Question

A student did the experiment on finding the speed of sound (say V) using a given resonance tube of diameter D. She used five tuning forks of different frequencies and observed the first and second resonance lengths in each case. She then plotted (separate) graphs of these first and second resonance lengths against the reciprocal of the corresponding tuning fork frequencies. The slopes of the two graphs were found to be m₁ and m₂ while the magnitudes of their intercepts, on the y–axis, were found to be C₁ and C₂ , respectively. We would then have

(1) v = 4M₁ = 4/3M₂ and D = 10/3|C₁| = 10/3|C₂|

(2) v = 4M₁ = 3/4M₂ and D = 10/3|C₁| = 10/3|C₂|

(3) v = 4M₁ = 3/4M₂ and D = 10|C₁| = 10/3|C₂|

(4) v = M₁/4 = 3/3M₂ and D = 10|C₁| = 10/3|C₂|

Answer 1

(1) v = 4M₁ = 4/3M₂ and D = 10/3|C₁| = 10/3|C₂|

We know that