In the experinment for the determinnation of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fu ndamental mode , with a tuning fork is `0.1 m` . When this length is changed to `0.35m` , the same tuning fork resonates with the first overtone. Calculate the end correction.
(a) `0.012 m`
(b) `0.0025 m`
(c) `0.05 m`
(d) `0.024 m`

Options

A. 0.012m
B. 0.025m
C. 0.05m
D. 0.024m

Answer

B

Explanation

`(1_1+x)=(lambda_1)/4implies lambda_1=4(1_1+x)`
`(1_2+x)=(3lambda_2)/4implies lambda_2=4/3 (1_2+x) therefore f_1=(v)/(lambda_1)=(v)/(4 (1_1+x))`
`therefore f_2=(v)/(lambda_2)=(3v)/(4(1_2+x)) Given F_1=f_2 implies (v)/(4(1_2
+x))=(3v)/(4(1_2+x))implies x=0.025 m`