Question

A wire of length L, diameter 'd' density of material 'e' is under tension 'T', having fundamental frequency of vibration n_A. Another wire of length 2L, tension 2T, density 2e and diameter 3d has fundamental frequency of vibration n_B. The ratio n_B: N_A is ______.

Options

• 1:2

• 1:4

• 1:6

• 1:8

Answer 1

A wire of length L, diameter 'd' density of material 'e' is under tension 'T', having fundamental frequency of vibration n_A. Another wire of length 2L, tension 2T, density 2e and diameter 3d has fundamental frequency of vibration n_B. The ratio n_B: N_A is 1:6.

Explanation:

n ∝ \[\frac {1}{lr}\]

\[\therefore\] n_Al_Ar_A = n_Br_Bl_B

n_Al_Ar_A = n_B 3r_B × 2l_B   ...(r ∝ d)

\[\therefore\] n_A = 6n_B

\[\therefore\] \[\frac {n_B}{n_A}\] = \[\frac {1}{6}\]