Two similar open organ pipes of length 50 , c | vedclass

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Question

(A) Given lengths are $L_{1} = 50 \, cm = 0.5 \, m$ and $L_{2} = 50.5 \, cm = 0.505 \, m$.For an open organ pipe,the fundamental frequency is given by

Vedclass · Accepted Answer

$303$

Vedclass · Answer

(A) Given lengths are $L_{1} = 50 \, cm = 0.5 \, m$ and $L_{2} = 50.5 \, cm = 0.505 \, m$.For an open organ pipe,the fundamental frequency is given by $n = \frac{v}{2L}$.Since $L_{2} > L_{1}$,the frequency $n_{1} > n_{2}$.The beat frequency is $n_{1} - n_{2} = 3 \, Hz$.Substituting the expressions for frequency: $\frac{v}{2L_{1}} - \frac{v}{2L_{2}} = 3$.$\frac{v}{2} \left( \frac{1}{0.5} - \frac{1}{0.505} ight) = 3$.$\frac{v}{2} \left( \frac{0.505 - 0.5}{0.5 	imes 0.505} ight) = 3$.$\frac{v}{2} \left( \frac{0.005}{0.2525} ight) = 3$.$v \left( \frac{0.005}{0.505} ight) = 3$.$v = \frac{3 	imes 0.505}{0.005} = 3 	imes 101 = 303 \, m/s$.

Two similar open organ pipes of length $50 \, cm$ and $50.5 \, cm$ produce $3$ beats per second when sounded together. The velocity of sound in air is ........ $m/s$.

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