Question

A tube of air open at only one end is vibrating in the 5th harmonic from a tuning fork of frequency 120 Hz placed at the open end. If this tube of air were to vibrate at its fundamental frequency, what frequency, in Hz, tuning fork would be needed at the open end

Answer 1

DATA:

SOLUTION

Frequency is defined as:

This equation is valid when we have a tube of air open at only one end.

Where,

is the tube length

is the speed of sound

is the harmonic.

Now, for the fifth harmonic () the equation (1) can be written as:

Isolating from equation (2) we have:

Now, for the first harmonic () the equation (1) can be written as:

Replacing equation (3) into equation (4) we have:

or

Replacing values of data given we have:

Solving we obtain: