Energy of Wave

Q. A sinusoidal wave on a string is described by the wave function
$y=0.3\sin (1.6x-100t)$
where $x$ and $y$ are in $\text{metre}$ and $t$ is in $\text{second}$. The mass per unit length of this string is $10\text{g/m}.$ Determine the power transmitted to the wave.

1. $260\text{J}$
2. $360\text{J}$
3. $281\text{J}$
4. $320\text{J}$

Q. Which of the following phenomena is due to propagation of a wave?

1. Vibration of a window panel when a supersonic aircraft passes
2. Transportation of particles of a medium when a wave passes
3. Breaking of glasses by opera singers by singing
4. Both (a) and (c)

Q. Mark out the correct options.
(a) The energy of any small part of a string remains constant in a travelling wave.
(b) The energy of any small part of a string remains constant in a standing wave.
(c) The energies of all the small parts of equal length are equal in a travelling wave.
(d) The energies of all the small parts of equal length are equal in a standing wave.

Q. A transverse wave of amplitude $0.5\text{mm}$ and frequency $100\text{Hz}$ is produced on a wire stretched to a tension of $100\text{N}$. If the wave speed is $100\text{m/s}$. What average power is the source transmitting to the wire?

1. $60\text{mJ/s}$
2. $49\text{mJ/s}$
3. $40\text{mJ/s}$
4. $70\text{mJ/s}$

Q. A taut string for which $\mu =15\times {10}^{-2}\text{kg/m}$ is under a tension of $240\text{N}$. How much power must be supplied to the string to generate sinusoidal waves at a frequency of $18.0\text{Hz}$ and an amplitude of $18\text{cm}$?

1. $1280\text{W}$
2. $1300\text{W}$
3. $1240\text{W}$
4. $1220\text{W}$

Q. How is energy transmitted in a wave motion??

Q. A $400\text{Hz}$ wave with amplitude $2\text{mm}$ travels on a long string of linear mass density $5\text{g/m}$ kept under a tension of $50\text{N}$. Find the average power and total energy associated with the wave in a $2\text{m}$ long portion of the string.

1. $6\text{W}$ , $1\text{J}$
2. $1\text{W}$ , $6\text{J}$
3. $6.32\text{W}$ , $0.13\text{J}$
4. None of the above