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It is not strictly simple harmonic because we make the assumption that Sinθ =θ, which is nearly valid only if θ is very small. 

Time period of a simple pendulum is,

T = 2π√{l/g}

When length is doubled, the time period

T' = √2 T

Since, time period is independent of the suspended mass, hence with the increase in mass, the time period of the pendulum will remain the same.

The stringed instrument are provided with hollow boxed in order to increase the surface area of vibration, which increases the loudness/ intensity (I) of the sound produces [As I ∝ a² ]. Moreover, the air inside the hollow box is set into forces vibration which also increases the loudness of sound produced.

No, the emission of light from atom is a random and rapid phenomena. The phase at a point due to two independent light sources will change rapidly and rapidly and randomly. Therefore, instead of beats, we shall get uniform intensity.

However, if light sources are laser beams of nearly equal frequencies, we may be able to observe the phenomenon of beats in light.

The audience is also absorber of sound. The total absorption in case of crowded hall is more, therefore, as per Sabine formula, reverberation time of a crowded hall is smaller than that of an empty hall.

(a) Time period : It is the least interval of time after which the periodic motion of a body repeats itself. S.l. units of time period is second. 

(b) Frequency : It is defined as the number of periodic motions executed by body per second. S.l unit of frequency is hertz (Hz).

(c) Displacement: Its deviation from the mean position is called Displacement.

It is a physical quantity, which completely express the position and direction of motion, of the particle at that instant with respect to its mean position. 

Y = a sin θ = a sin (ωt + φ₀) here θ = ωt + φ₀ = phase of vibrating particle. 

(i) Initial phase or epoch : It is the phase of a vibrating particle at t = 0. 

(ii) Same phase: Two vibrating particle are said to be in same phase, if the phase difference between them is an even multiple of n or path difference is an even multiple of (λ/2) or time interval is an even multiple of (T/2). 

(iii) Opposite phase : Opposite phase means the phase difference between the particle is an odd multiple of bar ω or the path difference is an odd multiple of λ or the time interval is an odd multiple of (T/2). 

(iv) Phase difference : If two particles performs S.H.M and their equation are y₁ = a sin (ωt + φ₁) and y₂ = a sin (ωt + φ₂) then phase difference ∆φ = (ωt + φ₂) – (ωt + φ₁) = φ₂ – φ₁ 

As \(v\propto\frac{1}{D}\) , therefore, wave speed becomes twice.

Here, v₀ = 331 ms^-1

Rise in temperature, t = 91ºC

Since velocity of sound is not affected by the change in pressure, therefore we have to see the effect of temperature alone.

As v₁ = \(v_0\sqrt{\frac{273+t}{273}}= 331\sqrt{\frac{273+91}{273}}\)

= 331\(\sqrt{1+\frac{91}{273}}\) = 331\(\sqrt{1+\frac{1}{3}}\)

= 331 × \(\frac{2}{\sqrt 3}\) = 382.2 ms^-1

as \(v\propto\sqrt T\), therefore, wave speed becomes twice.

Uniform form circular motion can be thought of as two simple harmonic motion operating at right angle to each other. 

When two sound waves of slightly different frequencies, travelling in a medium along the same direction, superimpose on each other, the intensity of the resultant sound at a particular position rises and falls regularly with time. This phenomenon is called beats.

Beat period : The time interval between two successive beats (i.e. two successive maxima of sound) is called beat period. 

Beat frequency : The number of beats produced per second is called beat frequency.

Time period 

√2 times, as T α √l