Answer:
Explanation:
Given
Original Frequency [tex]f=723\ Hz[/tex]
apparent Frequency [tex]f'=697\ Hz[/tex]
There is change in frequency whenever source move relative to the observer.
From Doppler effect we can write as
[tex]f'=f\cdot \frac{v-v_o}{v+v_s}[/tex]
where
[tex]f'=[/tex]apparent frequency
v=velocity of sound in the given media
[tex]v_s=[/tex]velocity of source
[tex]v_0=[/tex]velocity of observer
here [tex]v_0=0[/tex]
[tex]697=723\cdot (\frac{343-0}{343+v_s})[/tex]
[tex]v_s=(\frac{f}{f'}-1)v[/tex]
[tex]v_s=(\frac{723}{697}-1)\cdot 343[/tex]
[tex]v_s=12.79\approx 12.8\ m/s[/tex]
i.e.fork acquired a velocity of [tex]12.8 m/s[/tex]
distance traveled by fork is given by
[tex]v^2-u^2=2as[/tex]
where v=final velocity
u=initial velocity
a=acceleration
s=displacement
[tex]v_s^2-0=2\times 9.8\times s[/tex]
[tex]s=\frac{12.8^2}{2\times 9.8}[/tex]
[tex]s=8.35\ m[/tex]
This question involves the concepts of doppler's effect and the equations of motion.
The tuning fork has fallen by a height of "8.36 m".
From Doppler's Effect we have:
[tex]\frac{f_o}{f_s}=\frac{v+v_o}{v+v_s}[/tex]
where,
[tex]f_o[/tex] = apparent frequency of sound waves = 697 Hz
[tex]f_s[/tex] = actual frequency of sound waves = 723 Hz
v = speed of sound = 343 m/s
[tex]v_o[/tex] = speed of observer = 0 m/s
[tex]v_s[/tex] = speed of source = ?
Therefore,
[tex]\frac{697\ Hz}{723\ Hz}=\frac{343\ m/s + 0\ m/s}{343\ m/s+v_s}\\\\343\ m/s+v_s=\frac{343\ m/s}{0.964}\\\\v_s = 355.8\ m/s - 343\ m/s\\v_s = 12.8\ m/s[/tex]
Now, we will use the third equation of motion to find out the height fell by the tuning fork:
[tex]2gh=v_f^2-v_i^2[/tex]
where,
g = acceleration due to gravity = 9.8 m/s²
h = height fell = ?
vf = final speed of tuning fork = v_s = 12.8 m/s
vi = initial speed of tuning fork = 0 m/s
Therefore,
[tex]h=\frac{(12.8\ m/s)^2-(0\ m/s)^2}{2(9.8\ m/s^2)}\\\\[/tex]
h = 8.36 m
Learn more about equations of motion here:
brainly.com/question/20594939?referrer=searchResults
The attached picture shows the equations of motion.
