Question

Two sounding waves send waves at certain temperature in air of wavelength 50 cm and 50.5 cm repectively. The frequency of sources differ by 6 Hz. The velocity of sound in air at same temperature is

• A. \(330\text{ m/s}\)
• B. \(313\text{ m/s}\)
• C. \(303\text{ m/s}\)
• D. \(300\text{ m/s}\)

Hint:

Compare the first overtone of an open pipe with the second overtone of a closed pipe of the same length.

Answer 1

The Correct Option is C

Step 1: Open pipe:
Let the open pipe have fundamental \(f_0 = \frac{v}{2L}\). Its first overtone is the second harmonic, \(2f_0\).

Step 2: Closed pipe of the same length:
Closing one end gives a fundamental of \(\frac{v}{4L} = \frac{f_0}{2}\). A closed pipe has only odd harmonics, so its second overtone is the fifth harmonic: \(5\times\frac{f_0}{2} = 2.5f_0\).

Step 3: Difference:
\[ 2.5f_0 - 2f_0 = 0.5f_0 = 100\text{ Hz} \Rightarrow f_0 = 200\text{ Hz} \]

Final Answer:
The fundamental frequency of the open pipe is 200 Hz, option (A). \[ \boxed{200\text{ Hz}} \]