Question-04 A pipe open at both ends of length 1.5\ m is dipped in water at one end such that 2^{nd} overtone of vibrating air column is resonating with a tuning fork of frequency 330\ Hz. The length of the pipe immersed in water is (Speed of sound in air = 330\ m/s) (Neglect end correction)
(A) 1\ m
(B) 0.75\ m
(C) 0.5\ m
(D) 0.25\ m
Answer : (D)
Explanation:
Let the length of the pipe immersed in water be x.
For a pipe closed at one end, frequency of 2nd overtone is given as
f_3=\frac{5v}{4L}Where v is the speed of the sound wave and L is the length of vibrating air column
⇒ f_3=\frac{5v}{4(L-x)}
The 2nd overtone of vibrating air column is resonating with a tuning fork of frequency 330 Hz.
∴ 330=\frac{5v}{4(L-x)}=\frac{5\times330}{4(1.5-x)}
⇒ 1.5-x=1.25
⇒ x=0.25\ m