In a resonance tube experiment, an 80 cm air column in resonance with a turning fork in first overtone. Which equation can represent correct pressure variation in the air column (x=0 is the top point of the tube, neglect end correction, speed of sound =320 m//sec)

Options

A. `A "sin" (15pi)/8xcos600pit`
B. `A"cos"(15pi)/8xsin600pit`
C. `A"cos"(15pi)/8 x sin300pit`
D. `A"sin" (15pi)/ xsin300pit`

Answer

A

Explanation

At the open end pressure node is present So that at `x=0` P should be zero and `v=flambda`
for first over tone `(3lambda)/4 = 0.80`
`Rightarrow f=300`
`Rightarrow omega=2pif = 600t`
Hence `P=A"sin"(15pi)/8xcos600t`