Reflection and Refraction of Wave

A harmonic wave is travelling on a stretched string. At any particular instant, the smallest distance between two particles having same displacement, equal to half of amplitude is $8 \mathrm{cm}.$ Find the smallest separation between two particles which have same values of displacement (magnitude only) equal to half of amplitude.

The pulse shown in figure has a speed of $5 \mathrm{cm} {\mathrm{s}}^{-1}.$ If the linear mass density of the right string is $0.5$ that of the left string, find the ratio of the height of the transmitted pulse to that of the incident pulse.

Two wires of different linear mass densities are soldered together end to end and then stretched under a tension $F.$ The wave speed in the first wire is thrice than in the second. If a harmonic wave travelling in the first wire is incident on the junction of the wires and if the amplitude of the incident wave is, $A=\sqrt{13} \mathrm{cm},$ find the amplitude of reflected wave.

A harmonic wave is travelling on string $1.$ At a junction with string $2$ it is partly reflected and partly transmitted. The linear mass density of the second string is four times that of the first string, and that the boundary between the two strings is at $x=0.$ If the expression for the incident wave is $y_i=A_i\cos$$\left(k_{1}x-{\omega }_{1}t\right).$ Show that the average power carried by the incident wave is equal to the sum of the average power carried by the transmitted and reflected waves.

A plane wave $y=a\sin (kx+ct)$ is incident on a surface. Equation of the reflected wave is: $y^{\text{'}}=a^{\text{'}}\sin (ct-bx).$ Then which of the following statements are correct?

A harmonic wave is travelling on string $1.$ At a junction with string $2$ it is partly reflected and partly transmitted. The linear mass density of the second string is four times that of the first string, and that the boundary between the two strings is at $x=0.$ If the expression for the incident wave is $y_i=A_i\cos$$\left(k_{1}x-{\omega }_{1}t\right).$ What are the expressions for the transmitted and the reflected waves in terms of $A_p, k_1$ and ${\omega }_1?$

A progressive wave travels in a medium $M_1$ and enters into another medium $M_2$ in which its speed decreases to $75\%.$ What is the ratio of the amplitude of the Transmitted and the incident waves?

A progressive wave travels in a medium $M_1$ and enters into another medium $M_2$ in which its speed decreases to $75\%.$ What is the ratio of the amplitude of the Reflected and the incident waves ?

Consider the following wave functions:

$y=A\cos (\omega t+kx),$

Write the equations of reflected wave after reflection from a free and a fixed boundary. Also find the resulting stationary waves formed by the superposition of its reflected wave.

Consider the following wave functions:

$y=A\sin (\omega t+kx),$

Write the equations of reflected wave after reflection from a free and a fixed boundary. Also find the resulting stationary waves formed by the superposition of its reflected wave.

Consider the following wave functions:

$y=A\cos (kx-\omega t),$

Write the equations of reflected wave after reflection from a free and a fixed boundary. Also find the resulting stationary waves formed by the superposition of its reflected wave.

Consider the following wave functions:

$y=A\cos (\omega t-kx)$

Write the equations of reflected wave after reflection from a free and a fixed boundary. Also find the resulting stationary waves formed by the superposition of its reflected wave.

A progressive wave gets reflected at a boundary such that the ratio of amplitudes of the reflected and incident wave is $1: 2.$ Find the percentage of energy transmitted.

A bat emits the ultrasonic sound of frequency $1000 \mathrm{k}\mathrm{H}\mathrm{z}$ in air. If the sound meets a water surface, it gets partially reflected back and partially refracted (transmitted) in water. What would be the difference of wavelength transmitted to wavelength reflected (speed of sound in air $=330 \mathrm{m} {\mathrm{s}}^{-1}$. Bulk modulus of water $=2.25\times {10}^9, {\rho }_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}=1000 \mathrm{kg} {\mathrm{m}}^{-3})$.

A sound wave of wavelength $\lambda$ travels towards the right horizontally with a velocity $V$. It strikes and reflects from a vertical plane surface, travelling at a speed $v$ towards the left. The number of positive crests striking in a time interval of $3 \mathrm{s}$ on the wall is