A stationary wave is established in a string, which is 120 cm long and fixed at both ends. The string vibrates in four segments, at a frequency of 120 Hz. Determine its wavelength and the fundamental frequency. (Ans: 6.6ｘ10⁻⁹ rad)



Data Given:


Length of the string = L = 120 cm = 1.2 m

Frequency for fourth harmonic = f₄ =  

Number of segment = n = 4 


To Find:

Wavelength of third harmonic = Î»₄ = ?

Fundamental frequency = f₁ = ?

Solution:

The general formula to find wavelength of n number of loops

λₙ =  `\frac{2L}{n}`

for 4 loops  (n = 4)

λ₄ = `\frac{2L}{4}`

by putting values

λ₄ = `\frac{2 ｘ 1.2 m}{3}`

λ₄ = 0.6 m ------------Ans. 1


Now to find fundamental frequency we have general formula  

fâ‚™ = n f₁

or

f₁ = `\frac{fâ‚™}{n}`

for n = 4

f₁ = `\frac{f_4}{4}`

putting values 

f₁ = `\frac{120 Hz}{4}`

v = 30 Hz --------------Ans. 2



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