Assertion (A): For a string fixed at both ends, the frequency of the third harmonic is three times the frequency of the fundamental mode. Reason (R): In a string fixed at both ends, the wavelength of

Question

Assertion (A): For a string fixed at both ends, the frequency of the third harmonic is three times the frequency of the fundamental mode.

Reason (R): In a string fixed at both ends, the wavelength of the third harmonic is one-third the wavelength of the fundamental mode. A. Both A and R are true and R is the correct explanation of A. B. Both A and R are true but R is not the correct explanation of A. C. A is true but R is false. D. A is false but R is true.

TestHub · Accepted Answer

For a string fixed at both ends, the fundamental mode (first harmonic) has a wavelength $λ_{1} = 2 L$ , where $L$ is the length of the string. Its frequency is $f_{1} = v / λ_{1} = v / (2 L)$ .

The third harmonic corresponds to a standing wave with three loops, meaning its wavelength is $λ_{3} = 2 L /3$ . Its frequency is $f_{3} = v / λ_{3} = v / (2 L /3) = 3 v / (2 L) = 3 f_{1}$ . Thus, both the assertion and the reason are true, and the reason correctly explains why the frequency of the third harmonic is three times that of the fundamental mode.

Physics - Wave on String Question with Solution | TestHub

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