Question

A string vibrates in three loops when 8gram weight is placed in the pan. What mass should be kept in the pan to make it vibrate in six loops. Neglect the mass of string and mass of pan.

Answer 1

When string vibrates in p loops, its frequency `v=(p)/(2l)sqrt((T)/(m))`
As v,l,T and m are constants, therefore,
`psqrt(T)=` constant or `p^(2)T=` constant.
`:. (T_(2))/(T_(1))=(p_(1)^(2))/(p_(2)^(2))=(3^(2))/(6^(2))=(1)/(4), T_(2)=(T_(1))/(4)=(8)/(4)=2g`