Question
Physics Question on Waves
An organ pipe A, with both ends open, has fundamental frequency 300Hz. The third harmonic of another organ pipe B, with one end open, has the same frequency as the second harmonic of pipe A. The lengths of pipe A and B are (speed of sound in air = 343m/s)
A
57.2 cm and 42.9 cm
B
57. 2 cm and 45.8 cm
C
42.9 cm and 32.2 cm
D
42.9 cm and 34.0 cm
Answer
57.2 cm and 42.9 cm
Explanation
Solution
Given that fundamental frequency of open organ pipe (A)=300Hz
f1=300Hz=2l1v… (i)
Frequency of second harmonic-of open organ pipe (A)=l1v
and frequency of third harmonic of closed organ pipe =4l23v
Now according to question l1v=4l23v
⇒l2l1=(34)… (ii)
Form E (i), we get
300=2l1343
l1=600343=52.16=57.2cm
Now from E (ii), we get
l2=43×l1
=43×57.2=42.9cm