Resultant Amplitude

Q.

In a large room, a person receives direct sound waves from a source 120 metres away from him. He also receives waves from the same source which reach him, being reflected from the 25 metre high ceiling at a point halfway between them. The two waves interfere constructively for wavelength of

1. 20, 20/3, 20/5 etc

2. 10, 5, 2.5 etc

3. 10, 20, 30 etc

4. 15, 25, 35 etc

Q. The constituent waves of a stationary wave have amplitude, frequency and velocity as 8 cm25 Hz and 150 cm s-1 respectively. What is the amplitude of the stationary wave at x 2 cm

Q.

The amplitude of S.H.M at resonance is _______ in the ideal case of zero damping.

1. Zero

2. Maximum

3. Infinite

4. Minimum

Q.

Standing waves result from the superposition of two waves that have:

1. the same amplitude and frequency and opposite directions of propagation

2. the same amplitude, frequency, and direction of propagation

3. the same amplitude, slightly different frequencies, and opposite directions of propagation

4. the same amplitude, slightly different frequencies, and the same direction of propagation

Q. two waves of amplitude A & xA pass through a region . If x>1 the difference in the maximum and minimum resul†an t amplitude possible is (1) (x+1)A (2) (x-1)A (3)2xA (4)2xA

Q. Two waves are passing simultaneously through a string.
The equation of the waves are given by,
$y_1=A_1\sin k(x-vt)$
and $y_2=A_2\sin k(x-vt+x_0)$
Where the wave number $k=6.28{\text{cm}}^{-1}$ and $x_0=1.50\text{cm}$ The amplitudes are $A_1=5.0\text{mm}$ and $A_2=4.0\text{mm}$. Find the phase difference between the waves and the amplitude of the resulting wave.

1. $2\pi \text{and}1\text{mm}$
2. $3\pi \text{and}1\text{mm}$
3. $\pi \text{and}2\text{mm}$
4. $\pi \text{and}0.5\text{mm}$

Q. Two identical travelling waves, moving in the same direction, are out of phase by $\frac{\pi }{2}\text{rad}$. If amplitude of each wave is $A$, then find the resultant amplitude of the wave after superimposition.

1. $1.41A$
2. $2.16A$
3. $1.6A$
4. $6A$

Q. Two waves of equal amplitude $\left(A\right)$, frequency $\left(f\right)$ and intensity $\left(I\right)$ propagate along the same direction in a medium. The intensity of resultant wave will be:

1. $0$
2. $2I$
3. $4I$
4. Between $0\text{and}4I$

Q. Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitude of each wave is 4 mm and the phase difference between the waves is 90°, what is the resultant amplitude?

Q. Two waves are passing simultaneously through a string.
The equation of the waves are given by,
$y_1=A_1\sin k(x-vt)$
and $y_2=A_2\sin k(x-vt+x_0)$
where the wave number $k=6.28{\text{cm}}^{-1}$ and $x_o=1\text{cm}$.
The amplitudes are $A_1=2.0\text{mm}$ and $A_2=6.0\text{mm}$. Find the amplitude of the resulting wave.

1. $2\text{mm}$
2. $4\text{mm}$
3. $8\text{mm}$
4. $6\text{mm}$

Q. Explain why (or how):
(a) in a sound wave, a displacement node is a pressure antinode and vice versa,
(b) bats can ascertain distances directions, nature and sizes of the obstacles without any "eyes"
(c) a violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,
(d) solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and
(e) the shape of a pulse gets distorted during propagation in a dispersive medium.

Q. Two waves represented by $y=a\sin \left(\omega t-kx\right)$ and $y=a\cos \left(\omega t-kx\right)$ are superposed. The resultant wave will have an amplitude
(a) a
(b) $\sqrt{2}a$
(c) 2a
(d) 0.

Q. In a resonance column experiment, a tuning fork of frequency 400 Hz is used. The first resonance is observed when the air column has a length of 20.0 cm and the second resonance is observed when the air column has a length of 62.0 cm. (a) Find the speed of sound in air. (b) How much distance above the open end does the pressure node form?

Q. derive the equations for harmonic frequencies of standing waves formed in a string due to the superposition of waves.Draw the first two harmonies

Q. Two waves, $y_1=2a\cos \omega t$ and $y_2=3a\cos (\omega t+\frac{\pi }{2})$ meet at a point. The amplitude of the resultant wave is

1. $a$
2. $5a$
3. $3.6a$
4. $2.5a$

Q. Two sinusoidal waves produced by two vibrating sources $A$ and $B$ of equal frequencies, are propagating to the point $P$ along a straight line. The amplitude of both of the waves at $P$ is ${}^{\prime }{a}^{\prime }$ and the initial phase of $A$ is ahead by $\frac{\pi }{3}$ than that of $B$. The distance $AP$ is greater than $BP$ by $50\text{cm}$. If the wavelength is $1\text{m},$ then the resultant amplitude at the point $P$ will be

1. $2a$
2. $a\sqrt{3}$
3. $a\sqrt{2}$
4. $a$

Q. Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be
(a) A
(b) 2A
(c) 4A
(d) $\sqrt{2}A$.

Q. One end of a long string of linear mass density 8.0 $\times {10}^{-3}$ 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. Two waves of equal amplitude A, and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is
(a) 0
(b) A
(c) 2A
(d) between 0 and 2A.

Q. On the superposition of the two waves represented by equation $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\frac{\pi }{4})$, the resultant amplitude of oscillation will be:

1. $A\sqrt{2}$
2. $A\sqrt{2+\sqrt{2}}$
3. $A\sqrt{2+\sqrt{3}}$
4. $A\sqrt{1+\sqrt{2}}$

Q. On the superposition of the two waves represented by equation $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\frac{\pi }{4})$, the resultant amplitude of oscillation will be:

1. $A\sqrt{2}$
2. $A\sqrt{2+\sqrt{2}}$
3. $A\sqrt{2+\sqrt{3}}$
4. $A\sqrt{1+\sqrt{2}}$

Q. A sound wave of wavelength 0.31 m is travelling in air. The pressure at a point varied from (10^-5-14) pascalto( 10^5+14) pascal and particles vibrate in SHM with amplitude 5.5\ast10^-6m. Bulk modulus of air is

Q.

what happens to the amplitude of the reflected wave when it goes from rarer to denser medium.

Q. Three components of sinusoidal progressive waves travelling in the same direction along the same path having the same period, but with amplitudes $A,A/2$ and $A/3$. The phase of the vibration at any position $x$ on their path at time $t=0$ are $0,-\pi /2$ and $\pi$ respectively. Find the amplitude and phase of the resultant wave

1. $\frac{5A}{2},{\tan }^{-1}\left(4/3\right)$
2. $\frac{6A}{5},{\tan }^{-1}\left(2/3\right)$
3. $\frac{5A}{6},{\tan }^{-1}\left(3/4\right)$
4. $\frac{5A}{6},{\tan }^{-1}\left(4/3\right)$

Q. Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between (1.0 × 10⁵ ± 14) Pa and the particles of the air vibrate in simple harmonic motion of amplitude 5.5 × 10⁻⁶ m.