Question

A stationary wave is formed in a pipe which is open at one end. If two complete loops are formed and the wavelength of the wave is 10 cm, what is the length of the pipe? A. 10 cm B. 15 cm C. 12.5 cm​

Answer 1

Given:

A stationary wave is formed in a pipe which is open at one end. Two complete loops are formed and the wavelength of the wave is 10 cm.

To find:

Length of pipe ?

Calculation:

• Since 2 complete loops have formed , the length of the the stationary wave will be $\lambda/4+ \lambda/2 +\lambda/2=5\lambda/4$.

• This length of wave will be equal to the length of the pipe.

• See the diagram.

$\therefore 5\lambda/4 = L$

$\implies \: L = \dfrac{5\times10}{4} \: cm$

$\implies \: L = 12.5\: cm$

So , length of pipe will be 12.5 cm

Answer 2

Given:-

A stationary wave is formed in a pipe which is open at one end. Two complete loops are formed and the wavelength of the wave is 10 cm.

To find:

Length of pipe ?

Calculation:

• Since 2 complete loops have formed , the length of the the stationary wave will be \lambda/4+ \lambda/2 +\lambda/2=5\lambda/4λ/4+λ/2+λ/2=5λ/4 .
• This length of wave will be equal to the length of the pipe.
• See the diagram.

$= > l = \frac{5 \times 10}{4} cm$

$= > l = 12.5cm$

So , length of pipe will be 12.5 cm.

Thànk you :)