Answer :
Answer:
The speed of the bat is 5.02 m/s.
Explanation:
Given that,
Frequency = 30.0 kHz
Frequency of echo = 900 Hz
We need to calculate the frequency
Using formula of beat frequency
[tex]f_{b}=f_{1}-f_{2}[/tex]
Put the value into the formula
[tex]900=f_{1}-30\times10^{3}[/tex]
[tex]f_{1}=900+30000[/tex]
[tex]f_{1}=30900\ Hz[/tex]
We need to calculate the speed of the bat
Using Doppler equation
[tex]f_{apr}=f\times(\dfrac{v_{sound}+v_{observer}}{v_{s}-v_{source}})[/tex]
Put the value into the formula
[tex]30900=30000\times(\dfrac{340+v_{bat}}{340-v_{bat}})[/tex]
[tex]\dfrac{30900}{30000}=\dfrac{340+v_{bat}}{340-v_{bat}}[/tex]
[tex]1.03=\dfrac{340+v_{bat}}{340-v_{bat}}[/tex]
[tex]340\times1.03-340=v_{b}+1.03v_{b}[/tex]
[tex]10.2=2.03v_{bat}[/tex]
[tex]v_{bat}=\dfrac{10.2}{2.03}[/tex]
[tex]v_{bat}=5.02\ m/s[/tex]
Hence, The speed of the bat is 5.02 m/s.
The required speed of bat is 5.02 m/s.
Given data:
The frequency of sound emitted by bat is, f = 30.0 kHz.
The frequency of echo is, f' = 900 Hz.
The given problem can be resolved using the Doppler' effect. Then the expression for the beat frequency is given as,
[tex]f'=f_{1}-f[/tex]
here, [tex]f_{1}[/tex] is the apparent frequency. Then solving as,
[tex]900=f_{1}-(30 \times 10^{3})\\\\f_{1}=30900 \;\rm Hz[/tex]
Now use the Doppler equation as,
[tex]f_{1}=f \times (\dfrac{v'+v}{v'-v})[/tex]
Here,
v' is the speed of sound and v is the speed of bat.
Solving as,
[tex]30900=30000 \times (\dfrac{340+v}{340-v})\\\\v=\dfrac{10.2}{2.03}\\\\v=5.02\;\rm m/s[/tex]
Thus, we can conclude that the required speed of bat is 5.02 m/s.
Learn more about the Doppler's Equation here:
https://brainly.com/question/17107808