The sound from a very high burst of fireworks takes 5 s to arrive at the observer. The burst occurs 1662 m above the observer and travels vertically through two stratifier layers of air, the top one of thickness `d_1` at `0^@C` and the bottom one of thickness `d_2` at `20^@C`. Then (assume velocity of sound at `0^@C` is `330(m)/(s)`)

Options

A. `d_1=342m`
B. `d_2=1320m`
C. `d_1=1485m`
D. `d_2=342m`

Answer

A

Explanation

Time taken is given by
`T=t_1+t_2=(d_1)/(v_1)+(d_2)/(v_2)`
`v_1=v_(0^@C)=330(m)/(s)`
`v_2=(330+0.6t)=342(m)/(s)`
`d=1662m`
`T=(d_1)/(330)+((d-d_1))/(342)=5s`
`(d_1(342-330))/(330xx342)+(d)/(342)=5s`
`12d_1=5(342xx330)-330xx1662`
`d_1=1320m`
`d_2=342m`