Question

A vibrating source over the mouth of a closed organ pipe is in unison at temperature T .The beats produced when temperature rises by t are N.Find the frequency of the vibrating source:

• A. 5N/3t
• B. 2NT/t
• C. 2N(t-T)/t
• D. N(t+T)/t

Answer 1

The correct option is A 5N/3t

Closed organ pipe $f=\frac{V}{4l}$ ……….$\left(1\right)$ (v$=$ speed of s and at T)

$\Rightarrow$ Source has frequency$=$f

Now when $T+t$

$f^{\prime }=\frac{V(1+0.6t)}{4l}$ …………$\left(2\right)$

Given that $f^{\prime }-f=N$ …………$\left(3\right)$

$\Rightarrow$ Dividing $\left(1\right)$ by $\left(2\right)$, we get

$\frac{f}{f^{\prime }}=\frac{1}{1+0.6t}$

$\Rightarrow f^{\prime }=f(1+0.6t)$

$\Rightarrow f^{\prime }-f=f(1+0.6t)-f=0.6tf$

but $f^{\prime }-f=N$

$\Rightarrow N=0.6tf$

$\Rightarrow f=\frac{N}{0.6t}=\frac{5N}{3t}$.