Resonance: examples and uses - class-XI

A suction at the end of the tube draws air from further up the tube, and that in turn draws air from further up the tube and so on. So the result is that a pulse of high pressure air travelling down the tube is reflected as a pulse of low pressure air traveling up the tube. So the pressure wave has been reflected at the open end, with a change in phase of 180. In the open-open pipe, there is such a reflection at both ends. So the above argument is false.

For $I^{st}$ resonance

when one object vibrating at the same natural frequency of a second object forcesis called resonance.

$A=\dfrac{c}{a+b-c}$ : When  b = 0, a = c
Amplitude $A\rightarrow \infty$. This corresponds to resonance

Answer is C.

Resonance is a phenomenon that consists of a given system being driven by another vibrating system or by external forces to oscillate with greater amplitude at some preferential frequencies. Frequencies at which the response amplitude is a relative maximum are known as the system's resonant frequencies, or resonance frequencies. 
When both the bodies vibrate, they will start to vibrate with the same frequency.

One example of resonance involving visible and invisible light in the electromagnetic spectrum is resonance fluorescence. Fluorescence itself is a process whereby a material absorbs electromagnetic radiation from one source, then re-emits that radiation on a wavelength longer than that of the illuminating radiation. 

$Answer:-$ A,B,C,D

Resonance is a phenomenon in which the periodic oscillatory force acting on an object has a frequency of vibration same as the natural frequency of the object. In this, the object vibrates with a large amplitude.

$Answer:-$ A 

Resonance is cause of sound production in musical in instrument. this statement is true. Generally musical instrument have a hollow chamber, it contains air particle. when vibration is produced, it may be in the objects attached to it, the frequency of this object may match with a natural frequency of air particle inside the hollow chamber. Thus the air particles start to vibrate with the large amplitude which produces large sound. 

$Answer:-$ A

$\begin{array}{l} { l _{ 1 } }+e=\frac { V }{ { 4f } } \to \left( i \right)  \ { l _{ 2 } }+e=\frac { { 3V } }{ { 4f } } \to \left( { ii } \right)  \ Sub, , \left( { ii } \right) , , & , , \left( i \right)  \ { l _{ 2 } }-{ l _{ 1 } }=\frac { { 2V } }{ { 4f } }  \ { l _{ 2 } }-{ l _{ 1 } }=\frac { V }{ { 2f } }  \ \frac { { \Delta \left( { { l _{ 2 } }-{ l _{ 1 } } } \right)  } }{ { { l _{ 2 } }-{ l _{ 1 } } } } =\frac { { \Delta V } }{ V }  \ \Delta V=2f\Delta \left( { { l _{ 2 } }-{ l _{ 1 } } } \right) =2f\left( { \Delta { l _{ 1 } }+\Delta { l _{ 2 } } } \right) ......for, , man, , error \ =2\times 512\times \left( { 0.1+0.1 } \right) =204.8, , cm/s \end{array}$

This is a resonance in the circuit--- when you have a bunch of different

frequencies driving a resonant system, the response is only strong for

those frequencies which are close to the natural frequency of the

resonant oscillator. The frequency dependent amplification  is used to done through the resonance circuit for a desired frequency.

Third overtone of a closed pipe is 7v/4L1. First overtone of an open pipe is 2v/2L2 = v/L2. Equating: 7/4L1 = 1/L2. Thus L1/L2 = 7/4.

at resonance,the damping force becomes small enough so that the resulting oscillations have large amplitude.

The first resonant is$:-$

$f = \dfrac{nV}{2\ell}$

$1000 = \dfrac{n \times 332}{2 \times 16.6 \times 10^{-2}}$

$10 = \dfrac{n \times 332}{33.2}$

$n = 1$

The resonant frequency is always equal to natural frequency, hence option C is correct.

Resonance is a special case of forced vibrations, when frequency of the driving force is equal to the natural frequency of the body.
Resonance is the result of an external force vibrating at the same frequency as the natural frequency of a system. Natural frequency is a characteristic of every machine, structure and even animals. Often, resonance can be confused with the natural frequency or critical frequency. If equipment is operating in a state of resonance, the vibration levels will be amplified significantly, which can cause equipment failure and plant downtime. It is, therefore, important that the running speed of equipment be out of the resonance range.

At resonance, amplitude of oscillation is maximum
$\quad \Rightarrow 2\omega^2 - 36\omega + 9$ is maximum
$\quad \Rightarrow 4\omega - 36 = 0$ (derivative is zero)
$\quad \Rightarrow \omega = 9$

As the mother maintains the same tempo as the motion of the swing, it means frequency of mother and the swing is same, there is resonance. When mother tries to push at a faster tempo, frequency of mother changes and resonance is disturbed due to which, the arc of swing (amplitude) decreases.

A vibrating object will pick out its resonant frequencies from a complex excitation and vibrate at those frequencies, essentially "filtering out" other frequencies present in the excitation.

By turning ultrasound waves to the natural frequency of a kidney stone, we rely on resonance to parcels which the stones consist of vibrate with large amplitude and at a certain moment, this vibration causes breakdown of stone into pieces. So the given statement is true.

Resonance in an electrical circuit is a phenomenon in which the inductive reactance and the capacitive reactance become equal and cancel each other.

In a closed pipe : length of the pipe is length of the air column in fundamental.

If there was no damping in the swing, the swing would move with larger and larger amplitudes. However, most physical systems have damping, which limits the size of the amplitude. If you don not have damping the amplitudes will go to infinity.