Question

If the velocity of the wave is 330
m/s and having length of the closed
ended stretched string under some
tension generates the fundamental
frequency as 1320 Hz, then find out
the fundamental frequency that is
generated in case of the closed end
organ pipe of the same length as that
of the string.​

Answer 1

Given:

Velocity of the wave is 330 m/s and having length of the closed ended stretched string under some tension generates the fundamental frequency as 1320 Hz.

To find:

Fundamental frequency of closed organ pipe of same length?

Calculation:

For string, nodes are on two sides:

$\therefore \: \dfrac{ \lambda}{2} = l$

$\implies \: \lambda = 2l$

$\implies \: f = \dfrac{v}{ \lambda}$

$\implies \: 1320 = \dfrac{330}{2l}$

$\implies \:l = 8 \: m$

Now, the one sided closed organ pipe has 8 metres length !

$\therefore \: \dfrac{ \lambda}{4} = l$

$\implies \lambda = 4l$

$\implies \: f = \dfrac{v}{ \lambda}$

$\implies \: f = \dfrac{330}{4l}$

$\implies \: f = \dfrac{330}{4 \times 8}$

$\implies \: f = 10.3125 \: hz$

So,.the frequency will be 10.3125 Hz.