Two interfering waves have the same wavelength, frequency, and am… - Vidyadip

MCQ

Two interfering waves have the same wavelength, frequency, and amplitude. They are traveling in the same direction but are $90^o$ out of phase. Compared to the individual waves, the resultant wave will have the same.

A
amplitude and velocity but different wavelength
B
amplitude and wavelength but different velocity
✓
wavelength and velocity but different amplitude
D
amplitude and frequency but different velocity

✓

Answer

Correct option: C.

wavelength and velocity but different amplitude

c
let the equation of wave be $A \sin (k x-\omega t)$ and $A \sin \left(k x-\omega t+\frac{\pi}{2}\right)$ which can also be written as $A \cos (k x-\omega t)$

so the resultant is $S=A \sin (k x-\omega t)+A \cos (k x-\omega t)$

by observing both the waves on the graph we can see that the shape of the wave remain the same but with higher amplitude

$S=\sqrt{A^{2} \sin ^{2}(k x-\omega t)+A^{2} \cos ^{2}(k x-\omega t)+2 A^{2} \sin (k x-\omega t) \cos (k x-\omega t)}$

$S=\sqrt{A^{2}+2 A^{2} \sin (k x-\omega t) \cos (k x-\omega t)}$

$\sin 2 A=2 \sin A \cos A$ and $\sin 2 A=1-2 \sin ^{2} A$

$S=A \sqrt{1+\sin (2 k x-2 \omega t)}=A \sqrt{1+1-2 \sin ^{2}(k x-\omega t)}=\sqrt{2} A \cos (k x-\omega t)$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 14. waves and sound→14. waves and sound — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

Two resistors of resistances $R_1 = (300 \pm 3) \,\Omega $ and $R_2 = (500 \pm 4)$ are connected in series. The equivalent resistance of the series combination is

A homogeneous rectangular brick lies on a rough inclined plane of very small inclination. Which half part of brick exters greater contact force on plane

Which of the following statements is wrong

A particle describes a horizontal circle in a conical funnel whose inner surface is smooth with speed of $0.5 \,m/s$. What is the height of the plane of circle from vertex of the funnel ........ $cm$

A cube of edge length $10 \,cm$ is just balanced at the interface of two liquids $A$ and $B$ as shown in figure. If $A$ and $B$ has specific gravity $0.6$ and $0.4$ respectively, then mass of cube is ................ $g$

A wire is loaded by $6\, kg$ at its one end, the increase in length is $12\, mm.$ If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be ......... $mm$

A scooter is going round a circular road of radius $100 \,m$ at a speed of $10 \,m/s$. The angular speed of the scooter will be ......... $rad/s$

Two discs of same moment of inertia rotating about their regular axis passing through centre and perpendicular to the plane of disc with angular velocities $\omega_1$ and $\omega_2$ They are brought into contact face to face coinciding the axis of rotation. The expression for loss of energy during this process is

The bob of a pendulum was released from a horizontal position. The length of the pendulum is $10 \mathrm{~m}$. If it dissipates $10 \%$ of its initial energy against air resistance, the speed with which the bob arrives at the lowest point is : [Use, $\mathrm{g}: 10 \mathrm{~ms}^{-2}$ ]

An athlete completes one round of a circular track of radius $10\, m$ in $40\, sec$. The distance covered by him in $2 \,min$ $20 \,sec$ is ........ $m$