A `200cm` length of the wire weighs `0.6` gm. If the tension in the wire caused by a `500 gm` mass hanged from it. If the approximate wavelength of a wave of frequency `400Hz` sent down by it is `2^(n)xx10^(-2)m`. Find the value of `n` (`g=9.8m//s^(2)`)

Answer

5

Explanation

`mu=` Mass per unit length `=m/l=(0.6xx10^(-3))/2=3xx10^(-4)kg//m`
`T=mg=0.5xx9.8=4.9Nimplies` Tension in the string
`v=` speed of wave in string`=sqrt(T/(mu))`
`=sqrt(4.9/(3xx10^(-4)))=128m//s`
`lamdaimplies` wavelength of the wave `=v/f=128/400=32xx10^(-2)m=2^(5)xx10^(-2)m`
`implies n=5`