Explanation:

The angular width of the first maximum;

• θ=λ/b

The central maximum has the twice angular width of the first maximum;

• θc=2λ/b

Since wavelength λ and slit width b are not changed, the angular width must be constant. Therefore, the answer is C.

Given that the angular width is constant, increasing the distance D will cause the size of the central maximum on the screen to double, which indicates that option A is incorrect.

Explanation:
Diffraction is the spreading out of a wave while passing through an obstacle or aperture. The door of the room can be considered as the aperture. When the wavelength of the wave is comparable with the aperture size, diffraction is greater. The wavelength of the sound wave is much larger than the wavelength of the light wave and closer to the size of the door. Therefore, sound waves diffract more while passing through the door and reach the student while light waves do not. The answer is A.

Explanation:

The single slit diffraction effect can not be ignored when slit width is not negligible. Therefore, there will be modulation of the interference pattern. Greater slit widths allow more light reach to screen and makes the fringes brighter. The fringe width is dependent on wavelength, slit separation and distance between screen and slits. None of them have changed. Therefore the fringe width is not affected.

Explanation:
C: Correct. In simple harmonic motion, acceleration and displacement always have opposite directions and are proportional

A: Incorrect. Since total energy is the sum of kinetic and potential energies, and the total energy is conserved, so at the time kinetic energy is zero the potential energy must have the maximum value. Since that's not represented in graphs I and II, A is not a correct answer

B: Incorrect. Velocity will be zero at positions of maximum magnitude of acceleration, considering that acceleration and displacement are proportional in magnitude and opposite in direction. So B is not a correct answer.

D: Incorrect The graph of velocity variation with time can be concluded from the slope of displacement variation with time, so the velocity will be zero at positions of maximum magnitude of displacement. Which makes D not a correct answer.

Explanation:

With the increase of slits, more light passes through the diffraction grating and incident on the screen. Therefore, the intensity of light increases. The width of the primary maxima is decreased with an increase in the number of slits.

Explanation:
To calculate the wave speed, we can use the wave equation:

v=λf

Since

• $\to$ v=λ/T

The wavelength is determined from either displacement-distance graph:

• $\lambda =4cm$

To calculate the period, we notice that the difference between the first and second graphs means that the wave has travelled one quarter of a wavelength. This means the period is 4 times the time given between the two displacement-distance graphs.

• T=4(1 s)=4 s

Therefore,

• v=λ/T=4/4=1cm s^−1

Looking at the two graphs, we can also see a crest that is moved 1$cm$ in 1 second, which gives a wave speed of 1 cm s^−1.

Explanation:
The wave is faster in medium $Y$ than in medium $X$. As a result, the ray representing the wave is expected to bend away from the normal, refracting into the original medium.

If the angle of incidence exceeds the critical angle, however, the angle of refraction will be undefined and the wave will undergo total internal reflection.

This is exactly what is shown by Option D, which is the correct response.

Option A shows the ray bending towards the normal, Option C shows no bending at all, and Option B shows an impossible path for the wave to travel.

Explanation:

Doppler effect only occurs when there is relative motion between the observer and the source. In this case, the satellite and receiver are motionless relative to each other. Therefore, there will be no change in frequency.

Explanation:
Recall for simple harmonic motion, a ∝−x, therefore the object experiences maximum negative acceleration at maximum positive displacement from equilibrium.

Explanation:
The speed of a wave depends on the medium, and the frequency of the wave depends on the source.

Here, the source of the travelling wave is the vibration of the speaker up and down, and the medium of that wave is the string.

Statement I is correct. A decrease in the frequency of the sound from the speaker results in a decrease in the frequency of the travelling wave in the string. The wave speed is constant, as the medium of the travelling wave remains the string. The wavelength is inversely proportional to the frequency according to the wave equation:

v=λf→λ=v/f

As a result, the wavelength must increase.

Statement II is also correct. A louder sound means that the amplitude of the longitudinal sound wave in the air is larger. This is caused by greater amplitude vibrations from the speaker, which also produces larger amplitude vibrations in the string.

Statement III is incorrect. As previously mentioned, the wave speed is constant as the medium remains the same. Even though the frequency of the wave has increased, the wavelength will decrease in proportion to keep the wave speed equal to the wavelength times the frequency.

Therefore, the correct answer is B, I and II only.

Explanation:

A greater slit width allows more light to reach the screen. This increases the intensity. So the peaks will be higher. The angular width of maxima is proportional with λ/b. An increase of slit width $b$ results in a decrease in angular width of the maxima. Angular width and width of maxima are proportional. Therefore, the maxima will be narrower.

Explanation:
The y axis cannot represent the velocity of the pendulum, as a velocity-position graph would also show negative velocities to represent motion in both directions.

The formula for kinetic energy is given by 1/2mω^2(0x^2 −x2), which would be parabolic in shape, opening downwards as is shown in the graph.

The potential energy of the bob should be less at the equilibrium position than in the positions where displacement is maximum.

Explanation:
For a circle of diameter $d$, circumference is $\pi d$. Thus the cicrumference in this case is $15\pi$. In this instance the distance travelled by the bob is exactly equal to twice its circumference. The shadow, therefore, has travelled two complete oscillations and is at exactly the same point at which it started. The displacement, therefore, is zero.

Explanation:
Two conditions must be satisfied to define motion as simple harmonic motion;

• The acceleration is proportional to the displacement.
• The acceleration and displacement are in opposite directions.

The second condition indicates the existence of a negative sign in front of the displacement and the first condition demands to have $x$ instead of x^2 in the expression. These two conditions are satisfied in B.

Explanation:
Since it is pulled down by 10$cm$, that is the maximum displacement and hence the amplitude.

If it takes 0.5 s to return to the equilibrium position, then the complete oscillation is $(0.5)(4)=2s$.

Since f=1/T and $T=2s$, frequency is 0.5Hz.

Explanation:
Intensity falls off significantly from the principal maximum to secondary maxima. It decreases to approximately 5 % of the initial value. The exact location of $X$ is not known. The maximum intensity that $X$ can have is 5 % of the initial value. Therefore, the ratio should be equal to or less than 0.05.

Explanation:
Since frequency is 0.05 Hz, T=1/f=1/0.05=20 s

The amplitude is $4cm$ on either side of the equilibrium position because in one full cycle it travels four amplitudes (16/4=4 cm

Explanation:

• f′=f(v/[v−us])

  Where f′= frequency detected by observer

  $f$ = source frequency

  $v$ = speed of sound in still air

The observed frequency is higher than the emitted frequency as the wavelength shortens due to the motion of the train. As the train speed does not change, the observed frequency will remain constant, although its intensity will increase.