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**Hint:**Tuning forks permit us to review the fundamental qualities of sound first hand. An implement emits a pure musical tone (after waiting a moment) because it vibrates when you strike it. There are two basic qualities of sound: One is the Pitch which will be high and low and the other one is the volume which may be loud and soft.

**Formula used:**

Number of beats,

$ \Rightarrow {\delta _Q} - {\delta _P}$

Where, ${\delta _Q}{\text{ and }}{\delta _P}$are the beats of $Q$and $P$respectively.

**Complete step by step solution:**

Here in the question since there is a decrease in tuning fork frequency by $1\% $ in the fork s.

Whereas in another have $2\% $ more frequency. So we can write it as $99$ and $102$ as we had taken this after removing the percentage. For details see the below it will make more clear.

So from the above, we can make a mathematical equation which will be like this,

According to the question,

$ \Rightarrow \dfrac{{{\delta _P}}}{{{\delta _S}}} = \dfrac{{99}}{{100}}$

And

$ \Rightarrow \dfrac{{{\delta _Q}}}{{{\delta _S}}} = \dfrac{{102}}{{100}}$

As we know beats are equal to

$ \Rightarrow {\delta _Q} - {\delta _P}$

Since the total number of the beat is 9

Therefore,

$ \Rightarrow 9 = \dfrac{{102}}{{100}}{\delta _S} - \dfrac{{99}}{{100}}{\delta _S}$

Calculating for the value of ${\delta _S}$, we get

$ \Rightarrow \dfrac{{9 \times 100}}{3} = {\delta _S}$

Therefore,

$ \Rightarrow {\delta _S} = 300Hz$

Now

$ \Rightarrow {\delta _P} = \dfrac{{99}}{{100}}{\delta _S}$

Again we will calculate the value for this, we get

\[ \Rightarrow \dfrac{{99}}{{100}} \times 300\]

Therefore.

$ \Rightarrow {\delta _P} = 297Hz$

Similarly,

$ \Rightarrow {\delta _Q} = \dfrac{{102}}{{100}}{\delta _S}$

Now putting the values which we had calculated earlier, we get

\[ \Rightarrow \dfrac{{102}}{{100}} \times 300\]

Therefore,

$ \Rightarrow {\delta _Q} = 306Hz$

**Hence, the option $\left( c \right)$ is the required frequency, which is $297Hz,306Hz$.**

**Note:**A tuning fork could be a sound resonator that could be a two-pronged fork. The prongs, known as tines, are made of a U-shaped bar of metal (usually steel). This bar of metal will move freely. It resonates at a selected constant pitch once set moving by putting it against an object. It sounds a pure musical tone when waiting for a flash to permit some high overtone sounds to die out.

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