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

a) 100Hz`
` b) `y =( 0.5cm)cos[(pim^-1)x]sin[(200pis^-1)t]`

Explanation

`V=200m/s, 2A=0.5m `
a. The string is is vibrating is its 1st overtone `rarr lamda=L=2m`
`rarr f=v/lamda=200/2`
`=100Hz`
b. The stationary wave equation is given by
`y=2Acos((2pix)/lamda)sin((2piVt)/lamda)`
`=0.5cos((2pix)/2)cos((2pixx200t)/2)`
`=(0.5cm)cos`
`[(pim^-1)x]sin[(200pis^-1)t]`