The fundamental frequency of an open organ pipe at $15^{o} C$ is $156 Hz$ . At what temperature, will the fundamental frequency be $160 Hz$ ? neglect expansion of tube .

Open in App

Solution

We know that for open organ pipe first resonance occurs when
$l = \frac{λ}{2}$ or $λ = 2 l$
Hence
$156 = \frac{v_{15}}{2 l}$
$160 = \frac{v_{t}}{2 l}$
Also we know that velocity of sound $v_{T} \propto T$
$∴ \frac{v_{15}}{v_{t}} = \frac{156}{160} = \sqrt{\frac{273 + 15}{273 + t}}$
$∴ \frac{288}{273 + t} = \frac{39}{40} \times \frac{39}{40} :$
$273 + t = \frac{288 \times 40 \times 40}{39 \times 39} = \frac{32 \times 40 \times 40}{169} = \frac{51200}{169} = 303$
$∴ t = 303 - 273 = 30^{o} C$

Why this question?

Caution: While using the expression that velocity of sound at any temperature $T$ , $v_{T} \propto T$ , remember to take temperature $T$ in kelvin scale.

Suggest Corrections

Similar questions

Q. An open pipe vibrating in its fundamental frequency is suddenly closed at one end. As a result, the frequency of the third harmonic of the closed pipe is found to be higher by

100 Hz

. The fundamental frequency of the open pipe is :-

Q. In an open organ pipe, the fundamental frequency is 30Hz. If the organ pipe is closed at one end, the fundamental frequency will be

Q. The fundamental frequency of an open pipe is 30 Hz. If one end of the pipe is closed, then the fundamental frequency will be

Q. A closed organ pipe resonates in its fundamental mode at a frequency of 200 Hz with

O_{2}

in the pipe at a certain temperature. If the pipe now contains 2 moles of

O_{2}

and 3 moles of ozone, than what will be the fundamental frequency of same pipe at same temperature ?

An open pipe is suddenly closed at one end and with the result frequency of third harmonic of the closed pipe is found to be higher by 100 Hz than the fundamental frequency of the open pipe. What is the fundamental frequency of the open pipe?

Join BYJU'S Learning Program

The fundamental frequency of an open organ pipe at 15oC is 156 Hz. At what temperature, will the fundamental frequency be 160 Hz? neglect expansion of tube .

The fundamental frequency of an open organ pipe at $15^{o} C$ is $156 Hz$ . At what temperature, will the fundamental frequency be $160 Hz$ ? neglect expansion of tube .