Answer

Verified

20.4k+ views

**Hint:**In this solution, we will calculate the gravitational force exerted by the ring on the sphere. The force exerted by one on the other will have the same magnitude but opposite directions.

**Formula used:**In this solution, we will use the following formula:

-Resonant frequencies for closed pipe: $f = \dfrac{{nv}}{{4l}}$ where $n$ has odd values

- Resonant frequencies for open pipe: $f = \dfrac{{nv}}{{2l}}$ where $n$ are all positive integers

**Complete step by step answer:**

In the situation given to us, we want to find a frequency for which both the pipes can resonate. To find such a frequency, let us find the first few frequencies of resonance for both the pipes.

For the closed pipe, the frequencies of resonance can be found from

$f = \dfrac{{nv}}{{4l}}$

Substituting $v = 320\,m/s$ and $l = 1\,m$, we get

$f = n(80)$ where $n$ are odd.

So the first few frequencies are

$f = 80,240,400....$

For the open pipe, the frequencies of resonance will be

$f = \dfrac{{nv}}{{2l}}$ where $n$ are all integers

Substituting $v = 320\,m/s$ and $l = 1.6\,m$, we get

$f = n(100)$

So the first few frequencies are

$f = 100,200,300,400\,Hz$

So we can see that both the open and the closed pipe will resonate at 400 Hz. For the open pipe, the order or resonance will be the fifth harmonic and for the open pipe, it will be the fourth harmonic.

**Hence the correct choice is option (D).**

**Note:**While both the pipes resonate for 400 Hz, they can also resonate for higher frequency values but they are not given in the options. Also, the frequency at which both pipes will resonate doesn't need to correspond to the same order of resonance for both the pipes as well.

Recently Updated Pages

If a wire of resistance R is stretched to double of class 12 physics JEE_Main

Let f be a twice differentiable such that fleft x rightfleft class 11 maths JEE_Main

Find the points of intersection of the tangents at class 11 maths JEE_Main

For the two circles x2+y216 and x2+y22y0 there isare class 11 maths JEE_Main

The path difference between two waves for constructive class 11 physics JEE_MAIN

What is the difference between solvation and hydra class 11 chemistry JEE_Main

Other Pages

In order to convert Aniline into chlorobenzene the class 12 chemistry JEE_Main

A closed organ pipe and an open organ pipe are tuned class 11 physics JEE_Main

The correct order increasing acidic strength is A Phenol class 12 chemistry JEE_MAIN

The mole fraction of the solute in a 1 molal aqueous class 11 chemistry JEE_Main

Which of the following is not a redox reaction A CaCO3 class 11 chemistry JEE_Main

Assertion The melting point Mn is more than that of class 11 chemistry JEE_Main