Interference in Sound Waves

Q. The central fringe of the interference pattern produced by light of wavelength $6000\stackrel{o}{A}$ is found to shift to the position of $4^{th}$ bright fringe after a glass plate of refractive index $1.5$ is introduced in path of one of beams. The thickness of the glass plate would be

1. $4.8\mu \text{m}$
2. $8.23\mu \text{m}$
3. $14.98\mu \text{m}$
4. $3.78\mu \text{m}$

Q.

A tuning fork of frequency 256 Hz produces 4 beats per second with a wire of length 25 cm vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by which the wire be shortened so that it produces no beats with the tuning fork ?

Q. Three waves from three coherent sources meet at the same point. The Amplitude of each wave is $A_0$. Intensity corresponding to $A_0$ is $I_0$. At a point, the phase difference between the first wave and the second wave is ${60}^{\circ }$and the path difference between the first wave and the third wave is $\frac{\lambda }{3}$. The first wave lags behind in phase angle from the second and the third wave. The resultant intensity at this point is

1. $I_0$
2. $2I_0$
3. $3I_0$
4. $4I_0$

Q.

Two identical stringed instruments have frequency 100 Hz. If tension in one of them is increased by 4% and they are sounded together then the number of beats in one second is

1. 1

2. 8

3. 4

4. 2

Q.

Two point sources of sound are kept at a separation of $10cm$. They vibrate in phase to produce waves of wavelength $5cm$. What would be the phase difference between the two waves arriving at a point $20cm$ from the source.

1. on the line joining the sources and
2. on the perpendicular bisector of the line joining the sources?

Q. A point source emits sound waves of constant power with intensity inversely proportional to the square of the distance from the source. By how many decibels does the sound loudness drop, when you move from point $A$ to $B$ ? Distance of $B$ from the source is two times the distance of $A$ from the source. [Take ${\log }_{10}2=0.3$ ]

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

Q.

A source emitting sound of frequency 180 Hz is placed in front of a wall at a distance of 2 m from it. A detector is also placed in front of the wall at the same distance from it. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air = 360 $m{s}^{-1}$

1. 1 m

2. 2 m

3. 3 m

4. 4 m

Q.

Choose the correct statement.

1. Beats are due to destructive interference

2. Maximum beat frequency audible to a human being is $20$

3. Beats are a result of Doppler’s effect

4. Beats are due to the superposition of two waves of nearly equal frequencies

Q.

A whistle sends out 256 waves in a second. If the whistle approaches the observer with velocity 1/3 of the velocity of sound in air, the number of waves per second the observer will receive

1. 384

2. 192

3. 300

4. 200

Q. In a Quincke's tube experiment, the sound intensity being detected at an appropriate point, changes from minimum to maximum for the second time, when the sliding tube is drawn out by $18.0\text{cm}.$ If the speed of sound in air is $340\text{m/s}$, then find the frequency of this sounding source.

1. $1417\text{Hz}$
2. $2833\text{Hz}$
3. $1889\text{Hz}$
4. $944\text{Hz}$

Q. Interference fringes are produced by a double slit arrangement and a piece of plane parallel glass of refractive index $1.5$ is interposed in one of the interfering beam. If the fringes are displaced through $30$ fringe widths for light of wavelength $6\times {10}^{-5}\text{cm}$, find the thickness of the plate.

1. $1.8\times {10}^{-3}\text{cm}$
2. $5.4\times {10}^{-3}\text{cm}$
3. $3.6\times {10}^{-3}\text{cm}$
4. $7.2\times {10}^{-3}\text{cm}$

Q. A sound source emits two sinusoidal sound waves, both of wavelength $\lambda$, along paths $A$ and $B$. The sound travelling along the path $B$ is reflected from four surfaces and then merges at point $Q$ while sound travelling along the path $A$ goes straight to point $Q$, producing minimum intensity at point $Q$ due to superposition. The minimum value of $d$ in terms of $\lambda$ will be
(Assume that the sound wave is not undergoing any phase change due to reflection)

1. $\frac{\lambda }{8}$
2. $\frac{\lambda }{4}$
3. $\frac{\lambda }{5}$
4. $\frac{\lambda }{2}$

Q. Light waves from two coherent sources superimposes at a point. The waves at this point can be expressed as $y_1=a\sin \left({10}^{15}\pi t\right)$ and $y_2=2a\sin ({10}^{15}\pi t+\varphi )$. Here all quantities are in SI units.
Find the resultant amplitude $\left(\text{in m}\right)$, and frequency $\left(\text{in Hz}\right)$, of the resultant wave, if phase difference $\varphi$ is equal to $\pi /3$.

1. $a\sqrt{5},5\times {10}^{14}$
2. $a\sqrt{7},5\times {10}^{14}$
3. $a\sqrt{5},{10}^{15}$
4. $a\sqrt{7},{10}^{15}$

Q. Which of the following is not a physical quantity ?

1. Loudness
2. Frequency
3. Wavelength
4. Waveform

Q. Three sound waves of equal amplitudes have frequencies (v – 1), v, (v + 1). They superimpose to produce beats. The maximum number of beats produced per second will be:

1. $1$
2. $v$
3. $\frac{v}{2}$
4. $2$

Q.

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

Q. Give the condition for constructive and destructive interference in terms of phase difference and path difference.

Q. A vibrating tuning fork tied to the end of a string 1.988 m long is whirled round in a circle. If it makes two revolutions in a second, calculate the ratio of the frequencies of the highest and the lowest notes heard by a stationary observer situated in the plane of rotation of tuning fork at a large distance from the tuning fork. Speed of sound is $350m{s}^{-1}$. (In both case, the observer is assumed to be along the line of velocity sound).

1. 1
2. 1.278
3. 1.154
4. 1.732

Q.

What wavelength looks like?

Q.

Two stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of the speakers as shown in figure. find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = $320\frac{m}{s}$.

1. $200(2n+1)$

   where $n=0,1,2,......49$

2. $200(2n+1)$

   where $n=0,1,2,......49$

3. $320(2n+1)$

   where $n=0,1,2,......49$

4. $320(2n+1)$

   where $n=0,1,2,......49$

Q. A $YDSE$ apparatus is as shown in figure below. The condition for point $P$ to be a dark fringe is $(\lambda =$ wavelength of the light used)

1. $(l_1-l_2)+(l_3-l_4)=n\lambda$
2. $(l_1-l_3)+(l_3-l_4)=n\lambda$
3. $(l_1+l_2)-(l_3+l_4)=\frac{(2n-1)\lambda }{2}$
4. $(l_1+l_3)-(l_2+l_4)=\frac{(2n-1)\lambda }{2}$

Q. A light wave of wavelength ${\lambda }_0$ propagates from point $\text{A}$ to point $\text{B}$. We introduce in its path a glass plate of refractive index $n$ and thickness $l.$ The introduction of the plate alters the phase of the light at $B$ by an angle $\varphi .$ If $\lambda$ is the wavelength of light on emerging from the plate , then

1. $\Delta \varphi =0$
2. $\Delta \varphi =\frac{2\pi l}{{\lambda }_0}$
3. $\Delta \varphi =2\pi l(\frac{1}{{\lambda }_0}-\frac{1}{\lambda })$
4. $\Delta \varphi =\frac{2\pi l}{{\lambda }_0}(n-1)$

Q. Figure shows three different modes of vibration of a string of length l.
(i) Which of the vibration is of largest amplitude?
(ii) Which of the vibration is of least frequency?
(iii) What is the ratio of frequency between (a) and (c)?
(iv) What is the ratio of wavelength between (b) and (a)

Q. The distance between two points differing in phase by ${60}^{\circ }$ on a wave having a wave velocity $360m/s$ and frequency $500Hz$ is

1. $0.72m$
2. $0.18m$
3. $0.12m$
4. $0.36m$

Q.

Two loudspeakers $L_1$ and $L_2$ driven by a common oscillator and amplifier, are arranged as shown. The frequency of the oscillator is gradually increased from zero and the detector at D records a series of maxima and minima. If the speed of sound is $330m{s}^{-1}$, then the frequency at which the first maximum is observed is

1. 330 Hz

2. 496 Hz

3. 660 Hz

4. 165 Hz

Q. The path difference between the two waves $y_1=a_1\sin (\omega t-\frac{2\pi x}{\lambda })$ and $y_2=a_2\cos (\omega t-\frac{2\pi x}{\lambda }+\varphi )$

1. $\frac{\lambda }{2\pi }\varphi$
2. $\frac{\lambda }{2\pi }(\varphi +\frac{\pi }{2})$
3. $\frac{\lambda }{2\pi }(\varphi -\frac{\pi }{2})$
4. $\frac{2\pi }{\lambda }\varphi$

Q. Two sources of sound, $S_1$ and $S_2$, emitting waves of equal wavelength $20.0cm$, are placed with a separation of $20.0cm$ between them. A detector can be moved on a line parallel to $S_1{S}_2$ and at a distance of $20.0cm$ from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through which the detector should be shifted to detect a minimum of sound.

Q. Two particles execute SHM parallel to x-axis about the origin with the same amplitude and frequency. At a certain instant, they are found at distance A/3 from the origin on opposite sides but their velocities are found to be in the same direction. What is the phase difference between the two?

Q.

Two sources of sound, $S_1$, and $S_2$, emitting waves equal wavelength 20.0 cm, are placed with a separation of 20.0 cm between them. A detector can be moved on a line parallel to $S_1,S_2$ and at a distance of 20.0 cm from it. Initially, the detector is equidistant from the two sources. Assuming that the waves emitted by the sources are in phase, find the minimum distance through Which the detector should be shifted to detect a minimum of sound.

Q. Two waves of the same frequency and same amplitude are superimposed to produce a resultant disturbance wave of the same amplitude. What is the phase difference between the two original waves?