The amplitude of a sound wave must be decreased by a factor of √2
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Further explanation
Let's recall the speed of wave and intensity of wave formula as follows:
[tex]\large {\boxed {v = \lambda f}}[/tex]
f = frequency of wave ( Hz )
v = speed of wave ( m/s )
λ = wavelength ( m )
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[tex]\large {\boxed {I = 2 \pi^2 A^2 f^2 \rho v}}[/tex]
I = intensity of wave ( W/m² )
A = amplitude of wave ( m )
f = frequeny of wave ( Hz )
ρ = density of medium ( kg/m³ )
v = speed of wave ( m/s )
Let's tackle the problem!
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Given:
Amplitude of First Wave = A
Intensity of First Wave = I
Intensity of Second Wave = ¹/₂ I
Asked:
Amplitude of Second Wave = ?
Solution:
[tex]I : I' = 2 \pi^2 A^2 f^2 \rho v : 2 \pi^2 (A')^2 f^2 \rho v[/tex]
[tex]I : I' = A^2 : (A')^2[/tex]
[tex]I : \frac{1}{2}I = A^2 : (A')^2[/tex]
[tex]2 : 1 = A^2 : (A')^2[/tex]
[tex]2(A')^2 = A^2[/tex]
[tex](A')^2 = \frac{1}{2}A^2[/tex]
[tex]A' = \frac{A}{\sqrt{2}}[/tex]
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Conclusion:
The amplitude of a sound wave must be decreased by a factor of √2
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Learn more
- Doppler Effect : https://brainly.com/question/3841958
- Example of Doppler Effect : https://brainly.com/question/810552
- Sound Waves Cannot Travel In Space. : https://brainly.com/question/546436
- Frequency of The Beats - Doppler Effect : https://brainly.com/question/12367463
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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, Medium, Space
