Answer:
h = 15.34 m
Explanation:
given,
tuning fork vibration = 513 Hz
speed of sound = 343 m/s
frequency after deflection = 489 Hz
the source (the fork) moves away from the observer, its speed increases and hence the apparent frequency decreases
[tex]f_{apparent} = \dfrac{v}{v+u}f_0[/tex]
[tex]489 = \dfrac{343}{343+u}\times 513[/tex]
[tex]0.953 = \dfrac{343}{343+u}[/tex]
[tex]343+u = \dfrac{343}{0.953}[/tex]
[tex]343+u = 359.92[/tex]
u = 16.92 m/s
height of the building
v² = u² + 2 g s
16.92² = 2 x 9.8 x h
h = 14.61 m
time taken by sound to reach observer
[tex]t = \dfrac{14.61}{343}[/tex]
[tex]t =0.0426\ s[/tex]
in this time tuning fork has fallen one more now,
[tex]h' = u t + \dfrac{1}{2}gt^2[/tex]
[tex]h' = 16.92\times 0.0426 + \dfrac{1}{2}\times 9.8 \times 0.0426^2[/tex]
h' = 0.7296 m = 0.73 m
total distance
h = 14.61 + 0.73
h = 15.34 m
