Sinusoidal Wave

Q.

What is the unit of phase constant?

Q.

How do you find the amplitude of two waves?

Q.

A string of length$L$fixed at both ends vibrates in its fundamental mode at a frequency $v$, and maximum amplitude $A$.

$\left(a\right)$ Find the wavelength and the wave number$k$.

$\left(b\right)$ Take the origin at one end of the string and the $X-$axis along the string. Take the $Y-$axis along the direction of the displacement. Take$t=0$ at the instant when the middle point of the string passes through its mean position and is going in the positive $y-$direction. Write the equation describing the standing wave.

Q. When a sound wave of wavelength $\lambda$ is propagating in a medium, the maximum velocity of the particle is equal to the wave velocity. The amplitude of wave is:

1. $\lambda$
2. $\frac{\lambda }{2}$
3. $\frac{\lambda }{2\pi }$
4. $\frac{\lambda }{4\pi }$

Q. A transverse wave on a string has an amplitude of 0.2 m and a frequency of 175 Hz. Consider a particle of the string at x = 0. It begins with a displacement y = 0, at t = 0, according to equation $y=0.2sin(kx\pm \omega t)$. How much time passes between the first two instant when this particle has a displacement of y = 0.1 m?

1. 1.9 ms
2. 3.9 ms
3. 2.4 ms
4. 0.5 ms

Q. A $27\text{mW}$ laser beam has a cross-sectional area of $10{\text{mm}}^2$. The magnitude of the maximum electric field in this EM wave is given by $[$Given permittivity of space ${\epsilon }_0=9\times {10}^{-12}\text{F/m}$, speed of light $c=3\times {10}^8\text{m/s}]$

1. $2\text{kV/m}$
2. $1\text{kV/m}$
3. $0.7\text{kV/m}$
4. $1.4\text{kV/m}$

Q. The maximum acceleration of a particle in a sinusoidal wave is (symbols have their usual meaning)

1. A${\omega }^2$
2. A$\omega$
3. A${\omega }^3$
4. A${\omega }^4$

Q. The equation for a wave travelling in $x$ direction on a string is given as
$y=10\sin (\pi t-0.5x)$, where $y$ and $x$ are in $\text{m}$ and time$\left(t\right)$ in $\text{sec}$. Find the acceleration of a particle at $x=\pi \text{m}$ at time $t=1\text{sec}$.

1. $-10\pi {\text{m/s}}^2$
2. $-10{\pi }^2{\text{m/s}}^2$
3. $5\pi {\text{m/s}}^2$
4. $-5\pi {\text{m/s}}^2$

Q. Write the equation of the wave shown in figure, if its position is shown at $t=0.6\text{sec}$. The wavelength is $15\text{cm}$ and amplitude is $4\text{cm}$ and the crest $X$ was at $x=0$ at $t=0$.

1. $y(x,t)=\left(2\text{cm}\right)\sin \left[\right(1.68\text{rad/s})t-(1{\text{cm}}^{-1}\left)x\right]$
2. $y(x,t)=\sin \left[\right(3.2\text{rad/s})t-(0.42{\text{cm}}^{-1}\left)x\right]$
3. $y(x,t)=\left(2\text{cm}\right)\cos \left[\right(3.2\text{rad/s})t-(0.42{\text{cm}}^{-1}\left)x\right]$
4. $y(x,t)=\left(4\text{cm}\right)\cos \left[\right(1.68\text{rad/s})t-(0.42{\text{cm}}^{-1}\left)x\right]$

Q. Kinetic energy $\left(\text{in joule}\right)$ in one wave length of transverse wave is twice of its average kinetic energy per unit length The wave length of the transverse wave is

1. $0.2\text{m}$
2. $2\text{m}$
3. $3\text{m}$
4. $4\text{m}$

Q. A transverse wave on a string travelling along +ve x-axis has been shown in the figure below:

The mathematical form of the shown wave is $y=\left(3.0cm\right)sin[2\pi \times 0.1t-\frac{2\pi }{100}x]$ where t is in seconds and x is in centimeters. Find the total distance travelled by the particle at (1) in 10 min 15 s, measured from the
instant shown in the figure and direction of its motion at the end of this time.

1. 6 cm, in upward direction
2. 6 cm, in downward direction
3. 738 cm, in upward direction
4. 732 cm, in upward direction

Q. A transverse wave having amplitude $A=\frac{4}{\pi }\text{m}$ and frequency $f=2\text{Hz}$ is travelling on a string of linear mass-density $\mu =1\text{kg/m}$. If the total kinetic energy associated with one wavelength of the wave is $16\text{J}$. Then the wavelength of the transverse wave is

1. $0.5\text{m}$
2. $0.25\text{m}$
3. $0.75\text{m}$
4. $0.15\text{m}$

Q. In the equation representing wave function,
$y=A\sin (kx-\omega t+{\varphi }_0)$
The term phase is defined as:

1. ${\varphi }_0$
2. ${\varphi }_0-\omega t$
3. $kx+{\varphi }_0$
4. $kx-\omega t+{\varphi }_0$

Q. The equation of a wave is $y(x,t)=0.1\sin [\frac{\pi }{3}(10x-30t)-\frac{\pi }{6}]\text{m}$.
Find the acceleration of the particle at $x=0.85\text{m}$ and $t=0.25\text{s}$
[Assume, ${\pi }^2=10$ ; $\uparrow$ denotes positive $y-$direction and $\downarrow$ denotes negative $y-$direction ]

1. $40{\text{m/s}}^2\uparrow$
2. $50{\text{m/s}}^2\downarrow$
3. $40{\text{m/s}}^2\downarrow$
4. $50{\text{m/s}}^2\uparrow$

Q. A transverse wave having amplitude $A=\frac{4}{\pi }\text{m}$ and frequency $f=2\text{Hz}$ is travelling on a string of linear mass-density $\mu =1\text{kg/m}$. If the total kinetic energy associated with one wavelength of the wave is $16\text{J}$. Then the wavelength of the transverse wave is

1. $0.5\text{m}$
2. $0.25\text{m}$
3. $0.75\text{m}$
4. $0.15\text{m}$

Q. Kinetic energy $\left(\text{in joule}\right)$ in one wave length of transverse wave is twice of its average kinetic energy per unit length The wave length of the transverse wave is

1. $0.2\text{m}$
2. $2\text{m}$
3. $3\text{m}$
4. $4\text{m}$