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physics students are studying the effect of the temperature, T, on the speed of sound, S. They find that the speed of sound in meters per second is a function of the temperature in degrees Kelvin, K, by S(K)=√410K. The degrees Kelvin is a function of the temperature in Celsius given by K(C)=C+273.15. Find the speed of sound when the temperature is 30 degrees Celsius. Round to the nearest tenth.

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raphealnwobi

The speed of sound is 352.5 m/s

First of all, the temperature in kelvin is a function of the temperature in Celsius. The relationship is given by:

K(C)=C+273.15

Hence at 30 degrees Celsius, the temperature in Kelvin is:

K(30) = 30 + 273.15 = 303.15

Also, the speed of sound in meters per second is a function of the temperature in degrees Kelvin. It is given by the relationship:

[tex]S(K)=\sqrt{410K}[/tex]

Therefore at 30°C, K = 303.15 K, hence the speed of sound is:

[tex]S(303.15)=\sqrt{410*303.15}=352.5\ m/s[/tex]

Therefore the speed of sound at 30°C is 352.5 m/s.

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