Longitudinal Waves

This video explains the feature and parameters of the other kind of mechanical wave called longitudinal wave in which the particles of the medium oscillates along the direction of motion of the wave. One such example is sound waves which propagate through alternate compression and rarefaction along its direction.

Pressure & Disp

This video explains in detail the propagation of sound waves with its equation and parameters like angular frequency and angular wave number.

Speed of Sound

This video explains the method to determine the speed of sound in general medium depending upon the bulk modulus or young?s modulus of the respective medium.


The maximum pressure amplitude ?Pm that the human ear can tolerate is about 28 Pa. And the minimum pressure amplitude of the faintest sound detectable by human ear is 3 x 10-5 Pa. What is the displacement amplitude corresponding to the maximum and minimum pressures variations. Given the density of air, frequency of sound signal and a speed of sound in air.

Speed in Gases

This video explains the variation in the speed of sound in gases considering change in its parameters through a certain route.


A tuning fork sends sound waves in air. If the temperature of the air increases, which of the following parameters will change?
(a) Displacement amplitude
(b) Frequency
(c) Wavelength
(d) Time period


The velocity of sound in a tube containing air at a given temperature and a pressure is known. What will be its velocity when the pressure is increased and the temperature is kept constant?


Calculate the speed of sound in oxygen from the following given data: Molar heat capacity at constant volume, Molar heat capacity at constant pressure, Pressure, Temperature, Mass of 22.4 litre of oxygen at NTP.


This video defines the kinetic energy, potential energy, power and intensity of a longitudinal waves in equivalence to the respective elements for transverse waves.


Which of the following is correct when a wave propagates in a non absorbing medium?
(a) the wave intensity remains constant for a plane wave
(b) the wave intensity decreases as the inverse of the distance from the source for a spherical wave
(c) the wave intensity decreases as the inverse square of the distance from the source for a spherical wave
(d) the total intensity of a spherical wave over a spherical surface centered at the source remains constant at all times.


Intensity of sound from a point source is given at a distance of 10 m from the source. Find the Intensity at a distance of 100 m from the source.


This video discusses the different characteristics of sound like loudness (in decibel), pitch and quality along with their relation with intensity of the sound wave.


When we clap our hands, the sound produced is best described by which of the following equation
(a) s = A sin (kx - ?t)
(b) s = A sinkx cos?t
(c) s = A cos kx sin ?t
(d) s = ?An sin (?n t ? kn x)


A machine produces sound of intensity I with known decibel level. What is the decibel level of sound if two machines are turned on? (assume that the all the measurements are made from a point which is equidistant from all the machines, ignore interference)


This video explains the superposition of two longitudinal waves originates from coherent sources and the condition for the formation of constructive and destructive interferences.


Sound is made to travel through a closed tube as shown in figure. The frequency of the sound source can vary between 1000 and 3000 Hz. Find the frequencies at which maxima of intensity are detected.


Two audio speakers, separated from one another by a certain distance, are driven by the same amplifier system. A listener, in line with the speakers and in between them. If the frequency of the source is varies continuously from 1000 Hz to 3000 Hz, find the frequencies for which there is destructive interference at the place of the listener.


As shown in figure, two point sources S1 and S2, which are in phase and separated by distance D = 1.5 ?, emit identical sound waves of wavelength ?.
(a) Point P1 lies at the perpendicular bisector of line joining S1 and S2. What type of interference occurs at P1?
(b) Point P2 lies on the line joining S1 and S2. What type of interference occurs at P2?
(c) How many points are there on the full circle with Constructive Interference?

Quincke\'\'s Tube

This video explains the construction and mechanism of a simple apparatus called Quinck?s tube, which is used to demonstrate sound wave interferences.


In Quincks experiment, the intensity of sound at a particular point changes from a minimum value I to a maximum value of 9I when the sliding tube is pulled out by 1 cm.
(a) What if the frequency of source ?
(b) Find the ratio of the amplitudes of the waves arriving from the two sides.


This video explains the formation of longitudinal standing waves in closed, semi-closed or open pipes and its different modes of vibration by formation of nodes and anti-nodes.


Sound waves of given frequency fall normally on a perfectly reflecting wall. If the speed of sound is known, the shortest distance from the wall at which the air particles have the maximum amplitude of vibration is?.?


Neglecting end correction, the air column in the pipe of given length closed at one end can resonate with sound of frequency?.?


A cylindrical tube open at both ends, has a fundamental frequency f in air. The tube is dipped vertically in water so that half of it is under water. The fundamental frequency of the air column in the tube now is??


An open pipe is suddenly closed at one end with the result that the frequency of the third harmonic of the closed pipe is found to be higher by a given amount than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is??

Res Column Method

This video illustrates the mechanism of a simple apparatus called resonance column method which is used to measure the speed of sound in air.


In resonance air-column experiment, two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air-column is the second resonance. Then which of the following is correct?
(a) the intensity of the sound heard at the first resonance was more than that at the second resonance
(b) the prongs of the tuning fork were kept in a horizontal plane above the resonance tube
(c) the amplitude of vibration of the ends of the prongs is typically around 1 cm
(d) the length of the air-column at the first resonance was somewhat shorter than 1/4th of the wavelength of the sound in air


The smallest resonating length in a resonance tube experiment is given for a specified frequency of a tuning fork placed at the open end of an air column in a pipe of given radius. Find the speed of sound.

Kundt\'\'s Tube

It illustrates the construction and mechanism of a simple apparatus called Kundt?s tube which is used to measure the speed of sound in any given gas.


This video explains the superposition of two longitudinal waves with different frequency which when interfere results in a beat frequency.


A tuning fork whose frequency is stated as 510 Hz is being tested with an accurate oscillator. It is found that the fork produces a beat of 4 Hz when oscillator reads 514 Hz but produces a beat of 6 Hz when oscillator reads 512 Hz. The actual frequency of the fork is??


The forks A and B when sounded together produce 4 beat/sec. The fork A is in unison with 30 cm length of a sonometer wire, and B is in unison with the 25 cm length of the same wire at the same tension. Calculate the frequencies of the forks.


Two identical wires are stretched with tension T1 and T2 with T1 > T2. They produce a given beats per second when vibrated in fundamental mode. If the tension in one of them is changed slightly, it is observed that the beat frequency remain unchanged. Which of the following is/are possible?
(a) T1 was increased
(b) T1 was decreased
(c) T2 was increased
(d) T2 was decreased


A vibrating string of certain length L under a tension T resonates with a mode corresponding to the first overtone of an air column of given length inside a tube closed at one end. The string also generates 4 beats per second when excited along with a tuning fork of frequency n. Now when the tension of string is slightly increased the number of beats reduces to 2 per second. Find the frequency of the tuning fork.

Doppler Effect - 1

This video discusses the Doppler effect in details which gives the relation between the frequency originated by a source and the frequency perceived by an observer in the situation when source and observer are moving with a relative velocity. It shows the derivation of equation for frequency when the source is stationary and observer is moving.


A siren placed at a railway platform is emitting sound of given frequency. A passenger sitting in a moving train A records a frequency while the train approaches the siren. During his return journey in a different train B he records a different frequency while approaching the same siren. The ratio of the velocity of the B to that of train A is??

Doppler Effect - 2

This video shows the relation between in emitted and observed frequency for the situations in which sources is moving and observer is stationary.


A train moves towards a stationary observer with a given speed. The train sounds a whistle and its frequency registered by the observer is f1. If the speed of the train is reduced, the frequency registered is f2. If the speed of sound is knwon, the ratio f1 / f2 is??


A source of sound with given frequency is moving towards a detector. As the source crosses the detector, a change in frequency is detected. What is the speed of source? Velocity of sound in air is given.


Two tuning forks with given natural frequencies move relative to a stationary observer. One fork moves away from the observer while the other moves towards him at same speed. The overseer hears a beats of frequency. Find the speeds of the tuning forks.


A train blowing a whistle moves with a constant velocity u away from a stationary observer. The ratio of actual frequency of whistle to that measured by the observer is found to be 1.2. If the train is at rest and the observer moves away from it at the same velocity, the ratio will be?.?

Doppler Effect - 3

This video explains the relation between emitted and observed frequency when source and observer both are moving in same or opposite direction, along with equations.


A train approaching a hill at a speed sounds a whistle of known frequency when it is at a specified distance from a hill. A wind with a speed is blowing in the direction of motion of the train. Find
(a) frequency of whistle as heard by an observer on the hill.
(b) the distance from the hill at which the echo from the hill is heard by the driver and its frequency. Velocity of sound in air is given.

Shock Waves

This video explains a situation in which speed of the source of sound is greater than the speed of sound resulting in the formation of shock waves having very large amplitude.


A man standing in front of a mountain at a certain distance beats a drum at regular intervals. The drumming rate is gradually increased and he finds that the echo is not heard distinctly when the rate becomes 40 per minute. He then moves nearer to the mountain by 90 m and finds that the echo is again not heard when the drumming rate becomes 60 per minute. Calculate:
(1) the distance between the mountain and the initial position of the man,
(2) the velocity of sound.


The ratio of the speed of sound in nitrogen gas to that in helium gas at a specified temperature is?.?


The wavelength of a note emitted by a tuning fork of known frequency in air at a specified temperature is given. If the density of air at NTP is given, Find adiabatic constant (?) for air.


Calculate the velocity of sound in moist air. Given the saturated vapor pressure at given temperature and pressure, the ratio of the density of vapor to dry air at the same temperature and pressure, the velocity of sound in dry air at S.T.P.


Find the temperature at which the velocity of sound in nitrogen is equal to its velocity in oxygen at a given temperature. Given the ratio of atomic weights of oxygen and nitrogen are in the ratio.


The speed of sound in hydrogen is known. Calculate the speed of sound in a mixture of oxygen and hydrogen in which they are mixed in the given ratio by volume.


The velocity of sound in hydrogen is known at a given temperature. When some amount of oxygen is mixed with hydrogen keeping the pressure contant, the velocity decreases. Determine the ratio of hydrogen to Oxygen by volume in this mixture, given that the density of oxygen is 16 times that of hydrogen.


A point source emits sound equally in all directions in a non-absorbing medium. Two point P and Q are at a given distances from the source as shown in figure. The ratio of the amplitudes of the waves at P and Q is??


Some point sources emitting sound waves in phase are placed along a straight line as shown in the figure. Overall effect is a pulse of sound that travels radially outward from the line (cylindrical wavefronts). The total power of the emission is given.
(a) what is intensity of sound when it reaches a given distance from the line?
(b) An acoustic detector of known area is facing towards the line and located at a distance. What is the Power intercepted by the detector?


A person receives direct sound waves from a source at a distance away from him. He also receives waves from the same source after reflection from a high ceiling at a point half-way between them. For which wavelength, will these two sound waves interfere constructively?


Two speakers connected to the same source of fixed frequency are placed at a distance apart in a box. A sensitive microphone placed at a distance from their mid-point along the perpendicular bisector shows maximum response. The box is slowly rotated till the speakers are in a line with the microphone. Distance between the center of speakers and the microphone remains unchanged. Exactly 5 maximum responses are observed in the microphone in doing this. Calculate the wavelength of sound wave.


Sound of wavelength ? passes through a Quinckes tube, which is adjusted to give a maximum intensity I. Through what distance should the sliding tube be moved to given an intensity of I/ 2?


Two stations broadcast their programs with same Intensity I but at different frequencies f1 and f2 where difference between f1 and f2 is given. A detector receives the signals from the two stations simultaneously. It can only detect signals of intensity ? 2I. Then find the following.
(a) maximum intensity of the resultant signal received by detector
(b) time interval between successive maxima of intensity of the signal received
(c) time for which the detector remains idle in each cycle of the intensity of the signal.


In the experiment for the determination of the speed of sound in air using the resonance column, it is observed that 0.1 m of air column resonates with a tuning fork in the fundamental mode. When the length of the air column is changed to 0.35 m, the same tuning fork resonates with the first overtone. What is the end correction and diameter of the tube?


A pipe of given length closed at one end is filled with a gas and it resonates in its fundamental mode with a tuning fork. Another pipe of the same length but open at both ends is filled with air and it resonates in its fundamental with the same tuning fork. Calculate the velocity of sound at 0 degree centigrade in the gas, given that the velocity of sound in air where the experiment is performed.


A tuning fork having a known frequency is vibrated just above a cylindrical tube. The height of the tube is given. Water is slowly poured in it. What is the minimum height of water required for resonance?


A tube of certain diameter and length is open at both ends. Its fundamental frequency of vibration and the velocity of sound in air are given. Estimate the diameter of the tube. One end of the tube is now closed. Calculate the lowest frequency of resonance for the tube.


The air column in a pipe closed at one end is made to vibrate in its second overtone by a tuning fork of known frequency. The speed of sound in air is given. End corrections may be neglected. Let po be the mean pressure at any point in the pipe and ?po the maximum amplitude of pressure variation.
(a) Find the length L of air column.
(b) What is the amplitude of pressure variation at the middle of the column?
(c) What is the maximum and minimum pressure at the open end of the pipe?
(d) What is the maximum and minimum pressure at the closed end of the pipe?


An organ pipe P1, closed at one end and containing a gas of density ?1 is vibrating in its first harmonic. Another organ pipe P2, open at both ends and containing a gas of density ?2 is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes, the ratio of the lengths of ?1 and ?2 is?.?


Two pipes A and B have the same length. Pipe A is open at both ends and is filled with a monoatomic gas of molar mass MA. Pipe B is open at one end and closed at the other end and is filled with a diatomic gas of molar mas MB. Both gases are at the same temperature. If the frequency of the second harmonic of pipe A is equal to the frequency of the third harmonic in pipe B, find the ratio of gases MA/MB.


In the resonance tube experiment for determining the speed of sound in air using a tuning fork of frequency 480 Hz, the first resonance was observed at 17.7 cm of air column and the second at 53.1 cm. The maximum possible error in the speed of sound in air is??


A metallic rod of given length is rigidly clamped at its mid-point. Longitudinal stationary waves are set up in the rod in such a way that there are two nodes on either sides of mid-point. The amplitude of antinode is known. Write the equation of motion at a point at a distance from the mid-point.


AB is a cylinder of given length fitted with a thin flexible diaphragm C at the middle and two other thin flexible diaphragms A and B at the ends as shown in figure. The portions AC and BC contain hydrogen and oxygen gases respectively. The diaphragms A and B are set into vibrations of same frequency. What is the minimum frequency of these vibrations for which the diaphragm C is a node. Under the conditions of the experiment, the velocity of sound in hydrogen and oxygen is known.


The first overtone of an open organ pipe (of length Lo) beats with the first overtone of a closed organ pipe (of length Lc) with a given beat frequency. If the fundamental frequency of the closed pipe and the speed of sound is given, then find the lengths of open and closed pipes.


Sound wave passes from one medium to another medium. The velocity of sound in first medium is greater than in second medium. Assume that there is no absorption or reflection at the boundary. As the wave moves across the boundary, which of the following is correct?
(a) the frequency of sound will not change
(b) the wavelength will increase
(c) the wavelength will decrease
(d) the intensity of sound will not change.


An underwater swimmer sends a sound signal to the surface. If it produces a given beats/sec when compared with the fundamental tone of a pipe of given length closed at one end, what is the wavelength of sound in water ( velocity of sound in air and water is known)?


A closed pipe and an open pipe sounding together produce 5 beats/sec. If the length of the open pipe is 30 cm, by how much the length of the closed pipe must be changed to bring the two pipes in unison. (Velocity of sound = 330 m/s).


A metal wire of diameter 1 mm is held on two knife edges separated by a distance of 50 cm. The tension in the wire is 100 N. The wire vibrating with its fundamental frequency and a vibrating tuning fork together produce 5 beats /sec. The tension in the wire is then reduced to 81 N. When the two are excited, beats are heard at the same rate. Find
(a) the frequency of the fork and
(b) the density of the material of the wire.


A column of air at a given temperature and a tuning fork produces 4 beats per second. When the temperature is changed, the two produce 1 beat per second. Find the frequency of tuning fork.


A locomotive approaching a crossing at a speed of 80 miles per hour sounds a whistle of frequency 400 cycles/sec, when 1.00 mile from the crossing. There is no wind and the speed of sound in air is 0.200 mile/sec. what frequency is heard by an observer 0.60 miles from the crossing on the straight road which crosses the rail road at right angle?


A van sounding a horn of given frequency is moving rapidly towards a wall with a velocity. How many beats per second will be heard by an observer:
a) between wall and source
b) behind the source
c) moving with the source


A band playing music at frequency f is moving towards a wall at a speed vb. A motorist is following the band with a speed vs. If v is the speed of sound; obtain an expression for the beat frequency heard by the motorist.


A van, moving at 22 km-1, chases a motor-cyclist. The van sounds a horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz.If the motorcyclist does not observe any beats, his speed must be?.?


A boat is travelling in a river with a speed along the stream flowing with a known speed. From this boat, a sound transmitter is lowered into the river through a rigid support. The wavelength of the sound emitted from the transmitter inside the water is given. Assume that attenuation of sound in water and air is negligible. Find
(a) frequency detected by a receiver kept inside the river downstream
(b) frequency detected when both transmitter and detector is kept in air with speed of the air given.


Two trains A and B are moving with given speeds in the same direction on the same straight track, with B ahead of A. The engine of train A blows a long whistle. Assume that the sound of whistle is composed of components varying in frequency from f1 = 800 HZ to f2 = 1120 HZ as shown on figure.


A source of sound is moving along circular orbit with an angular velocity. A sound detector located far away from the source is executing simple harmonic motion along the line AB with given amplitude as shown in figure. The frequency of oscillation of the detector is known. The source is at point R when the detector is at the point B. If the source emits a continuous sound wave of given frequency, find the maximum and the maximum frequencies recorded by the detector.

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