A wave travelling on a string at a speed of `10 ms^-1` causes each particle of the string to oscillate with a time period of 20 ms. (a) What is the wavelength of the wave ? (b) If the displacement of a particle is 1.5 mm at a certain instant, what will be the displacement of a particle 10 cm away from it at the same instant ?

Answer

A, B, C

Explanation

Wave speed `=v=10m/sec`
`Time period =T=20 ms`
`=20xx10^-32xx10^-2sec`
a. Wavelength `lamda=vt=10xx2xx10^-2`
`=0.02m=20cm`
b. wavelength`lamda=20cm`
`:. Phase difference `=((2pi)/lamda).x`
`=((2pi)/20)xx10=pirad`
`y_1=asin(omegat-kx)`
`rarr 1.5=asin(omegat-kx)`
So, the displacement of the particle ast diatance `x=10cm
`=[phi=(2pix)/lamda=2pixx10/20=pi]` is given by
`y_2=asin(omegat-kx+pi)`
`=asin(omegat-kx)=1.5mm`
`:. displacement =1.5mm