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 $300 \mathrm{~m} / \mathrm{s}$, the frequency difference between the fundamental and second harmonic of this pipe is \_\_\_\_ Hz .

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Waves & Sound

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 .

Answer: 106

The speed of sound in a medium is

v = B / ρ

, so in a gas of twice the density of air the speed becomes

v_{g a s} = v_{ai r} / 2 = 300/ 2

m/s. A pipe open at both ends carries harmonics

f_{n} = n v /2 L

, so its fundamental is

f_{1} = v_{g a s} /2 L

and its second harmonic is

f_{2} = 2 v_{g a s} /2 L

. The difference between them is

f_{2} - f_{1} = v_{g a s} /2 L = \frac{300}{2 2 \times 1} = \frac{150}{2} \approx 106

Hz.

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Integer answer