Sinusoidal Wave

Q.

A travelling wave passes a point of observation. At this point, the time interval between successive crests is 0.2 seconds and

[MP PMT 1990]

1. The wavelength is 5 m

2. The frequency is 5 Hz

3. The velocity of propagation is 5 m/s

4. The wavelength is 0.2 m

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. 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. 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. An object of density $\rho =500{\text{kg/m}}^3$ is hanging from a thin steel wire. The fundamental frequency of transverse standing wave on the wire is $200\text{Hz}$. The set up is now immersed in water, so that one third of the object's volume is submerged. The new fundamental frequency (in $\text{Hz}$) is: [Given : Density of water $\left({\rho }_w\right)=1000{\text{kg/m}}^3$]

1. $100$
2. $200$
3. $200\sqrt{3}$
4. $\frac{200}{\sqrt{3}}$

Q.

The equation of a transverse wave travelling on a rope is given by $y=10sin\pi (0.001x-2.00t)$ where y and x are in centimeters and t in seconds. The maximum transverse speed of a particle in the rope is about.

1. 63 cm/s

2. 75 cm/s

3. 100 cm/s

4. 121 cm/s

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. For a travelling wave represented by equation, $y=0.2\sin 2\pi (x-110t+\frac{1}{2})$ (SI units).
The phase difference between particles at $x_1=4.5\text{m}$ and $x_2=7\text{m}$ is

1. $\pi$
2. $3\pi$
3. $5\pi$
4. $7\pi$

Q.

Two vibrating strings are of same material but lengths l, 2l and radii 2r, r respectively are stretched under the same tension. Both are vibrating in their fundamental modes. The experimental arrangement is such that first string has both ends fixed, second string vibrates with one end fixed and other end as free.

If the frequencies of vibration of first and second wire are $n_1$ and $n_2$, then $\frac{n_1}{n_2}$= ________

1. 6

2. 3

3. 2

4. 4

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. The equation of a tranverse wave propagating through a medium is given by $y=10\sin (\pi t+0.5x)$. Choose the correct statement for the velocity of particle present at $x=0$.

1. At $t=0$, velocity of particle is $0\text{m/s}$
2. At $t=0.5\text{sec}$, velocity of particle is $\pi \text{m/s}$
3. At $t=3\text{sec}$, velocity of particle is $10\pi \text{m/s}$
4. At $t=0.5\text{sec}$, velocity of particle is $0\text{m/s}$

Q. For a travelling wave represented by equation, $y=0.2\sin 2\pi (x-110t+\frac{1}{2})$ (SI units).
The phase difference between particles at $x_1=4.5\text{m}$ and $x_2=7\text{m}$ is

1. $\pi$
2. $3\pi$
3. $5\pi$
4. $7\pi$