Q. 46

# Three resonant fr

Answer :

A. 30 Hz B. 3rd, 5th and 7th

C. 2nd, 4th and 6th

D. 48 m s^{−}^{1}

The highest fundamental frequency is the gcd (greatest common divisor) of all other frequencies.

Since, we know that gcd of 90,150 and 210 is 30, so,

(A)

Now, f_{1, f}2, f_{3} are integral multiples of f.

_{1}=3

_{2}=5

_{3}=7 (B)

We know that nth overtone is (n+1)th frequency.

So, 3f -> 2^{nd} overtone and 3^{rd} harmonic.

So, 5f -> 4^{th} overtone and 6^{th} harmonic.

So, 7f -> 6^{th} overtone and 7^{th} harmonic. (C)

We know that, _{1}=

So,

We get, K=48 m/s (D)

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