How many harmonics in the audible range are present in the vibrations of air column in a closed organ pipe of length 0.2m. Given velocity of sound $= 340 m s^{- 1}$

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

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

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

Open in App

Solution

The correct option is C 24
$= f = \frac{v}{4 l} = \frac{340}{4 \times 0.2} = \frac{340}{0.8} = 425 H_{Z}$
This is in the audible range. (20 Hz to 20000 Hz)
The next overtones are 3f, 5f . . . . which are present in the pipe
Let there be n harmonics
$n f \leq 20000$
$n \leq \frac{20000}{425} = 47$
The $n^{t h}$ harmonic present in the pipe is 19975. So the harmonics are 425, 1275, . . . . 19975
Number of terms in this A.P
$19975 = 425 + (n - 1) 850 = 425 + 850 n - 850 19975 + 425 = 850 n 400 = 850 n ∴ n = \frac{20400}{850} = 24$

Ans: 24

Suggest Corrections

Similar questions

Q. How many harmonics in the audible range are present in the vibrations of air column in a closed organ pipe of length 0.2m. Given velocity of sound

= 340 m s^{- 1}

An open organ pipe has a length of 5 cm. (a) Find the fundamental frequency of vibration of this pipe. (b) What is the highest harmonic of such a tube that is in the audible range ? Speed of sound in air is $340 m s^{- 1}$ and the audible range is 20-20,000 Hz.

A closed organ pipe can vibrate at a minimum frequency of 500 Hz. Find the length of the tube. Speed of sound in air = $340 m s^{- 1}$

A closed organ pipe can vibrate at a minimum frequency of 500 Hz. Find the length of the tube. Speed of sound in air = $340 m s^{- 1}$ .

Q. What is meant by harmonics? Show that only odd harmonics are present as overtones in the case of an air column vibrating in a pipe closed at one end.
The wavelengths of two sound waves in air are

\frac{81}{173} m

and

\frac{81}{170} m

. They produce

10

beats per second. Calculate the velocity of sound in air.

Join BYJU'S Learning Program

How many harmonics in the audible range are present in the vibrations of air column in a closed organ pipe of length 0.2m. Given velocity of sound =340 ms−1

How many harmonics in the audible range are present in the vibrations of air column in a closed organ pipe of length 0.2m. Given velocity of sound $= 340 m s^{- 1}$