1.

What is the ratio of the first three harmonics produced in a stretched string fixed at two ends ?

Answer»

Answer:

To FIND:

Ratio of frequency of 1st 3 harmonics on a stretched string fixed at 2 ends.

Concept:

When the string is fixed at 2 ends , it means that there is formation of nodes(of standing WAVES) at the 2 ends.

Harmonics are integral frequencies of a reference frequency.

Diagram:

Please look at the ATTACHED photo to understand better.

Calculation :

LET string length be L and wavelengths be λ

For 1st harmonic : L = λ/2 => λ = 2L

freq.1 = \dfrac{v}{ \lambda} = \dfrac{v}{2L}

For 2nd harmonic : L = λ/2 + λ/2 = λ

freq.2 = \dfrac{v}{ \lambda} = \dfrac{v}{L}

For 3rd harmonic : L = λ/2 × 3 = 3λ/2

=> λ = 2L/3

freq.3 = \dfrac{v}{ \lambda} = \dfrac{v}{ (\frac{2L}{3}) } = \dfrac{3v}{2L}

So the ratio is as follows :

freq1 : freq.2 : freq3

= 1 : 2 : 3

So final answer :

\boxed{ \huge{ \blue{1 : 2 : 3}}}


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