A well with vertical side and water at the bottom resonates at 3 Hz and at no other lower frequency. The air in the well has density 1.10 kg m-3 and bulk modulus of 1.32 x 105 Nm-2 Nm, then the depth of well is
(a) 30 m
(b) 29 m
(c) 25 m
(d) 32 m
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A well with vertical side and water at the bottom resonates at 3 Hz and at no other lower frequency. The air in the well has density 1.10 kg m-3 and bulk modulus of 1.32 x 105 Nm-2 Nm, then the depth of well is
(a) 30 m
(b) 29 m
(c) 25 m
(d) 32 m
A well with vertical side and water at the bottom resonates at 3 Hz and at no other lower frequency. The air in the well has density 1.10 kg m-3 and bulk modulus of 1.32 x 105 Nm-2 Nm, then the depth of well is
(a) 30 m
(b) 29 m
(c) 25 m
(d) 32 m
Answer is : (b) 29 m
For air, \(\rho\) = 1.10 kgm-3
K = 1.32 x 105 Nm-2
Speed of sound in air,
v = \(\sqrt{\frac{K}{\rho}}\)
\(\sqrt{\frac{1.32\times 10^5}{1.10}}\)
= 3.46 x 102
= 346 ms-1
It is similar to a closed organ pipe, hence fundamental frequency of well is
v = \(\frac{v}{4L}=\frac{346}{4\times L}\)
\(\Rightarrow L=\frac{346}{4\times 3}\) = 29 m