Question

The length of a wave propagated on a long stretched string is taken as the positive x axis. The wave equation is given by 

y=y₀e -(t/T-x/λ)² where y₀ =4 mm,

T =1.0s and λ =4cm.

(a) Find the velocity of the wave. 

(b) Find the function finding the displacement of the particle at x = 0. 

(c) Find the function giving the shape of the string at = 0. 

(d) Plot the shape of the string at t =0. 

(e) Plot the shape of the string at t=5s.

Answer 1

The wave moves having natural frequency of ν and wavelength λ has velocity V = νλ . As the frequency is v = 1/T the velocity of the wave is then V =λ/T.

(a) The wave equation may be written as 

Comparing with the general equation we see that v = λ/1.0s = 4cm = 4cm/sec

(b) Putting x = 0 in the given equation  f(t) = y₀e -(t/T)² … (i)

(c) Putting t = 0 in the given equation g(t) =y₀e -(x/λ)² … (ii)