Question

At a temperature of $27^{\circ }C$. two identical organ pipes produce notes of frequency $140Hz$.
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, $n_0=140Hz,T_0=27^{\circ }C=300K$ and
$T_2=57.75^{\circ }C=330.75K$
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.
$v_t=v_0\sqrt{\frac{330.75}{300}}=1.05v_0$
Hence, the beats produced in oragan pipe.
Number of beats, $n=n_t-n_0=140\times 1.05-140=7$
$\left(\because n_t=\frac{v_t}{4L}\text{ and }{n}_0=\frac{v_0}{4L}\right)$