Question:

The fundamental frequency of a closed pipe is 220 Hz. If $\frac{1}{4}$ of the pipe is filled with water, the frequency of the first overtone of the pipe now is

Updated On: Jun 23, 2023
  • 220 Hz
  • 440 Hz
  • 880 Hz
  • 1760 Hz
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The Correct Option is C

Solution and Explanation

FundamentaI frequency of closed pipe $\hspace25mm n =\frac{v}{4l}=220\, Hz$ $\Rightarrow \hspace20mm v =220 \times 4l$ If $\frac{1}{4}$ of the pipe is filled with water then remaining length of air column is $\frac{3l}{4}.$ Now, fundamental frequency $=\frac{v}{4\big(\frac{3l}{4}\big)}=\frac{v}{3l}$ and First overtone= 3 $\times$ fundamental frequency. $\hspace35mm = 3 \times \frac{v}{3L} =\frac{3 \times 220 \times 4l}{3l}= 880\, Hz$
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Concepts Used:

Oscillations

Oscillation is a process of repeating variations of any quantity or measure from its equilibrium value in time . Another definition of oscillation is a periodic variation of a matter between two values or about its central value.

The term vibration is used to describe the mechanical oscillations of an object. However, oscillations also occur in dynamic systems or more accurately in every field of science. Even our heartbeats also creates oscillations​. Meanwhile, objects that move to and fro from its equilibrium position are known as oscillators.

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Oscillation- Examples

The tides in the sea and the movement of a simple pendulum of the clock are some of the most common examples of oscillations. Some of examples of oscillations are vibrations caused by the guitar strings or the other instruments having strings are also and etc. The movements caused by oscillations are known as oscillating movements. For example, oscillating movements in a sine wave or a spring when it moves up and down. 

The maximum distance covered while taking oscillations is known as the amplitude. The time taken to complete one cycle is known as the time period of the oscillation. The number of oscillating cycles completed in one second is referred to as the frequency which is the reciprocal of the time period.