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Figure 7.20 shows a tube structure in w...

Figure `7.20` shows a tube structure in which signal is sent from one end and is received at the other end . The frequency of the sound source can be varied electronically between `2000 to 5000 Hz`. Find the frequencies at which maxima of intensity are detected . The speed of sound in air `340 m//s`.

Text Solution

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The path difference between the sound going through the tubes
`Delta x = ABCD - AED`
` = ( 10 + 20 + 10) - ( sqrt(500) + 10) = 7.64 cm`
The wavelength of the sound
`lambda = (v)/(f) = (340)/(f) m`
For maximum intensity , `Delta x = n lambda`
`7.64 xx 10^(-2) = n xx (340)/f`
`f = n (340)/( 7.64 xx 10^(-2)) = n 4450 Hz`
Here ` nge 1`. for ` n = 1 , f = 4450 Hz and for n = 2 , f = 8900 Hz`. Thus the frequency within the specified range is `4450 Hz`.
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