Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Mohini kannan Grade: 12
        wat is the equation of a standing wave?
7 years ago

## Answers : (1)

AKASH GOYAL AskiitiansExpert-IITD
419 Points
										Dear Mohini
Harmonic waves travelling in opposite directions can be represented by the equations below:
$y_1\; =\; y_0\, \sin(kx - \omega t)\,$
and
$y_2\; =\; y_0\, \sin(kx + \omega t)\,$
where:

y0 is the amplitude of the wave,
ω (called angular frequency, measured in radians per second) is 2π times the frequency (in hertz),
k (called the wave number and measured in radians per metre) is 2π divided by the wavelength λ (in metres), and
x and t are variables for longitudinal position and time, respectively.

So the resultant wave y equation will be the sum of y1 and y2:
$y\; =\; y_0\, \sin(kx - \omega t)\; +\; y_0\, \sin(kx + \omega t)\,$.
Using a trigonometric identity (the 'Sum to Product' identity for 'sin(u)+sin(v)') to simplify:
$y\; =\; 2\, y_0\, \cos(\omega t)\; \sin(kx)\,$.
This describes a wave that oscillates in time, but has a spatial dependence that is stationary: sin(kx). At locations x = 0, λ/2, λ, 3λ/2, ... called the nodes the amplitude is always zero, whereas at locations x = λ/4, 3λ/4, 5λ/4, ... called the anti-nodes, the amplitude is maximum. The distance between two conjugative nodes or anti-nodes is λ/2.

All the best.
AKASH GOYAL
AskiitiansExpert-IITD

Please feel free to post as many doubts on our discussion forum as you can. We are all IITians and here to help you in your IIT JEE preparation.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.
Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..


7 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

## Other Related Questions on Wave Motion

View all Questions »
• Complete Physics Course - Class 12
• OFFERED PRICE: Rs. 2,756
• View Details
• Complete Physics Course - Class 11
• OFFERED PRICE: Rs. 2,968
• View Details

## Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details