 Click to Chat

1800-1023-196

+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
`        explain formation of stationary waves in streched string`
2 months ago

```							 Stationary Waves When two progressive waves of same amplitude and wavelength travelling along a straight line in opposite directions superimpose on each other, stationary waves are formed.Analytical methodLet us consider a progressive wave of amplitude a and wavelength λ travelling in the direction of X axis.y1 = a sin 2π [t/T – x/λ]         …... (1)This wave is reflected from a free end and it travels in the negative direction of X axis, theny2 = a sin 2π [t/T + x/λ]         …... (2)According to principle of superposition, the resultant displacement is, y = y1+y2= a [sin 2π (t/T – x/λ) + sin 2π (t/T + x/λ)]= a [2sin (2πt/T) cos  (2πx/λ)]So, y = 2a cos (2πx/λ) sin (2πt/T)         …... (3)This is the equation of a stationary wave.(a) At points where x = 0, λ/2, λ, 3λ/2, the values of cos 2πx/λ = ±1∴ A = + 2a. At these points the resultant amplitude is maximum. They are called antinodes as shown in figure.(b) At points where x = λ/4, 3λ/4, 5λ/4..... the values of cos 2πx/λ = 0.∴ A = 0. The resultant amplitude is zero at these points. They are called nodes. The  distance  between  any  two successive antinodes or nodes is equal to λ/2 and the distance between an antinode and a node is λ/4.(c) When t = 0, T/2, T, 3T/2, 2T,.... then sin 2πt/T = 0, the displacement is zero.(d) When t = T/4, 3T/4, 5T/4 etc,....sin 2πt/T = ±1,  the displacement is maximum.
```
2 months ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Wave Motion

View all Questions »  ### Course Features

• 101 Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution  ### Course Features

• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions