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(x0^2−x^2), 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​:

When the observer and source of the wave are approaching each other, the observed frequency is greater than the frequency of the produced wave. There is no relative motion between the car and the car driver. Therefore, $f$ is equal to the frequency of the sound of the horn.

Since the observed frequency is greater than the original frequency of the sound of the horn, there should be a relative approach between the car and the cyclist. This can only happen when the car has a greater speed than the cyclist according to the given figure.

Explanation​:
The object is going fastest through the equilibrium position. At this location, all of the energy of the system is kinetic energy. There is zero elastic potential energy at this point as there is no displacement in the spring.

Explanation​:
The fringe separation equation is given by s=λ/Dd where $s$ is the fringe separation, λ is the wavelength, $D$ is the distance between the double slit barrier and the screen and s is the distance between the two slits on the double slit barrier. The question is asking which change will increase the value of s.

• A. Moving the screen closer to the double slit barrier will decrease $D$. Since $D$ is directly proportional to $s$, $s$ will also decrease.
• B. Violet light has a higher frequency / shorter wavelength than blue light. Using violet light instead of blue light will decrease the value of $\lambda$, and since $\lambda$ is also directly proportional to $s$, $s$ will subsequently decrease.
• C. Since $d$, the space between the two slits on the double slit barrier, is inversely proportional to $s$, as $d$ decreases, $s$ will increase.
• D. As long as the aperture is not completely closed, it will have no bearing on the spacing of the double slit interference pattern and will only reduce its intensity. The purpose of the single slit is to produce coherent light through diffraction, which then falls on the double slits.

Explanation​:
A wave travelling on a rope is an example of a transverse wave, where particles of the medium move up and down in a direction perpendicular to the direction of propagation. As the wave moves to the right, particle $P$ oscillates only up and down.

After half a period, the particle will be in the position shown below.

The wave is moving to the right. This means that a very short time after the current position, the solid line representing the waveform will be higher at the current position of $P$. As a result, point $P$ is moving upwards, and the velocity vector will be directed upwards.

To determine the magnitude of the velocity, we can recognize that because particle P has moved through half a period of its cycle, particle $P$ will be displaced from equilibrium the exact same distance as before - half of the amplitude.

This means that the particle will be moving at the exact same speed as before.

Explanation​:
Acceleration is proportional to the resultant force. Therefore, force and acceleration must be in the same direction

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​:
The principle of superposition states that the resultant wave is the sum of displacement from equilibrium of each wave.

The amplitude of the wave is the maximum displacement from equilibrium, which can be read off the graph as $7cm-5cm=2cm$.

Since each of the waves have an amplitude of 2cm and the equilibrium water level is $5cm$, after superimposing the two waves we find that the amplitude of the resultant wave is $4cm$.

Therefore, the maximum and minimum water levels can be determined as: 5cm+4 cm=9 cm for the maximum level and $5cm-4cm=1cm$ for the minimum level.

Explanation​:

The distance between wavefronts is equal to the wavelength. Since the wavefronts towards the child are more separated than wavefronts in the other direction, the child will receive wavefronts less frequently. Therefore, the child hears the sound with less frequency than $f$. The observed frequency is less than the frequency of the wave created by the source when the source and observer are receding from each other.

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

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.

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 energy of the incident pulse is shared with reflected and transmitted pulses. Therefore, the amplitude of the incident pulse should be greater than the one of the reflected pulse. Pulses are inverted after reflection from the heavy boundaries. Hence, the incident pulse should have a negative displacement. Therefore the answer is C.