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Two consecutive harmonics in stationary ...

Two consecutive harmonics in stationary waves produced in a string of length 100 cm have frequencies 300 Hz and 400 Hz. It has maximum amplitude 10 cm. Obtain equation of stationary waves in this string when it oscillates with fundamental frequency.

Text Solution

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We have
`f _(n) = n f _(1)`
`f _(n +1) = (n +1) f _(1)`
` therefore f _(n +1) 1 -f _(n) =nf _(1) + f _(1) - nf _(1)`
`therefore 400 -300 =f _(1)`
`therefore f _(1) = 100 Hz`
`therefore omega _(1) = 2pi f _(1) = 200 pi rad//s`
Also we have,
`lamda_(n) = (2L)/(n)`
`therefore lamda_(1) = (2 xx 100)/(1) = 200 cm`
`therefore k _(1) = (2pi )/( lamda_(1)) = (2pi )/( 200) = (pi)/(100) (rad)/(cm)`
Required equation is,
`y =-2 A sin (k _(1) x ) cos (omega _(1) t )`
`y =- 10 sin ((pi )/(100 ) x) cos (200 pit)`
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