A 2 m-long string fixed at both ends is set into vibrations in its first overtone. The wave speed on the string is 200 m s and the amplitude is 0.5 cm. (a) Find the wavelength and the frequency. (b) Write the equation giving the displacement of different points as a function of time. Choose the X-axis along the string with the origin at one end and t = 0 at the instant when the point x= 50 cm has reached its maximum displacement.

Answer

(0.5cm) sin (pix) cos(200 pi t)]

Explanation

As left end is node, we consider it as origin so we use equation of stationary wave as
`y = A_(0) sin(kx)cosomegat`
we choose `cos omega t` as at x = 50 cm there is an antinode in this case (first overtone) so wire start from extreme position.
`k = (2pi)/(lambda) = pi and omega = 2pin = 200 pi`
`y = (0.5) sin(pix)cos(200pit)cm`