Answer:
The values is [tex]f_b =14.9 \ beats/s[/tex]
Explanation:
From the question we are told that
The speed of the fire engine is [tex]v = 5\ m/s[/tex]
The frequency of the tone is [tex]f = 500 \ Hz[/tex]
The speed of sound in air is [tex]v_s = 340 \ m/s[/tex]
The beat frequency is mathematically represented as
[tex]f_b = f_a - f[/tex]
Where [tex]f_a[/tex] is the frequency of sound heard by the people in the fire engine and is is mathematically evaluated as
[tex]f_a = [\frac{v_s + v }{v_s -v} ]* f[/tex]
substituting values
[tex]f_a = [\frac{340 + 5 }{340 -5} ]* 500[/tex]
[tex]f_a = 514.9 \ Hz[/tex]
Thus
[tex]f_b =514.9 - 500[/tex]
[tex]f_b =14.9 \ beats/s[/tex]
