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

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​:
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​:
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​:
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​:
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 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​:
Light will refract away from the normal at a boundary where there is an increase in speed as in a glass to air boundary. Answers A and C show this. A light ray will not refract at a boundary if its angle of incidence is 0°. It must therefore enter the curved edge aligned with the center of the straight side as in A. Therefore the answer is A.

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​:
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 $=2s$.

Since f=T1​ and $T=2s$, frequency is 0.5 Hz

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​:
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​:
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​:
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​:
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.