Choose the correct option: When an air column in a pipe closed at one end vibrates such that three nodes are formed in it, the frequency of its vibrations is _____ times the fundamental frequency.

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When an air column in a pipe closed at one end vibrates such that three nodes are formed in it, the frequency of its vibrations is 5 times the fundamental frequency. Explanation: Express the relation for the one node vibrational frequency. v = V/lambda .....(1) Here, v is the frequency, λ is the wavelength and V is the velocity. Express the relation for the wavelength for the fundamental frequency. λ = 4L Here, λ is the wavelength and L is a length. Substitute the value of λ in equation (1). v = V/(4L) .....(2) Express the relation for three nodes vibrational frequency. v' = V/lambda ......(3) Here, v' is the frequency, λ is the wavelength and V is the velocity. Express the length-wavelength relationships for three nodes vibration frequency. λ = ($\frac{4}{5}$)L Here, λ is the wavelength and L is a length. Substitute the value of λ in equation (3). v' = (5V)/(4L) ......(4) Substitute the value of (V/(4L)) from equation (2) in equation (4). V' = 5v

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