Answer
409.8k+ views
Hint: The intensity of the sound wave is related to the pressure amplitude of the longitudinal sound waves. The speed depends on the density of the medium and the speed of sound in the medium.
Formula used: In this solution, we will use the following formula
The intensity of a sound wave: $ I = \dfrac{{{{(\Delta P)}^2}}}{{2\rho v}} $ where $ \Delta P $ is the pressure amplitude, $ \rho $ is the density of the medium, and $ v $ is the velocity of the sound wave in the medium.
Complete step by step answer
Sound waves are longitudinal waves which mean they travel in regions of high and low pressure which is also known as pressure amplitudes. The regions of high pressures are called compressions of the medium and the regions of low pressure are called rarefactions.
The intensity of the sound wave is related to its velocity as
$ I = \dfrac{{{{(\Delta P)}^2}}}{{2\rho v}} $
We can rewrite the above equation to find the velocity of sounds wave as
$ v = \dfrac{{{{(\Delta P)}^2}}}{{2\rho I}} $
Now substituting the value of $ (\Delta P) = 2 \times {10^{ - 4}}\,N/{m^2} $ , $ \rho = 1\,kg/{m^3} $ and $ \;I{\text{ }} = {\text{ }}{10^{ - 10}}Wm $ , we get
$ v = \dfrac{{{{(2 \times {{10}^{ - 4}}\,)}^2}}}{{2(1) \times {{10}^{ - 10}}}} $
Which gives us
$ v = 200\,m/s $
Hence the velocity of the sound wave will be $ v = 200\,m/s $ .
Note
To answer such questions, we should be aware of the relation between the sound wave intensity and its pressure amplitude. The typical speed of sound in the air is $ 343\,m/s $ . The frequency of the sound wave is inconsequential to us since it won’t affect the velocity of the sound wave. Sound waves like all other longitudinal waves need a medium to travel and their velocity will change in different mediums, unlike transverse waves which don’t need a medium to travel.
Formula used: In this solution, we will use the following formula
The intensity of a sound wave: $ I = \dfrac{{{{(\Delta P)}^2}}}{{2\rho v}} $ where $ \Delta P $ is the pressure amplitude, $ \rho $ is the density of the medium, and $ v $ is the velocity of the sound wave in the medium.
Complete step by step answer
Sound waves are longitudinal waves which mean they travel in regions of high and low pressure which is also known as pressure amplitudes. The regions of high pressures are called compressions of the medium and the regions of low pressure are called rarefactions.
The intensity of the sound wave is related to its velocity as
$ I = \dfrac{{{{(\Delta P)}^2}}}{{2\rho v}} $
We can rewrite the above equation to find the velocity of sounds wave as
$ v = \dfrac{{{{(\Delta P)}^2}}}{{2\rho I}} $
Now substituting the value of $ (\Delta P) = 2 \times {10^{ - 4}}\,N/{m^2} $ , $ \rho = 1\,kg/{m^3} $ and $ \;I{\text{ }} = {\text{ }}{10^{ - 10}}Wm $ , we get
$ v = \dfrac{{{{(2 \times {{10}^{ - 4}}\,)}^2}}}{{2(1) \times {{10}^{ - 10}}}} $
Which gives us
$ v = 200\,m/s $
Hence the velocity of the sound wave will be $ v = 200\,m/s $ .
Note
To answer such questions, we should be aware of the relation between the sound wave intensity and its pressure amplitude. The typical speed of sound in the air is $ 343\,m/s $ . The frequency of the sound wave is inconsequential to us since it won’t affect the velocity of the sound wave. Sound waves like all other longitudinal waves need a medium to travel and their velocity will change in different mediums, unlike transverse waves which don’t need a medium to travel.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)