t- Then- what will be the ratio of their amplitudes-

Y_1=10sin ( 3 π t+π3 ) nbsp; nbsp;... (i) and y_2= nbsp;5 (sin 3 π t+√(3)cos 3 π t) nbsp; =5 × 2 [ 12×sin 3 π t + √(3)2×cos 3 π t ] y=10 [cos nbsp; ...

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

Byju's Answer

Standard XII

Physics

String Open at One End

The equation ...

Question

The equation of displacement of two waves are given as ; $y_{1} = 10 sin (3 π t + \frac{π}{3}), y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)$ . Then, what will be the ratio of their amplitudes?

1 : 2

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

2 : 1

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

1 : 1

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

None of these

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

Open in App

Solution

The correct option is C $1 : 1$
$y_{1} = 10 sin (3 π t + \frac{π}{3})$ ... (i)
and $y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)$
$= 5 \times 2 [\frac{1}{2} \times sin 3 π t + \frac{\sqrt{3}}{2} \times cos 3 π t]$
$y = 10 [cos \frac{π}{3} sin 3 π t + sin \frac{π}{3} cos 3 π t]$
$= 10 [sin (3 π t + \frac{π}{3})]$ ... (ii)
$(∵ sin (A + B) = sin A cos B + cos A sin B)$
Comparing equation (i) and (ii), we get ratio of amplitude $1 : 1$ .

Suggest Corrections

Similar questions

Q. The equation of displacement of two waves are given as

y_{1} = 10 s i n (3 π t + \frac{π}{3})

y_{2} = 5 (s i n 3 π t + \sqrt{3} c o s 3 π t)

Then, the ratio o f their amplitude will be

Q. The equation of displacement of two waves are given as

y_{1} = 10 s i n (3 π t + π / 3)

y_{2} = 5 (s i n 3 π t + \sqrt{3} c o s 3 π t)

, then what is the ratio of their amplitude;

Q. The equations of displacement of two waves are given as

Y_{1} = 10 sin (π t + π / 3)

Y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t

), then the ratio of their amplitude is

Q. Two simple harmonic motions are represented by the equations

Y_{1} = 10 sin (3 π t + \frac{π}{4})

and

Y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)

Their amplitudes are in the ratio of;

Q. Two simple harmonic motions are represented by the equations

y_{1} = 10 sin (3 π t + π / 4)

and

y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)

. Their amplitudes are in the ratio of _________.

Join BYJU'S Learning Program

The equation of displacement of two waves are given as ; y1=10sin(3πt+π3),y2=5(sin3πt+√3cos3πt). Then, what will be the ratio of their amplitudes?

The correct option is C 1:1y1=10sin(3πt+π3) ... (i) and y2=5(sin3πt+√3cos3πt) =5×2[12×sin3πt+√32×cos3πt] y=10[cosπ3sin3πt+sinπ3cos3πt] =10[sin(3πt+π3)] ... (ii) (∵sin(A+B)=sinAcosB+cosAsinB) Comparing equation (i) and (ii), we get ratio of amplitude 1:1.

The equation of displacement of two waves are given as ; $y_{1} = 10 sin (3 π t + \frac{π}{3}), y_{2} = 5 (sin 3 π t + \sqrt{3} cos 3 π t)$ . Then, what will be the ratio of their amplitudes?