Question 82: Waves

Question

A one metre long (both ends open) organ pipe
is kept in a gas that has double the density of
air at STP. Assuming the speed of sound in air
at STP is 300 m/s, the frequency difference
between the fundamental and second harmonic
of this pipe is ________ Hz.

Accepted Answer

Velocity of sound v = $$\sqrt {{B \over ho }} $$
$$ 	herefore $$ $${{{v_{pipe}}} \over {{v_{air}}}} = \sqrt {{{{B \over {2ho }}} \over {{B \over ho }}}} $$
$$ \Rightarrow $$ v
pipe
= $${{{{v_{air}}} \over {\sqrt 2 }}}$$ = $${{{300} \over {\sqrt 2 }}}$$ = 150$${\sqrt 2 }$$
We know, for open organ pipe
f
n
= $$\left( {n + 1} ight){{{v_{pipe}}} \over {2l}}$$
Difference between 2
nd
and fundamental frequency
f
1
- f
0
= $${{{v_{pipe}}} \over {2l}}$$ = $${{150\sqrt 2 } \over {2\left( 1 ight)}}$$ = 106.06 Hz

Waves

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fundamental and second harmonic of this pipe is ________ Hz.

Integer / Numeric Answer Type