Chapter 16: Q80P (page 477)

When played in a certain manner, the lowest resonant frequency of a certain violin string is concert A (440 Hz). What is the frequency of the (a) second and (b) third harmonic of the string?

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Step by step solution

Lowest frequency is $f_{1} = 440 Hz$

We have to usetheformula for nth harmonic frequency which is n timesthefundamental frequency.

Formula:

The frequency of oscillation of n-loops, $f_{n} = n \times \frac{v}{2 L} . . . . . . . . (1)$

The lowest frequency is given. It means that the first harmonic frequency is 440 Hz , and using equation (1) and the frequency, it is given as:

$440 = \frac{v}{2 L} . . . . . . (2)$

Now the second harmonic frequency using equations (1) and (2) is given as follows:

role="math" localid="1660993667219" $f_{2} = 2 \times \frac{v}{2 L} = 2 \times 440 = 880 Hz$

Hence, the value of second-harmonic frequency is 880 Hz

Third harmonic using equations (1) and (2) is given as follows:

$f_{3} = 3 \times \frac{v}{2 L} = 3 \times 440 = 1320 Hz$

Hence, the value of third-harmonic frequency is 1320 Hz

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