Question

At a temperature of $27^{\circ}C$. two identical organ pipes produce notes of frequency $140\, Hz$.
If the temperature of one pipe is raised to $57.75^{\circ}C$. the number of beats produced per second is

• A. 7
• B. 5
• C. 3
• D. 9

Answer 1

Answer: (A)

Here, $n_{0}=140\, Hz , T_{0}=27^{\circ} C =300 \,K$ and
$T_{2}=57.75^{\circ} C =330.75 \,K$
The variation of speed of sound with temperature,
$\frac{v_{t}}{v_{0}}=\sqrt{\frac{T}{T_{0}}}$
Let $v_{0}=$ speed of sound at the room temperature.
$v_{t}=v_{0} \sqrt{\frac{330.75}{300}}=1.05 \,v_{0}$
Hence, the beats produced in oragan pipe.
Number of beats, $n=n_{t}-n_{0}=140 \times 1.05-140=7$
$\left(\because n_{t}=\frac{v_{t}}{4 L} \text { and } n_{0}=\frac{v_{0}}{4 L}\right)$