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: Use wavelengths and length:
Open pipe overtone 1: $f = \frac{2v}{2L} = \frac vL$. Closed pipe overtone 2: $f = \frac{5v}{4L}$.

Step 2: Subtract:
$\frac{5v}{4L} - \frac vL = \frac{v}{4L} = 100$ Hz, so $\frac vL = 400$ Hz. The open pipe fundamental is $\frac{v}{2L} = 200$ Hz (A).

Final Answer:
200 Hz. \[ \boxed{200\text{ Hz}} \]