Question

A string fixed between two rigid supports vibrates with a frequency of second harmonic. How

many loops will be obtained between the two fixed points.​

Answer 1

Given:

A string fixed between two rigid supports vibrates with a frequency of second harmonic.

To find:

Loops obtained between the two fixed points ?

Calculation:

Since the string is fixed between two rigid supports the two ends can be considered as nodes when the the wave undergoes resonance.

Now, the 2nd harmonic can be considered as attached in the image.

We can see that there are two loops when the resonance occurs in second harmonic.

$\boxed{\sf \: answer \: is \: 2 \: loops}$

Additional information and calculations:

Let length of wire be L , such that the frequency of second harmonic resonance be f :

$\sf\therefore \: \dfrac{ \lambda}{2} + \dfrac{ \lambda}{2} = L$

$\sf\implies \: \lambda = L$

Now, frequency will be :

$\sf \therefore \: f = \dfrac{velocity}{ \lambda}$

$\sf \implies\: f = \dfrac{v}{ L}$

Hence, frequency will be v/L for 2nd harmonic.