Question

By what factor must the amplitude of a sound wave be decreased in order to decrease the intensity by a factor of 2?

Answer 1

I believe that the answer to the question asked  above is the following

sound intensity = sound power / (4 pi R2)

so if you decrease the intensity by a factor of 2 the sound wave will also decrease by a factor of 2.


Hope my answer would be a great help for you.    If you have more questions feel free to ask here at Brainly.

Answer 2

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:

$\large {\boxed {v = \lambda f}}$

f = frequency of wave ( Hz )

v = speed of wave ( m/s )

λ = wavelength ( m )

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$\large {\boxed {I = 2 \pi^2 A^2 f^2 \rho v}}$

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:

$I : I' = 2 \pi^2 A^2 f^2 \rho v : 2 \pi^2 (A')^2 f^2 \rho v$

$I : I' = A^2 : (A')^2$

$I : \frac{1}{2}I = A^2 : (A')^2$

$2 : 1 = A^2 : (A')^2$

$2(A')^2 = A^2$

$(A')^2 = \frac{1}{2}A^2$

$A' = \frac{A}{\sqrt{2}}$

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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 : brainly.com/question/3841958
• Example of Doppler Effect : brainly.com/question/810552
• Sound Waves Cannot Travel In Space. : brainly.com/question/546436
• Frequency of The Beats - Doppler Effect : 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