A steel wire of length 60 cm and area of cross section `10^(-6)m^(2)` is joined with a n aluminium wire of length 45 cm and are of cross section `3xx10^(-6)m^(2)`. The composite string is stretched by a tension of 80 N. Density of steel is `7800kgm^(-3)` and that of aluminium is `2600kgm^(-3)` the minimum frequency of tuning fork. Which can produce standing wave in it with node at joint is

Options

A. 357.2 Hz
B. 275.3 Hz
C. 337.5 Hz
D. 325.5 Hz

Answer

C

Explanation

`f_(1)=f_(2) (m rarr` no. of loops in steel wire `n rarr` no. ofn loops in aluminimum wire)
`rArr (m)/(2L_(1))sqrt((T)/(rho_(1)A_(1)))=(n)/(2L_(2))sqrt((T)/(rho_(2)A_(2)))`
`rArr (m)/(2xx60)sqrt((80)/(7800xx10^(-6)))=(n)/(2xx45)sqrt((80)/(2600xx3xx10^(-6)))`
`rArr (m)/(n)=(4)/(3)`
`:.f=(m)/(2L_(1))sqrt((T)/(rho_(1)A_(1)))=(4)/(2xx0.6)sqrt((80)/(7800xx10^(-6)))`
`337.5 Hz`.