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Since on a cloudy day, the air is wet i.e. it contains a lot of moisture, As a result of which the density of air is less and since velocity is inversely proportioned to density, hence velocity increases. 

If the difference in the distances of the loudspeakers from the listener is an odd multiple of λ/2, then due to destructive interference very feeble sound will be heard. If one loudspeaker is put off, the no interference will take place and the full sound of the other speaker will be heard.

Equation of the wave is represented by:

y = A sin (ωt - kx)

Differentiating it with respect to t, we get

O = A cos (ωt - kx) [ω - k.dx/dt]

And the velocity of wave,

dx/dy = ω/k

Similarly the velocity of the particle

dx/dy = ωA cos (ωt - kx)

And the acceleration of a point particle is given by

d²y/dt² = ω² A sin (ωt - kx)    ....(i)

Differentiating the y with respect to x

dx/dy = -Ak cos (ωt - kx)

and d²y/dx² = -Ak² sin (ωt - kx)   ...(ii)

From eqn. (i) and eqn. (ii) we get

d²y/dx² = v² d²y/dx²

Correct answer is (d) B, E

Correct answer is (a) increases

Fundamental frequency of an open organ pipe

v₀ = v/2L

Fundamental frequency of a closed organ pipe is,

v_c = v/4L

Hence, v₀/v_c = 2

or, v₀ = 2v_c

The person would be hearing nothing if he is moving away from the source with the speed of sound. It is so, because the relative velocity of sound waves with respect to the person is zero.

Therefore, the sound waves cannot strike the drum of the person's ears and no sensation of hearing is produced.

We are given that,

v = √{γp/ρ}

We know that pV = nRT

⇒ pV = m/M RT

where m is the total mass and M is the molecular mass of the gas.

p = m/M.RT/V = ρRT/M

⇒ p/ρ = RT/M

(a) For gas at constant temperature,

p/ρ = constant

As p increases, ρ also increases and vice versa. This implies that

v = √{γp/ρ} = const.

i.e., velocity is independent of pressure of the gas.

(a) Since p/ρ = RT/M

Therefore, v = √{γp/ρ} = √{γRT/M}

Clearly v α √T, i.e., Speed of sound in air increases with increase in temperature.

(c) Increase in humidity decreases the effective density of air.

Therefore, the velocity (v x 1/√ρ) increases.

Mass per unit length of the wire,

µ = \(\frac{2.10kg}{12.0m}\) = 0.175 kg m^-1

The speed of wave on a string is

given by, v = \(\sqrt \frac{T}μ \)

Given v = 343 ms^-1

∴ T = µv² =0.175 × 3432

= 20588.575 = 2.06×10⁴ N.

The periodic variations in the intensity of sound due to the superposition of two sound waves of slightly different frequencies are called beats. One rise and one fall of intensity constitute one beat. The number of beats produced per second is called beat frequency.

The lowest intensity of sound that can be perceived by the human ear is called threshold of hearing. 

The intensity of sound at any point may be defined as the amount of sound energy passing per unit time per unit area around that point in a perpendicular direction.

When a wave is reflected from a rigid boundary or a closed end, it is reflected back with a phase reversal or phase difference of radians but reflection at an open boundary takes place without any phase change.

The stages of large auditorium have curved backs because when speaker stands at or near the focus of curved surface his voice is rendered parallel after reflection from the concave or parabolic seer face. Hence the voice can be heard at larger distances.

The stringed instruments are provided with a hollow box called sound box. When the strings are set into vibration, forced vibrations are produced in the sound box. Since sound box has a large area, it sets a large volume of air into vibration. This produces a loud sound of the same frequency of that of the string. 

The hollow boxes in the instruments are set into forced vibrations along with the strings. The loudness is higher if area of the vibrating body is move. So, the hollow boxes attached increase the loudness of sound.

No, mechanical waves can not travel through vacuum.

Mechanical waves transfer only energy from one point to another.

Velocity of sound in air increases by 0.61 ms^-1, when temperature rises by 1°C

f' = (n +1)f

f – fundamental frequency, n = 1,2, 3….

for 1^st and 2^nd …. overtones.

[Frequency of the first over tone in a closed pipe is = 3f = 3 × 500 = 1500 Hz].

[Frequency of the first over tone in a closed pipe is f' = 3f = 3 × 500 = 1500 Hz].

[Reason: Frequency f ∝ 1/. As / is doubled f is halved].

Overtones, which are an integral multiple of the fundamental frequency, are called harmonics.

Number of beats per second

= \(\frac{10}{2} = 5\) 

∴ ∆ f = f₁ ~ f₂ = 5 Hz.

Frequencies greater than fundamental frequency are called overtones.

The vibration of a body with the lowest frequency is called the fundamental frequency.

(d) 5000 Hz

\(f' = (\frac{330 + 220}{330 -220})\) x 1000 = 5000 Hz

The wave formed due to the superposition of two identical waves travelling with the same speed in opposite directions is called a stationary wave or standing wave.

Reverberation is defined as the persistence of audible sound even after the source has ceased to produce the sound.

The time interval between two consecutive maxima or minima is called beat period. It is also equal to the reciprocal of beat frequency.

A) 320 sec^-1

n' = n(v+v_o/v-v_s) n

⇒ 400 = n(360 + 40/360 - 40)

⇒ n = 320cps

It is a kind of disturbance which travels through a medium due to the repeated vibrations of the particles of the medium about their mean positions, the disturbance being handed over from one particle to the next. In a wave both information and energy propagate from one point to another but there is no motion of matter as a whole through medium. 

Three types of waves: 

(i) Mechanical waves: The waves which requires a mechanical medium for their propagation are called mechanical waves or elastic waves. For their propagation, the medium must possess the properties of inertia and elasticity. For example, water waves, sound waves, etc. 

(ii) Electromagnetic waves: The waves which travel n in the form of oscillating electric and magnetic fields are called electromagnetic waves. Such waves do not require any material medium for their propagation. For example, visible light, radio waves, etc. 

(iii) Matter waves: The waves associated with microscopic particles, such as electrons, protons, neutrons, atoms, molecules, etc.

A wave that moves from one point of medium to another is called a progressive wave.

Characteristic of a musical sound: 

These are 

(i) Pitch: It is the characteristic of musical sound that helps the listener in distinguishing a shrill note from a grave (flat or dull) one. It depends on frequency. 

(ii) Quality: It is the characteristic of the musical sound that distinguishes between two sound of same pitch and loudness from one another. It depends on the number or intensity of overtones. 

(iii) Loudness: The sensation of hearing which enables us to distinguish between a loud and a faint sound is called loudness. It depends on intensity.

The unit of loudness of a sound is bel. The loudness of a sound is said to be 1 bel, if its intensity is 10 times that of the threshold of hearing.  

A series of notes arranged such that their fundamental frequencies have definite ratios is called a musical scale.