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At 16^(@)C, two open end organ pipes, wh...

At `16^(@)C,` two open end organ pipes, when sounded together give 14 beats in 2 pipes, when sounded together give 14 beats in 2 seconds. How many beats per second will be produced if the temperature is raised to `51^(@)C` ? Neglect increase in length of the pipes.

Text Solution

Verified by Experts

If `l_(1),l_(2)` are lengths of the two pipes, then as
`m=n_(1)-n_(2)=(upsilon_(16))/(2l_(1))-(upsilon_(16))/(2l_(2))`
`=upsilon_(16)[(1)/(2l_(1))-(1)/(2l_(2))]=7`
and `=upsilon_(51)[(1)/(2l_(1))-(1)/(2l_(2))]=m`
Divide (ii) by (i),
`(upsilon_(51))/(upsilon_(16))=(m)/(7)=sqrt((273+51)/(273+16))=sqrt((324)/(289))`
`(m)/(7)=(18)/(17) or m=(18xx7)/(17)=7.4s^(-1)`
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