A tension of 400 N causes a 300 g wire of length 1.6 m to vibrate with a frequency of 40 Hz. What is the wavelength of the transverse waves? (1.15m)


Given:

Tension = 400 N
Total mass of wire = M = 300 g = 0.3 kg
Length of the wire = L = 1.6 m 
Frequency = f = 40 Hz 

To Find:

The wavelength of transverse wave = Î» = ?

Solution:

The general relation among wavelength (λ), speed (v), and frequency (f) is following:

v = f Î» 

or 

λ = `\frac{v}{f}` ------------(1)

So, first, we will find the speed v of the progressive waves along the wire which is given by

v = `\sqrt frac {TｘL}{M}`

v = `\sqrt frac {400 Nｘ1.3 m}{0.3 kg}`

v = 46.2 m s⁻¹

now putting values in equation (1)

λ = `\frac{46.2 m s⁻¹}{40 Hz}` 

λ = 1.6 m ------------Ans.



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