At Normal Temperature And Pressure The Speed Of Sound In Air Is 332 M/s. What Will Be The Speed Of Sound In Hydrogen (i) At Normal Temperature And Pressure, (ii) At 546oC Temperature And 3 Atmospheric Pressure? (Air Is 16 Times Heavier Than Hydrogen).

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Question

At normal temperature and pressure the speed of sound in air is 332 m/s. What will be the speed of sound in hydrogen (i) at normal temperature and pressure, (ii) at 546oC temperature and 3 atmospheric pressure? (Air is 16 times heavier than hydrogen).

Solution

Correct option is

 

(i) The speed of sound in a gas given by

                          

Where P is the pressure of the gas, d is the density and γ is the ratio of the two specific heats of the gas. Thus, if at normal temperature and pressure the speed of sound in air be va and in hydrogen be vh, then  

                        

Where dh and du are the densities of hydrogen and air respectively. It is given that   

                          

or           

(ii) On changing the pressure of the gas the speed of sound remains the same, but on changing the temperature the speed changes. The speed of sound is directly proportional to the square-root of the ‘absolute’ temperature of the gas. Hence, if the speed of sound in hydrogen at normal temperature (0oC) be v0, and at 546oC be v546, then   

                          

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