Answer:
The distance traveled by the tuning fork is 9.37 m
Explanation:
Given;
source frequency, [tex]f_s[/tex] = 683 Hz
observed frequency, [tex]f_o[/tex] = 657 Hz
The speed at which the tuning fork fell is calculated by applying Doppler effect formula;
[tex]f_o = f_s [\frac{v}{v + v_s} ][/tex]
where;
[tex]v[/tex] is speed of sound in air = 343 m/s
[tex]v_s[/tex] is the speed of the falling tuning fork
[tex]657 = 683[\frac{343}{343 + v_s} ]\\\\\frac{657}{683} = \frac{343}{343 + v_s}\\\\0.962 = \frac{343}{343 + v_s}\\\\0.962(343 + v_s) = 343\\\\343 + v_s = \frac{343}{0.962} \\\\343 + v_s = 356.55\\\\v_s = 356.55 - 343\\\\v_s = 13.55 \ m/s[/tex]
The distance traveled by the tuning fork is calculated by applying kinematic equation as follows;
[tex]v_s^2 = v_o^2 + 2gh[/tex]
where;
[tex]v_o[/tex] is the initial speed of the tuning fork = 0
g is acceleration due to gravity = 9.80 m/s²
[tex]v_s^2 = 0 + 2gh\\\\h = \frac{v_s^2}{2g} \\\\h = \frac{13.55^2 }{2\times 9.8} \\\\h = 9.37 \ m[/tex]
Therefore, the distance traveled by the tuning fork is 9.37 m
