A tuning fork vibrats with frequnecy `256 Hz` and gives one beat per seond with the third normal mode of vibration of an open pipe. What is the length of the pipe (Speed of sound in air is `340 ms^(-1)`)

Options

A. 220 cm
B. 200 cm
C. 190 cm
D. 180 cm

Answer

B

Explanation

Organ pipe will have frequency either 255 Hz or 257 Hz.
Third mode means there are three loops in organ pipe. Hence
`3 (lambda)/(2) = l rArr (2l)/(3)`
`f = (upsilon)/(lambda) = (3 upsilon)/(2l) rArr l = (3 upsilon)/(2f)`
Using f = 255 Hz
`l = (3 xx 340)/(2 xx 255) m = 2` m
`rArr " "l = 200` cm
Using f = 257 Hz
`l = (3 xx 340)/(2 xx 257) m = 1.98` m
`rArr " "l = 198` cm
We can see that best option is (b).