The frequency of the beats is about 9.2 kHz
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Further explanation
Let's recall the Doppler Effect formula as follows:
[tex]\large {\boxed {f' = \frac{v + v_o}{v - v_s} f}}[/tex]
f' = observed frequency
f = actual frequency
v = speed of sound waves
v_o = velocity of the observer
v_s = velocity of the source
Let's tackle the problem!
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Given:
actual frequency = f = 41.2 kHz
velocity of the car = v_c = 33.0 m/s
speed of sound in air = v = 330 m/s
Asked:
frequency of the beats = Δf = ?
Solution:
Firstly , we will use the formula of Doppler Effect as follows:
[tex]f' = \frac{v + v_c}{v - v_c} \times f[/tex]
[tex]f' = \frac{330 + 33}{330 - 33} \times 41.2[/tex]
[tex]f' = \frac{363}{297} \times 41.2[/tex]
[tex]f' = \frac{11}{9} \times 41.2[/tex]
[tex]f' = 50 \frac{16}{45} \texttt{ kHz}[/tex]
[tex]f' \approx 50.4 \texttt{ kHz}[/tex]
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Next , we could calculate the frequency of the beats as follows:
[tex]\Delta f = f' - f[/tex]
[tex]\Delta f \approx 50.4 - 41.2[/tex]
[tex]\Delta f \approx 9.2 \texttt{ kHz}[/tex]
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Conclusion:
The frequency of the beats is about 9.2 kHz
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Learn more
- Doppler Effect : https://brainly.com/question/3841958
- Example of Doppler Effect : https://brainly.com/question/810552
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Answer details
Grade: College
Subject: Physics
Chapter: Sound Waves
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Keywords: Sound, Wave , Wavelength , Doppler , Effect , Policeman , Stationary , Frequency , Speed , Beats
