Question

A string with a frequency `n` and `B` string with a frequency `1//8` that of `A`. If the energy remains the same and the amplitude of `A` is `a`, then amplitude of `B` will be
A. `2a`
B. `8a`
C. `4a`
D. `a`

Answer 1

Correct Answer - B
The energy of a wave travelling with velocity `v` is given by
`E= 1/2 mv^(2)`
Also `v= amplit udexxangu lar ve locity`
`implies v= a omega`
`:. E= 1/2ma^(2)omega^(2)`
Also `omega= 2pin`
Where `n` is frequency.
`:. E= 1/2 ma^(2)(2pin)^(2)`
`implies E prop a^(2)n^(2)`
It is given that energy remains the same.
Hence, `E_(A)=E_(B)`
`:. (a_(A)/(a_(B)))^(2)=(n_(B)/(n_(A)))^(2)` Given,`n_(A)=n,n_(B)=n/8`
`:. (a_(A))/(a_(B))=(n//8)/(n)=1/8`
`implies a_(B)=8a_(A)= 8a`