Answer
Verified
91.2k+ 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.
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
Name the scale on which the destructive energy of an class 11 physics JEE_Main
Write an article on the need and importance of sports class 10 english JEE_Main
Choose the exact meaning of the given idiomphrase The class 9 english JEE_Main
Choose the one which best expresses the meaning of class 9 english JEE_Main
What does a hydrometer consist of A A cylindrical stem class 9 physics JEE_Main
A motorcyclist of mass m is to negotiate a curve of class 9 physics JEE_Main
Other Pages
The vapour pressure of pure A is 10 torr and at the class 12 chemistry JEE_Main
Electric field due to uniformly charged sphere class 12 physics JEE_Main
3 mole of gas X and 2 moles of gas Y enters from the class 11 physics JEE_Main
If a wire of resistance R is stretched to double of class 12 physics JEE_Main
Derive an expression for maximum speed of a car on class 11 physics JEE_Main
Velocity of car at t 0 is u moves with a constant acceleration class 11 physics JEE_Main