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Bats emit ultrasonic waves of very small wavelength (high frequencies) and so high speed. The reflected waves from an obstacle in their path give them idea about the distance, direction, nature and size of the obstacle.

Bats emit ultrasonic waves of large frequencies. When these wave are reflected from the obstacles in their path, they give them the idea about the distance, direction, size and nature of the obstacle.

Explosion at the bottom of lake or sea create enormous increase in pressure of medium (water). A shock wave is thus a longitudinal wave travelling at a speed which is greater than that of ordinary wave.

On a hot day, the velocity of sound will be more since (frequency proportional to velocity) the frequency of sound increases and hence its pitch increases. 

According to Sabine, acoustic of a room depends upon its time of reverberation which can be adjusted by placing such things in the room which may absorb the sound falling on them. As dampers and furniture in the room absorb the sound produced in the room, they help to control the time of reverberation of the room. Therefore the presence of draperies and furniture often improve the acoustics of the room.

Comparision of simple harmonic motion and angular harmonic motion

Consider the spring be made of combination of three springs in series each of spring constant k. The effective spring constant K is given by:

\(\frac{1}{K}=\frac{1}{k}+\frac{1}{k}+\frac{1}{k}=\frac{3}{k}\)

Or K = \(\frac{k}{3}\) 

Or k = 3K

∴ Time period of vibration of a body attached to the end of this spring.

T = \(2\pi\sqrt{\frac{m}{K}}\)

= \(2\pi\sqrt{\frac{m}{(\frac{k}{3})}}\)

= \(2\pi\sqrt{\frac{3m}{k}}\) …(i)

When the spring is cut into three pieces, the spring constant = k. Time period of vibration of a body attached to the end of this spring.

T₁ = \(2\pi\sqrt{\frac{m}{k}}\) …(ii)

From the equation (i) and (ii),

\(\frac{T_1}{T}=\frac{1}{\sqrt3}\)

Or  T₁ = \(\frac{T}{\sqrt 3}\)

Length for each loop = \(\frac{\lambda}{2}\)

Now,

L = \(\frac{n\lambda}{2}\) 

λ = \(\frac{2L}{n}\)   (1)

But v = vλ   or  λ = \(\frac{v}{u}\)

Putting in eqn, (1)

\(\frac{v}{u}=\frac{2L}{n}\)

v = \(\frac{n}{2L}\)u  

v = \(\frac{n}{2L}\sqrt{\frac{T}{\mu}}\)    [∵ u = \(\sqrt{\frac{T}{\mu}}\) ]

For n = 1, v₁ = \(\frac{1}{2L}\sqrt{\frac{T}{m}}\) = v₀

For n = 2, v₂ = \(\frac{1}{2L}{\sqrt{\frac{T}{m}}}\) = 2v₀

Therefore, u₁: u₂:u₃: u₄ = n₁: n₂: n₃:n₄

u₁: u₂:u₃: u₄ = 1: 2: 3: 4

The oscillation in which the loss of oscillator is compensated by the supplying energy from an external source are known as maintained oscillation.

In SHM, The velocity leads the displacement by a phase π/2 radians and acceleration leads the velocity by a phase π/2 radians.

No, it is a circular and periodic motion but not SHM.

(1) Periodic motion : A motion that repeats itself at definite intervals of time is said to be a periodic motion. 

Examples : The motion of the hands of a clock, the motion of the Earth around the Sun.

(2) Oscillatory motion : A periodic motion in which a body moves back and forth over the same path, straight or curved, between alternate extremes is said to be an oscillatory motion. 

Examples : The motion of a taut string when plucked, the vibrations of the atoms in a molecule, the oscillations of a simple pendulum.

[Note : The oscillatory motion of a particle is also called a harmonic motion when its position, velocity and acceleration can be expressed in terms of a periodic, sinusoidal functions-sine or cosine, of time.

No, it is circular and periodic motion but not to and fro about a mean position which is essential for S.H.M., ∴ it cannot be taken S.H.M.

(i) sin ωt - cos ωt

= \(\sqrt 2[sin\,\omega tcos\frac{\pi}{4}-\,cos\,\omega t\,sin\,\frac{\pi}{4}]\)

= \(\sqrt 2\, sin\,(\omega t\,-\,\frac{\pi}{4})\)

This function represents S.H.M., having period

T = \(\frac{2\pi}{\omega}\) and initial phase = − \(\frac{\pi}{4}\)rad.

(ii) sin²ωt = (1 – cos²ωt)

The function is periodic, having a period

T = \(\frac{2\pi}{2\omega}=\frac{\pi}{\omega}\)

But does not represent S.H.M.

Yes, uniform circular motion is the example of it.

The motion in which a body moves to and fro or back and forth repeatedly about a fixed point in a definite interval of time. Oscillatory motion is also called as harmonic motion. 

Example : The motion of the pendulum of a wall clock.

A motion, which repeat itself over and over again after a regular interval of time is called a periodic motion and the fixed interval of time after which the motion is repeated is called period of the motion. 

Examples : Revolution of earth around the sun (period one year).

Correct option is: (A) 1/6 m 

T = 2π√{l/g}

In both the cases, T is the same l ∝ g.

On the moon, the value of acceleration due to gravity is 1/6th of that on the surface of earth. So length of the second's pendulum is 1/6m.

l_m = (1/6)l_E =(1/6)m 

For a simple pendulum, time period (T) is given by; T = \(2\pi\sqrt{\frac{l}{g}}\)

At Earth, T = \(2\pi\sqrt{\frac{l}{g}}\)    (i)

At Moon, T’=\(v2\pi\sqrt{\frac{l'}{g'}}\)   (ii)

Here, T = T’ and g’ = \(\frac{1}{6}g\)

So, from equation (i) & (ii)

\(\frac {l}{g}=\frac{l'}{g'}\)

or,\(l'=\frac{g'}{g}\times l\)

= \(\frac{1}{6}g\times\frac{1}{g}\times l\) 

= \(\frac{1}{6}\times l\) 

= \(\frac{1}{6}\)× 100 cm

= 16.7 cm

1. Amplitude: Maximum displacement of the particle from the mean position is called amplitude. 

2. Period : Time taken by the particle to complete one oscillation is called time period. (T) 

3. Frequency : The number of oscillations completed by the particle in one second is called frequency (f) 

4. Phase: Phase of a particle is defined as the fraction of the time period that has elapsed since the particle last passed through its mean position in the positive direction.