Waves And Sound Question 5
Question 5 - 2024 (31 Jan Shift 1)
The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $60 cm$, the length of the closed pipe will be :
(1) $60 cm$
(2) $45 cm$
(3) $30 cm$
(4) $15 cm$
Show Answer
Answer: (4)
Solution:
$\frac{\lambda}{4}=L _1 \quad 2\left(\frac{\lambda}{2}\right)=\lambda$
$v=f \lambda \quad f _2=\frac{2 v}{2 L _2}$
$v=f _1\left(4 L _1\right) \quad f _2=\frac{v}{L _2}$
$f _1=\frac{v}{4 L _1}$
$f _1=f _2$
$\frac{v}{4 L _1}=\frac{v}{L _2}$
$\Rightarrow L _2=4 L _1$
$60=4 \times L _1$
$L _1=15 cm$
