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:
Speed is always positive and it should have maximum and minimum values twice in one complete oscillation. Therefore the answer is C.

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 the nth harmonic has frequency of $n$ times of first harmonic frequency and the ratio of frequencies is 4/2=2. Using $v=f\lambda$ and knowing that the speed of the wave in the string $v$ is unchanged, the ratio of wavelengths is 1/2.

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:

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:
Sound travels faster in water. According to Snell's law, the waves will refract away from the normal as seen in options $A$ and $C$.

Because $v=f\lambda$ and f is constant across the boundary, favelength also increases when the speed increases as seen in choices $B$ and C.

Therefore C is the correct answer.

Explanation:
It can be seen on the diagram that when the waves cross the boundary, the wavelength decreases. At a boundary, the frequency of a wave is unchanged because the number of waves entering the boundary every second must equal the number of waves that leave the boundary every second.

From the relationship v=fλ, if f remains constant and $\lambda$ decreases, the $v$ must also decrease.

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:
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:

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:
Potential energy is in its maximum value at boundaries (extreme points), kinetic energy at a maximum value at equilibrium point. So at $t=0$, for $P$ kinetic energy is a maximum, for $Q$ potential energy is a maximum but kinetic energy is zero. For both masses, the kinetic energy will maximise every half cycle.

At t=T/2 again for $P$ kinetic energy is a maximum, for $Q$ potential energy is a maximum.

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

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.