Two tuning forks A and B give 5 beats per second. Fork A resonates with a closed air column 20 cm long and fork B with an open air column 40.5 cm long. Neglecting end correction, the frequencies of tuning forks A and B are respectively.

Step-by-step solution

The tuning forks produce 5 beats per second, establishing the relationship | f_A - f_B | = 5 Hz. Tuning fork A resonates with a closed air column of length L_A = 0.20 m. The fundamental frequency is f_A = v 4L_A = v 0.8 . Tuning fork B resonates with an open air column of length L_B = 0.405 m. Its fundamental frequency is f_B = v 2L_B = v 0.81 . Since 0.8 f_B , yielding f_A - f_B = 5 Hz. Substituting the expressions: v 0.8 - v 0.81 = 5 v ( 1 0.8 - 1 0.81 ) = 5 v ( 0.01 0.648 ) = 5 v = 5 0.648 0.01 = 324 m/s The fre