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

Explanation:
The frequency of the vibration generator will be the same as the frequency of the wave in the string, 5Hz=5s^−1.

From the graph provided, the distance peak-to-peak is $5cm$, and so the wavelength of the wave is $5cm$.

As a result, the wave speed is:

v=λf=(5)(5)=25 cm s^−1

Explanation:
It is important to locate the mass when t=10s for identifying directions of velocity and acceleration. The time needed for mass to move from one end to the other end is $6s$. The motion of the mass is identical for both sides of the equilibrium position. Therefore, the time needed to cover from one end to equilibrium is $3s$. When mass moves for 10 seconds, it passes the equilibrium position for the second time towards point $X$ and is located between the equilibrium point and point $X$ as shown in the diagram below.

The direction of velocity is towards $X$ (right). The retarding force is always towards equilibrium. Therefore, the acceleration is also towards equilibrium (left).

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:
Waves are produced in the same medium. This means they have the same speed.

They also have the same period, implying that their wavelengths are also equal.

Since the waves start half a period apart, the phase difference between the sources is half a cycle, and remains constant since they are produced at the same frequency.

Point $C$ is five wavelengths from $A$, and four wavelengths from $B$, making the path difference one wavelength or a whole cycle. But after every single cycle, the two waves maintain a constant phase difference of $\pi$, leading to destructive interference.

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=fλ 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:
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 x2 in the expression. These two conditions are satisfied in B.

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:
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.

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 displacements in the diagram shows there are three antinodes and two nodes. This can be represented using a transverse standing wave pattern as shown.

The standing wave is in the second harmonic

For an open pipe, the second harmonic frequency is double that of the first harmonic frequency, therefore statement I is correct.

As the frequency has doubled and the speed of sound has remained the same, through v=fλ, the wavelength will be halved, or λ/2 which means that statement II in incorrect but statement III is correct.

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.