The harmonic mode which resonates with a closed pipe of length $22$ cm, when excited by a $1875$ Hz source and the number of nodes present in it respectively are (velocity of sound in air $= 330 m s^{- 1}$ ):

1^{s t}, 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3^{r d}, 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

3^{r d}, 2

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5^{t h}, 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5^{t h}, 3

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is E $5^{t h}, 3$
Velocity of sound $= 330 m s^{- 1}$
Length of closed pipe $= 22 c m = 22 \times 10^{- 2}$ m
Fundamental frequency of stationary wave,
$v_{0} = \frac{v}{4 l} = \frac{330}{4 \times 22 \times 10^{- 2}}$
$v_{0} = \frac{330 \times 10^{2}}{4 \times 22} = \frac{3000}{8}$
$v_{0} = 375$ Hz
$3 v_{0} = 375 \times 3 = 1125$
$5 v_{0} = 5 \times 375 = 1875$
Thus we get $5$ th harmonic
and number of nodes $= 3$
Note: In closed pipe, odd harmonics are produced.

Suggest Corrections

Similar questions

Q. A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source ? Will the same source be in resonance with the pipe if both ends are open ? (speed of sound in air is 340 m

s^{- 1}

)

A pipe 20 cm long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a 430 Hz source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is 340 m s^–1).

Q. A string of length

l c m

is clampled at both ends. Initially the string is resonating in 3rd harmonic. After some time, string resonates in 5th harmonic. The gap between nodes in 3rd harmonic is

10 c m

greater than gap between nodes in 5th harmonic. Length of string is

Q. A pipe

17 c m

long is closed at one end. Which harmonic mode of the pipe resonates with

1.5 k H z

?
(Speed of sound in air

= 340 m s^{- 1}

)

Q. A closed organ pipe of radius

r_{1}

and an open pipe of radius

r_{2}

and having same length 'L' resonate when excited with a given tunning fork. Closed organ pipe resonates in its fundamental mode where as open organ pipe resonates in its first overtone, then :

Join BYJU'S Learning Program

The harmonic mode which resonates with a closed pipe of length 22cm, when excited by a 1875Hz source and the number of nodes present in it respectively are (velocity of sound in air =330ms−1):

The harmonic mode which resonates with a closed pipe of length $22$ cm, when excited by a $1875$ Hz source and the number of nodes present in it respectively are (velocity of sound in air $= 330 m s^{- 1}$ ):