`S_(1)`: The particles speed can never be equal to the wave speed in sine wave if the amplitude is less then wavelength divided by `2pi`.
`S_(2)`: In transverse wave of amplitude A, the maximum particle velocity is four times its wave velocity. Then, the wave length of the wave is `piA`
`S_(3)`: the phase difference between two points separated by 1m in a wave of frequency 120 Hz is `90^(@)`. the velocity of the wave is 480 m/s

Options

A. FTT
B. TTF
C. TFT
D. FFF

Answer

C

Explanation

`S_(1)`: True
`S_(2)` : False
Amplitude of the wave =A
Maximum velocity of wave `upsilon_(max)=4 upsilon` (where `upsilon` is the wave velocity)
The relation for the maximum velocity is
`upsilon_(max)=4 omega`
`4 upsilon=4 omega`
`omega=(4 upsilon)/A`
wavelength of the wave is given by
`lambda=(upsilon)/f=(upsilon)/((omega)/(2pi))=(2piupsilon)/((4upsilon)/(A))=(piA)/2`
Where f is the frequency `f=(omega)/(2pi)` from `omega=2pif`
`S_(3)` : True
distance between two points `Deltax=1m` frequency n=120Hz
Phase difference `phi=90^(@)=0.5 pi`
The relation for the phase difference is
`phi=(2pi)/(lambda)xxDeltax`
or `lambda=(2pixxDeltax)/(phi)=(2pixx1)/(0.5pi)=4m`
The velocity of wave is given by
`upsilon=nlambda`
`=120xx4=480 m//s`