Question

An open organ pipe has a fundamental frequency of 300hz. The lengrh of pipe is

Answer 1

Given An open organ pipe has a fundamental frequency of 300 Hz. The first overtone of a closed organ pipe has the same frequency as the first overtone of the open pipe. Velocity of sound in air =330m/s. The length of the pipes are

Frequency is v/2L = 300 hz

So first overtone will be v/l = 600 hz

So frequency of 1st overtone of open pipe is equal to frequency of 1st overtone of closed pipe.

Speed of sound is 330 m/s

 Now 3v/4l = 600

 600 x 4l = 3v

 4l = 3v/600

 4l = 3v/600

l = 3 x 330/600 x 4

l = 33/80

l = 0.4125 m

l = 41.25 cm

length of pipe is 41.25 cm

Answer 2

for an open organ pipe,

wave propagates from midpoint of pipe as shown in figure.

if we assume $\lambda$ is wavelength of wave and l is length of open organ pipe.

then, $\frac{\lambda}{4}+\frac{\lambda}{4}=l$

or, $\frac{\lambda}{2}=l\implies\lambda=2l$......(1)

so, frequency of wave, $\nu=\frac{\mathbf{v}}{\lambda}$

where, $\mathbf{v}$ denotes velocity of sound in air, e.g., $\mathbf{v}=332m/s$

now, $\nu=\frac{\mathbf{v}}{2l}$ [ from equation (1)]

given, $\nu=300Hz$

so, $300=\frac{332}{2l}$

or, $2l=\frac{332}{300}=1.107m$

hence, length of organ pipe ≈ 55cm