Question

Derive and expression for the equation of stationary wave on stretched string .​

Answer 1

Answer:

The equation of two waves having the same amplitude, wavelength, and speed but propagating in opposite directions is

y

1

​

=asin

λ

2π

​

(vt−x) and

y

2

​

=asin

λ

2π

​

(vt+x)

Where a is the amplitude, λ is the wave-length and v is the velocity of the wave. A stationary wave is formed due to the superposition of these two waves. The resultant displacement of a particle is given by,

y=y

1

​

+y

2

​

=asin

λ

2π

​

(vt−x)+asin

λ

2π

​

(vt+x)

Using the relation,

sinC+sinD=2sin

2

C+D

​

cos

2

C−D

​

,

we have y=2acos

λ

2π

​

x⋅sin

λ

2π

​

vt

=Asin

λ

2π

​

vt

where A=2acos

λ

2π

​

x represents the amplitude of the resultant wave.

Explanation: