Sound Wave:Displacement Equation

Q.

A traveling wave in a stretched string is described by the equation;

y = A sin (kx- $\omega$t). The maximum particle velocity is :

1. A $\omega$

2. $\frac{\omega }{k}$

3. $\frac{d\omega }{dk}$

4. $\frac{x}{\omega }$

Q.

A wave is represented by the equation

y = (0.001 mm) sin[(50 $s^{-1}$)t + (2.0 $m^{-1}$)x].

1. The wavelength = 2.0 m.

2. The wave velocity = 100 m/s.

3. The frequency = $\frac{25}{\pi }$ Hz.

4. The amplitude = 0.01 mm.

Q.

The displacement of a particle in string stretched in X direction is represented by y. Among the following expressions for y, those describing wave motions are

1. cos($k^3$ $x^3$ - ${\omega }^3$ $t^3$)

2. 

3. 

4. 

Q.

A traveling wave in a stretched string is described by the equation;

y = A sin (kx- $\omega$t). The maximum particle velocity is :

1. 

2. 

3. 

4. A ω

Q.

A simple harmonic wave of amplitude 2 units is travelling along x - axis. At a given instant, displacements for two different particles on the wave are 1 unit and $\sqrt{2}$
units. If the wavelength of wave is $\lambda$, find the distance between them.

1. λ/12

2. λ/8

3. λ/24

4. λ/16

Q. The equation of a sound wave in air is given by $\Delta p=0.09\sin (400t-9x)$ where all variable are in SI units. If the equilibrium pressure of air is $1$ atm, then

[$1\text{atm}=1.013\times {10}^5{\text{N/m}}^2$]

1. Frequency of sound wave is $\frac{200}{\pi }\text{Hz}$.
2. Speed of the sound wave is $90\text{m/s}$.
3. Maximum pressure at a point is $(1.013\times {10}^5+0.09){\text{N/m}}^2$.
4. Minimum pressure at a point is $(1.013\times {10}^5-0.09){\text{N/m}}^2$.

Q.

The displacement of a particle in string stretched in X direction is represented by y. Among the following expressions for y, those describing wave motions are

1. cos($k^3$ $x^3$ - ${\omega }^3$ $t^3$)

2. $k^2$ $x^2$ - ${\omega }^2$ $t^2$

3. cos (kx + $\omega$ t)

4. cos($k^2$ $x^2$ - ${\omega }^2$ $t^2$)

Q. displacement time equation of a particle executing simple harmonic motion is x=4sinwt + 3sin(wt+pi/3). given x is in cm and time is in sec. find the amplitude of oscillation

Q. (i) For the wave on a string described in Exercise do all the points on the
string oscillate with the same (a) frequency (b) phase (c) amplitude ? Explain
your answers (ii) what is the amplitude of a point 0.375 m away from one end ?

Q. The displacement of a particle along x axis is given by x=acos^2wt. Find if it correspond to SHM or not. Find its frequency

Q.

A wave is represented by the equation

y = (0.001 mm) sin[(50 $s^{-1}$)t + (2.0 $m^{-1}$)x].

1. The wave velocity = 100 m/s.

2. The wavelength = 2.0 m.

3. The frequency = $\frac{25}{\pi }$ Hz.

4. The amplitude = 0.01 mm.

Q. One end of a long string of linear mass density 8.0 × 10–3 kg m–1 is connected to an electrically driven tuning fork of frequency 256 Hz. The other end passes over a pulley and is tied to a pan containing a mass of 90 kg. The pulley end absorbs all the incoming energy so that reflected waves at this end have negligible amplitude. At t = 0, the left end (fork end) of the string x = 0 has zero transverse displacement (y = 0) and is moving along positive y-direction. The amplitude of the wave is 5.0 cm. Write down the transverse displacement y as function of x and t that describes the wave on the string.

Q. The transverse displacement of a string (clamped at its both ends) is given by
$y(x,t)=0.06\sin \left(\frac{2\pi x}{3}\right)\cos \left(120\pi t\right)$
where x and y are in m and t in s. The length of the string is 1.5 m and its mass is $3.0\times {10}^{-2}$ kg.
Answer following :
(a) Does function represent a travelling wave or a stationary wave?
(b) Interpret the wave as a superposition of two waves travelling in opposite
directions. What is the wavelength, frequency, and speed of each wave ?
(c) Determine the tension in the string.

Q. The displacement of a particle along x axis is given by x=asin^2wt. Find if it correspond to SHM or not. Find its frequency

Q.

A simple harmonic wave of amplitude 2 units is travelling along x - axis. At a given instant, displacements for two different particles on the wave are 1 unit and $\sqrt{2}$ units. If the wavelength of the wave is $\lambda$, find the distance between them.

1. $\frac{\lambda }{12}$

2. $\frac{\lambda }{8}$

3. $\frac{\lambda }{24}$

4. $\frac{\lambda }{16}$

Q.

A simple harmonic wave of amplitude 2 units is travelling along x - axis. At a given instant, displacements for two different particles on the wave are 1 unit and $\sqrt{2}$ units. If the wavelength of the wave is $\lambda$, find the distance between them.

1. $\frac{\lambda }{12}$

2. $\frac{\lambda }{8}$

3. $\frac{\lambda }{24}$

4. $\frac{\lambda }{16}$

Q. The equation of a travelling sound wave along $x-axis$ is given as $S=9\sin (400t-2.7x)$, where $S$ is measured in ${10}^{-4}\text{m}$, $t$ in seconds and $x$ in metres. Then:

1. Ratio of displacement amplitude to wavelength of wave is $3.86\times {10}^{-4}$.
2. The velocity amplitude of the particle is $36\times {10}^{-2}\text{m/s}$.
3. Ratio of the velocity amplitude of the particle to the wave speed is $2.43\times {10}^{-3}$.
4. The velocity amplitude of the particle is $3.6\times {10}^{-2}\text{m/s}$.