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Question
Solve the following problem.
If the velocity of sound in air at a given place on two different days of a given week are in the ratio of 1:1.1. Assuming the temperatures on the two days to be same what quantitative conclusion can your draw about the condition on the two days?
Solution
Let v1 and v2 be the velocity of sound on day 1 and day 2 respectively.
`"v"_1/"v"_2 = 1/1.1`
We know, `"v" prop 1/sqrtrho`
Let ρ1 and ρ2 be the density of air on day 1 and day 2 respectively.
∴ `sqrt((rho_2)/(rho_1)) = 1/1.1`
∴ `rho_2/rho_1 = (1/1.1)^2`
∴ `rho_1 = 1.1^2 rho_2 = 1.21 rho_2`
From above equation, we can conclude,
ρ1 > ρ2
∴ v2 > v1 i.e., the velocity of sound is greater on the second day than on the first day.
We know, speed of sound in moist air (vm) is greater than speed of sound in dry air (vd).
∴ We can conclude, air is moist on the second day and dry on the first day.
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