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The equation of a wave travelling on a s...

The equation of a wave travelling on a string is `y=(0.10mm)sin[(3.14m^-1)x+(314s^-1)t]`. (a) In which direction does the wave travel ? (b) Find the wave speed, the wavelength and the frequency of the wave. (c) What is the maximum displacement and the maximum speed of a portion of the string ?

Text Solution

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The correct Answer is:
A, B, C, D
The equation of the wave is given by
`y=[(01 mm)sin(314m^-1)x+(31.4s^-1)t]`
`y=rsin{((2pix)/lamda)+omegat}`
a. Negative x -direction ltbr. b.`k=31.4m^-1`
`rarr (2pi)/lamda=31.4`
`rarr lamda=(2pi)/31.4=0.2m=20cm`
Again `w=314s^-1`
`rarr 2pif=314`
`rarr f=314/(2pi)`
`=314/(2xx3.14)`
`=50sec^1=50Hz`
wave speed
`v=lamdaf=20xx50`
`=1000cm/s`
`c. Max displacement =0.10mm
`Max. velocity =`aw=0.1xx10^-1xx314`
`=3.14cm/sec`
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