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Explain the concepts of fundamental frequency, harmonics and overtones in detail.

Answer» <html><body><p></p>Solution :Let us know keep the rigid boundries at x=0 and x=L and produce a standing wavves bt wiggling the string (as in plucking atrings in a guitar). Standing waves with a specofic wavelength are produced . Since the amplitude must vanish at the boundries, therefore, the displacement at tge boundry must satisfy the following conditions <br/> y(x=0,t)=0 and y(x=L,t)=0 <br/> Since, the nodes formed are at a distance `((lamda_(n))/(2))` apart , we have `n((lamda_(n))/(2))=L`, where n is an ineger, L is the <a href="https://interviewquestions.tuteehub.com/tag/length-1071524" style="font-weight:bold;" target="_blank" title="Click to know more about LENGTH">LENGTH</a> between the two boundaries and `lamda_(n)` is the specific wavelength that satisfy the <a href="https://interviewquestions.tuteehub.com/tag/specified-1221578" style="font-weight:bold;" target="_blank" title="Click to know more about SPECIFIED">SPECIFIED</a> boundry condition Hence <br/> Therefore, not all wavelengths are allowed, The (allowed) wavelengthsshould fit with specified boundary condition for n=1, the first mode vibration has specified wavelength `lamda_(1)=2L`. Similarly for n=2 the second mode of vibration has specific wavelength. <br/> `lamda_(2)=((2L)/(2))=L` <br/> The lowest natural frequency is called the fundamental frequency. <br/> `f_(1)=(v)/(lamda_(1))=((v)/(2L))` <br/> The second frequency is called the first over tone. <br/> `f_(2)=2((v)/(2L))=(1)/(L)sqrt(T/mu)` <br/> The third frequncy is called the second over tone .<br/> `f_(<a href="https://interviewquestions.tuteehub.com/tag/3-301577" style="font-weight:bold;" target="_blank" title="Click to know more about 3">3</a>)=3((v)/(2L))=3((1)/2Lsqrt(T/mu))` <br/> If natural frequency are written as integral multiple of fundamental frequencies then the frequencies are called harmonics. Thus the first harmonic is `f_(1)=f_(1)` (the fundamental frequency is called first harmonic), the second harmoinc is `f_(2)=2f_(1)`, the third harmonic is `f_(3)=3f_(1)` etc.</body></html>


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