Question

A loudspeaker that produces signals from $50Hz$ to $500Hz$ is placed at the open end of a closed tube of length $1.1m.$ If velocity of sound is $330m/s,$ then frequencies that excites resonance in the tube are:

• A. $75Hz$
• B. $150Hz$
• C. $200Hz$
• D. $300Hz$

Answer 1

The correct option is A $75Hz$

If the length of the tube is $l$

then $l=\frac{x}{4}\Rightarrow \lambda =4l$

where $\lambda$ is the wavelength of the sound wave inside the tube If corresponding frequency is $V$ than

$V\lambda =V$

$\therefore V=\frac{V}{\lambda }=\frac{V}{4l}=\frac{330}{4.\left(1.1\right)}$

$\therefore V=75Hz$

Therefore the fundamental tone freq of the tube is $V=75Hz$

This frequencies of the overtones are $3v,5v,3v....$

i.e. $225,373,525$

If the loud speaker produces signals from $0Hz$ to $500Hz$ then frequencies that excites resonance in the tube are

$75Hz,225Hz,375Hz$