Download App

PART - 2 CH - 14 Waves — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 14 Waves2 Marks
Question
The wave $y_1=a \sin (\omega t-k x)$ is superimposed by another wave $y_2=a \sin (\omega t+k x)$ then find the ampli-tude of the resultant wave and also explain what are the condition for the amplitude to be maximum and minimum?
✓

Answer

According to the principle of superposition the amplitude of the resultant wave is
$y = y _1+ y _2$
$\therefore \quad y=a \sin (\omega t-k x)+a \sin (\omega t+k x)$
Therefore, $y =2 a \sin \omega t \cos kx$ or $y =(2 a \cos kx ) \sin \omega t$ so, resultant wave amplitude $A=(2 a \cos k x)$
For maximum amplitude
$\begin{aligned} \cos k x= \pm 1 \Rightarrow & k x= m \pi \\ & (\text { where } m =0,1,2, \ldots \ldots \ldots .)\end{aligned}$
$x=\frac{ m \pi}{ k }($ where $m =0,1,2, \ldots \ldots \ldots)$
For minimum amplitude
$\begin{aligned} \cos k x=0 \Rightarrow & k x=(2 m-1) \pi \\ & (\text { where } m =1,2,3, \ldots \ldots \ldots \ldots .)\end{aligned}$
$\begin{aligned} \therefore \quad & x=\frac{(2 m-1) \pi}{ k } \\ & (\text { where } m =1,2,3, \ldots \ldots \ldots \ldots)\end{aligned}$

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 "2 Marks Questions" from PART - 2 CH - 14 Waves→PART - 2 CH - 14 Waves — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

At what rate should the earth rotate so that the apparent g at the equator becomes zero? What will be the length of the day in this situation?
→
A farsighted person cannot see objects placed closer to 50cm. Find the power of the lens needed to see the objects at 20cm.
→
Interatomic and intermolecular forces are similar in certain aspects. Justify.
→
These days people use steel utensils with copper bottom. This is supposed to be good for uniform heating of food. Explain this effect using the fact that copper is the better conductor.
→
If a drop of water falls on a very hot iron, it does not evaporate for a long time. Give reason.
→
Find the dimensions of :
  1. Electric dipole moment $p$.
  2. Magnetic dipole moment $M$.
The defining equations are $p = q.d$ and $M = IA$, where $d$ is distance, $A$ is area, $q$ is charge and $I$ is current.
→
Is a 'single isolated force' possible in nature?
→
Find the work done in increasing the radius of a soap bubble from 4cm to 6cm. The value of surface tension for the soap solution is 30 dyne $cm^{-1}$.
→
It is advised not to stand near a running train. Why?
→
In a standing wave pattern in a vibrating air column, nodes are formed at a distance of 4.0cm. If the speed of sound in air is 328m/s, what is the frequency of 73 the source?
→