A closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio:

1 : 2

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2 : 3

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3 : 4

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4 : 5

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Solution

The correct option is B $3 : 4$
Let $L$ and $L^{'}$ be the lengths of open organ pipe and closed pipe respectively .
frequency of first overtone of open pipe ,
$n_{2} = v / L$ ,
frequency of first overtone of closed pipe ,
$n_{2}^{'} = 3 v / 4 L$ ,
given $n_{2} = n_{2}^{'}$
therefore , $v / L = 3 V / 4 L^{'}$ ,
or $L^{'} / L = 3 / 4$
or $L^{'} : L = 3 : 4$

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A closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio:

The correct option is B 3:4Let L and L′ be the lengths of open organ pipe and closed pipe respectively .frequency of first overtone of open pipe , n2=v/L ,frequency of first overtone of closed pipe , n′2=3v/4L ,given n2=n′2therefore , v/L=3V/4L′ ,or L′/L=3/4 or L′:L=3:4