Amplitude Variation

Q. The displacement of a particle executing periodic motion is given by $y=4{\cos }^2\left(\frac{t}{2}\right)\sin \left(1000t\right)$. The number of independent constituent simple harmonic motion is

1. $1$
2. $2$
3. $3$
4. $4$

Q. The amplitude of a wave represented by the displacement equation $y=\frac{1}{\sqrt{a}}\sin \omega t\pm \frac{1}{\sqrt{b}}\cos \omega t$ will be

1. $\frac{a+b}{ab}$
2. $\frac{\sqrt{a}+\sqrt{b}}{ab}$
3. $\frac{\sqrt{a}\pm \sqrt{b}}{ab}$
4. $\sqrt{\frac{a+b}{ab}}$

Q. An oscillator of frequency $680\text{Hz}$ drives two speakers. The speakers are fixed on a vertical pole at a distance $3\text{m}$ from each other as shown in figure. A person whose height is almost the same as that of the lower speaker walks towards the lower speaker in a direction perpendicular to the pole. Assuming that there is no reflection of sound from the ground and sound speed is $v=340\text{m/s}$, choose the correct option(s):

1. The person hears the first minimum sound intensity at $18\text{m}$ away from the pole.
2. The person hears the second minimum intensity at a distance of $5.6\text{m}$ from the speaker.
3. The person hears a minimum sound intensity for a total of $6$ times.
4. The person hears a maximum sound intensity for a total of $8$ times.

Q.

Two sound waves move in the same direction in the same medium. The pressure amplitudes of the waves are equal but the wavelength of the first wave is double the second. Let the average power transmitted across a cross section by the first wave be $P_1$ and that by the second wave be $P_2$. Then

1. $P_1=P_2$

2. $P_1=4P_2$

3. $P_2=2P_1$

4. $P_2=4P_1$

Q.

A wave travels along the positive x-direction with a speed of $20m{s}^{-1}$. The amplitude of the wave is 0.20 cm and the wavelength 2.0 cm. (a) Write a suitable wave equation which describes this wave. (b) What is the displacement and velocity of the particle at x = 2.0 cm at time t = 0 according to the wave equation written ? Can you get different values of this quantity if the wave equation is written in a different fashion ?

Q.

If two waves, each of intensity $I$ having the same frequency but differing by a constant phase angle of $60°$ superpose at a certain point in space, then the intensity of the resultant wave is:

Q. Two stereo speakers $S_1$ and $S_2$ are separated by a distance of $2.40\text{m}$. A person $\left(P\right)$ is at a distance of $3.20\text{m}$ directly in front of one of the speakers as shown in the figure. The frequency in the audible range$(20–20000\text{Hz})$ for which the listener can hear minimum sound intensity is (Take speed of sound in air as $320\text{m/s}$)

1. $200\text{Hz}$
2. $100\text{Hz}$
3. $900\text{Hz}$
4. $700\text{Hz}$

Q. A wave moving with constant speed on a uniform string passes the point x =0 with amplitude$A_0,{\omega }_0$ and average rate of energy transfer $P_0$. As the wave travels down the string, it gradually loses energy and at the point x =l, angular frequency and amplitude are, respectively

1. less than ${\omega }_0$ and $A_0$
2. $\frac{{\omega }_0}{\sqrt{2}}$
3. $\frac{{\omega }_0}{\sqrt{2}}$ and $\frac{A_0}{\sqrt{2}}$
4. ${\omega }_{0}and\frac{A_0}{\sqrt{2}}$
   

Q. In a standing wave, all the particles between two consecutive node and antinode have different amplitudes.

1. False
2. True

Q. Two speakers are separated by a distance of $3\text{m}$. A person stands at a distance of $4\text{m}$, directly in front of one of the speakers. If $n$ stands for any integer, find the frequencies (in audible range) for which the listener will hear a minimum sound intensity. Speed of sound in air is $320\text{m/s}$.

1. $200(2n+1)\text{Hz}$
2. $160(2n+1)\text{Hz}$
3. $320(2n+1)\text{Hz}$
4. $80(2n+1)\text{Hz}$

Q.

A wave motion travels at the same ____ in all directions in any medium.

Q. Intensity (I) is related to amplitude (A) as:

1. $I\propto A^2$
2. $I\propto A^4$
3. $I\propto A^{-1}$
4. $I\propto A$

Q. The displacement $Y$ of a particle executing simple harmonic motion is given by

$Y=2\sin t{\cos }^2\frac{t}{2}$

This expression may be considered to be a result of the superposition of how many simple harmonic motions?

1. $1$
2. $2$
3. $3$
4. $4$

Q.

How do you use a doppler equation?

Q.

When the interference occurs with non-coherent sources, _______ of the superimposing waves add like _______.

1. amplitudes, vectors

2. intensities, scalars

3. intensities, vectors

4. amplitudes, scalars

Q. The equation of an a.c voltage is $V=100\sqrt{2}\sin \left(100\pi t\right)$. Find the rms value and the frequency of the voltage.

Q. The minimum phase difference between two simple harmonic oscillations, $y_1=\frac{1}{2}sin\omega t+\frac{\sqrt{3}}{2}cos\omega t,y_2=sin\omega t+cos\omega t$, is:

1. $\frac{\pi }{6}$ rad
2. $\frac{7\pi }{12}$ rad
3. $\frac{\pi }{3}$ rad
4. $\frac{\pi }{12}$ rad

Q. If the tension is $10N$ and the linear mass density is $4g/m$. what is the fundamental frequency(in $Hz$)?

1. $17$
2. $25$
3. $12$
4. $41$

Q.

A wave disturbance in a medium is described by y(x , t)= 0.02 cos (50 $\pi$ t + $\frac{\pi }{2}$) cos (10 $\pi$x) where x and y are in metre and t in second

1. An antinode occurs at x = 0.3 m

2. The wavelength of the wave is 0.1m

3. A displacement node occurs at x = 0.5 m

4. The speed of the wave is 50.0 m/s

Q. The amplitude of a wave represented by the displacement equation:
$y=\frac{1}{\sqrt{a}}\sin \omega t\pm \frac{1}{\sqrt{b}}\cos \omega t$
will be,

1. $\frac{a+b}{ab}$
   
2. $\frac{\sqrt{a}+\sqrt{b}}{ab}$
   
3. $\frac{\sqrt{a}\pm \sqrt{b}}{ab}$
   
4. $\sqrt{\frac{a+b}{ab}}$

Q. The amplitude of a wave represented by the displacement equation $y=\frac{1}{\sqrt{a}}\sin (kx-\omega t)\pm \frac{1}{\sqrt{b}}\cos (kx-\omega t)$ will be

1. $\frac{a+b}{ab}$
2. $\frac{\sqrt{a}+\sqrt{b}}{ab}$
3. $\frac{\sqrt{a}\pm \sqrt{b}}{ab}$
4. $\sqrt{\frac{a+b}{ab}}$

Q. The minimum distance between the particles in a medium vibrating with the same phase is known as

1. frequency
2. amplitude
3. wavelength
4. phase

Q.

Doppler effects would not hold for

Q. A $40cm$ long wire having a mass $3.2gm$ and area of c.s $1m{m}^2$ is stretched between the support $40.05cm$ apart. In its fundamental mode. It vibrate with a frequency $1000/64Hz$. Find the young's modulus of the wire.

1. $1\times {10}^{9}N{m}^2$
2. $2\times {10}^{9}N{m}^2$
3. $1\times {10}^{8}N{m}^2$
4. $4\times {10}^{9}N{m}^2$

Q. A transverse wave propagating on a stretched string of linear density $3\times {10}^{-4}kg{m}^{-1}$ is represented by the equation :
$y=0.2\sin (1.5x+60t)$ where $x$ is in metre and $t$ is in seconds
The tension in the string in $N$

1. $0.24$
2. $0.48$
3. $1.20$
4. $1.80$

Q. Three source of sound of equal intensities have frequencies 251, 252 and 253 Hz respectively. When sounded together, the number of beats heard per second will be

1. 3
2. 2
3. 1
4. none of thesr

Q. The physical quantity that remains unchanged when a sound wave goes from one medium to another is

1. Wavelength
2. Amplitude
3. Frequency
4. Speed
5. Phase

Q. The amplitude of a wave represented by the displacement equation $y=\frac{1}{\sqrt{a}}\sin (kx-\omega t)\pm \frac{1}{\sqrt{b}}\cos (kx-\omega t)$ will be

1. $\frac{a+b}{ab}$
2. $\frac{\sqrt{a}+\sqrt{b}}{ab}$
3. $\frac{\sqrt{a}\pm \sqrt{b}}{ab}$
4. $\sqrt{\frac{a+b}{ab}}$

Q. If the ratio of amplitudes of two waves at any point in the medium is $1:3$, then the ratio of maximum and minimum intensities because of their superposition will be

1. $2:1$
2. $3:1$
3. $4:1$
4. $2:3$

Q. Assertion :Sound waves cannot be polarised. Reason: Sound waves are longitudinal in nature.

1. If both assertion and reason are true and reason is the correct explanation of assertion.
2. If both assertion and reason are true and reason is not the correct explanation of assertion.
3. If assertion is true but reason is false.
4. If both assertion and reason are false.