To find the distance `d` over which a signal can be seen clearly in foggy conditions, a railways-engineer uses dimensions and assumes that the distance depends on the mass density `rho` of the fog, intensity (power/area) `S` of the light from the signal and its frequency `f`. the engineer finds that `d` is proportional to `S^(1//n)`. the value of `n` is
To find the distance `d` over which a signal can be seen clearly in foggy conditions, a railways-engineer uses dimensions and assumes that the distance depends on the mass density `rho` of the fog, intensity (power/area) `S` of the light from the signal and its frequency `f`. the engineer finds that `d` is proportional to `S^(1//n)`. the value of `n` is
Text Solution
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The correct Answer is:
`3`
`d = rho^(a) S^(b) f^( c)`
` d = ((kg)/( m^(3)))^(a) xx (( w)/(m^(2))) ^(b) xx ((1)/( sec))^(c )`
`d = (ML^(-3))^(a) ((ML^(2) T^(-3))/(L^(2)))^(b) ((1)/( sec))^( c )`
`L^(1) = M^(a + b L^(-3a) T^(-3b -c )`
` -3a = 1 rArr a = -(1)/(3)`
` a + b = 0` `( :. b = (1)/(3))`
`- 3b -c = 0` `( :. c = 1)`
`:. rho^-(1)/(3) S^(1)/(3) f^(1)`
`:. d prop S^(1//n) ( :. n = 3)`
` d = ((kg)/( m^(3)))^(a) xx (( w)/(m^(2))) ^(b) xx ((1)/( sec))^(c )`
`d = (ML^(-3))^(a) ((ML^(2) T^(-3))/(L^(2)))^(b) ((1)/( sec))^( c )`
`L^(1) = M^(a + b L^(-3a) T^(-3b -c )`
` -3a = 1 rArr a = -(1)/(3)`
` a + b = 0` `( :. b = (1)/(3))`
`- 3b -c = 0` `( :. c = 1)`
`:. rho^-(1)/(3) S^(1)/(3) f^(1)`
`:. d prop S^(1//n) ( :. n = 3)`
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The mass suspended from the stretched string of a sonometer is 4 kg and the linear mass density of string 4 xx 10^(-3) kg m^(-1) . If the length of the vibrating string is 100 cm , arrange the following steps in a sequential order to find the frequency of the tuning fork used for the experiment . (A) The fundamental frequency of the vibratinng string is , n = (1)/(2l) sqrt((T)/(m)) . (B) Get the value of length of the string (l) , and linear mass density (m) of the string from the data in the problem . (C) Calculate the tension in the string using , T = mg . (D) Substitute the appropriate values in n = (1)/(2l) sqrt((T)/(m)) and find the value of 'n' .
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