Question

An air column is of length 17 cm long. Calculate the frequency of 5th overtone if the air column is
(a) closed at one end and (b) open at both ends. (velocity of sound in air = 340 ms-').​

Answer 1

Explanation:

the frequency of fifth overtone of an air column vibrating in a pipe closed at one end is 2230

Answer 2

Answer:

The frequency of the 5th overtone of the air column closed at one end and open at both ends are 5500 Hz and 6000Hz respectively.

Explanation:

(a) Closed at one end

$f=\frac{(2n+1)V}{4L}$    (1)

Where,

f=frequency of nth overtone

V=velocity of sound in air

n=number of overtone

L=length of the organ pipe

From the question we have,

L=17cm=17×10⁻²m

V=340m/s

n=5

By substituting the value of "L" ,"n",and "V" in equation (1) we get;

$f=\frac{(2\times 5+1)\times 340}{4\times 17\times 10^-^2}$

$f=5500Hz$     (2)

(b)Open at both ends

$f=\frac{(n+1)V}{2L}$    (3)

Where,

f=frequency of nth overtone

V=velocity of sound in air

n=number of overtone

L=length of the organ pipe

From the question we have,

L=17cm=17×10⁻²m

V=340m/s

n=5

By substituting the value of "L" , "n", and "V" in equation (3) we get;

$f=\frac{(5+1)\times 340}{2\times 17\times 10^-^2}$

$f=6000Hz$     (4)

Hence, the frequency of the 5th overtone of the air column closed at one end and open at both ends are 5500 Hz and 6000Hz respectively.