Question

A 160cm long string has two adjacent resonance at 85hz frequencies . calculate : 1- the fundamental frequency , 2- the speed of the wave

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Answer 1

Length=l=160cm=1.6m

Frequency=85Hz

#1

Fundamental frequency be v

`\\ \sf\bull\longmapsto v=(\\u)/(2\ell)`

`\\ \sf\bull\longmapsto v=(85)/(2(1.6))`

`\\ \sf\bull\longmapsto v=(85)/(3.2)`

`\\ \sf\bull\longmapsto v=26.6Hz`

#2

First we have to find wavelength

`\\ \sf\bull\longmapsto \lambda=(c)/(v)`

`\\ \sf\bull\longmapsto \lambda=(3* 10^8ms^(-1))/(26.6)`

`\\ \sf\bull\longmapsto \lambda=0.112* 10^8m`

`\\ \sf\bull\longmapsto \lambda=112* 10^5m`

`\\ \sf\bull\longmapsto \lambda=1.12* 10^6m`

Now..

Velocity be v

`\\ \sf\bull\longmapsto v=f\lambda`

• f is frequency

`\\ \sf\bull\longmapsto v=26.5*1.12* 10^6m`

`\\ \sf\bull\longmapsto v=29.68* 10^6`

`\\ \sf\bull\longmapsto v=2.9* 10^7m/s`