Question

A sonometer wire 110 cm long produces a resonance with a tuning fork. When its length is decreased by 10 cm, 9 beats per second are heard. The frequency of tuning fork is __________.

• A. $90$ Hz
• B. $85$ Hz
• C. $82$ Hz
• D. $75$ Hz

Answer 1

Answer: (A)

$90$ Hz

We know that for a sonometer wire frequency is inversely proportional to length of sonometer wire.

Let the frequency of tuning fork be $f$.
This is in resonance with a sonometer wire of length $110cm$
So, $f=\frac{k}{110}$

When the length of the wire is decreased by $10cm$, new length of the wire $l^{\prime }=110-10=100cm$

Frequency changes to $f^{\prime }=\frac{k}{100}$
It is given that beats with a frequency of $9Hz$ are formed i.e. $f^{\prime }-f=9$

Therefore, $9=\frac{k}{100}-\frac{k}{110}$

$\Rightarrow k=9\times 1100$

So, $f=\frac{9\times 1100}{110}=90Hz$