Question

In a pipe open at both ends the fundamental note is produced when its length is equal to

• A. $\lambda$ (wavelength of sound)
• B. $\frac{\lambda }{4}$ (quarter wavelength)
• C. $\frac{\lambda }{2}$ (half wavelength)
• D. 2$\lambda$ (twice wavelength)

Answer 1

Answer: (C)

$\frac{\lambda }{2}$ (half wavelength)

Frequency of nth mode of vibration in a pipe open at both ends ${\nu }_n=\frac{nv}{2L}$

where $L$ is the length of pipe.

For fundamental mode of frequency $n=1$

$\therefore$ ${\nu }_1=\frac{v}{2L}$

Comparing it with ${\nu }_1=\frac{v}{\lambda }$

We get $2L=\lambda$

$⟹$ $L=\frac{\lambda }{2}$