1.

For air at room temperature the atmospheric pressure is 1.0 xx 10^(5) Nm^(-2)and density of air is 1.2 kg m^(-3). For a tube of length 1.0 m closed at one end the lowest frequency generated is 84 Hz. The value of y (ratio of two specific heats) for air is

Answer»

2.1
1.5
1.8
1.4

Solution :Here, `l= 1M`
`P_(0) =1.0 xx 10^(5) Nm^(-2)`
`rho = 1.2 kg m^(-3)`
`u_(0) = 84 Hz, gamma =?`

For FUNDAMENTAL FREQUENCY,
`l = lambda/4 rArr lambda = 4l = 4m`
Also, `u_(0) = v/lambda rArr 84 = v/4 rArr v = 336 ms^(-1)`
Also `v=sqrt((gammaP_(0))/rho) rArr gamma =(v^(2)rho)/P_(0)`
`gamma =((336)^2 xx 1.2)/(1 xx 10^(5)) = 1.35 = 1.4`


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