The fundamental frequency of vibration of a s | vedclass

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(A) Given:Fundamental frequency $f = 50\,Hz$Mass of the string $m = 18\,g = 0.018\,kg$Linear mass density $\mu = 20\,g/m = 0.02\,kg/m$Step $1$: Find t

Vedclass · Accepted Answer

$90$

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(A) Given:Fundamental frequency $f = 50\,Hz$Mass of the string $m = 18\,g = 0.018\,kg$Linear mass density $\mu = 20\,g/m = 0.02\,kg/m$Step $1$: Find the length of the string $(L)$.We know that $\mu = \frac{m}{L}$,so $L = \frac{m}{\mu} = \frac{18\,g}{20\,g/m} = 0.9\,m$.Step $2$: Relate frequency to wave speed.For the fundamental mode of a string fixed at both ends,the length $L$ is equal to half the wavelength: $L = \frac{\lambda}{2}$,which implies $\lambda = 2L$.Substituting $L = 0.9\,m$,we get $\lambda = 2 	imes 0.9 = 1.8\,m$.Step $3$: Calculate the wave speed $(v)$.The speed of the wave is given by $v = f \lambda$.$v = 50\,Hz 	imes 1.8\,m = 90\,m/s$.Thus,the speed of the transverse waves is $90\,m/s$.

The fundamental frequency of vibration of a string stretched between two rigid supports is $50\,Hz$. The mass of the string is $18\,g$ and its linear mass density is $20\,g/m$. The speed of the transverse waves produced in the string is $..........\,m/s$.

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