Waves

If '\(l\)' is the length of the open pipe, '\(r\)' is the internal radius of the pipe and '$V$ ' is the velocity of sound in air then fundamental frequency of open pipe is

The equation of the wave is \(\mathrm{Y}=10 \sin \left(\frac{2 \pi \mathrm{t}}{30}+\alpha\right)\) If the displacement is \(5 \mathrm{~cm}\) at \(\mathrm{t}=0\) then the total phase at \(\mathrm{t}=7.5 \mathrm{~s}\) will be $$\left(\sin 30^...

A progressive wave is given by, \(\mathrm{Y}=12 \sin (5 \mathrm{t}-4 \mathrm{x})\). On this wave, how far away are the two points having a phase difference of \(90^{\circ}\) ?

A string is stretched between two rigid supports separated by \(75 \mathrm{~cm}\). There are no resonant frequencies between \(420 \mathrm{~Hz}\) and \(315 \mathrm{~Hz}\). The lowest resonant frequency for the string is

A source of sound is moving towards a stationary observer with \(\left(\frac{1}{10}\right)^{\text {th }}\) the of the speed of sound. The ratio of apparent to real frequency is

A sonometer wire \(49 \mathrm{~cm}\) long is in unison with a tuning fork of frequency '\(n\)'. If the length of the wire is decreased by \(1 \mathrm{~cm}\) and it is vibrated with the same tuning fork, 6 beats are heard per second. The val...

A wire \(P Q\) has length \(4.8 \mathrm{~m}\) and mass \(0.06 \mathrm{~kg}\). Another wire QR has length \(2.56 \mathrm{~m}\) and mass \(0.2 \mathrm{~kg}\). Both wires have same radii and are joined as a single wire. This wire is under tens...

Sound waves of frequency \(600 \mathrm{~Hz}\) fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration is (speed of sound \(=300 \mathrm{~ms}^{-1}\) )

A passenger is sitting in a train which is moving fast. The engine of the train blows a whistle of frequency '\(n\)'. If the apparent frequency of sound heard by the passenger is '\(f\)' then

A uniform wire \(20 \mathrm{~m}\) long and weighing \(50 \mathrm{~N}\) hangs vertically. The speed of the wave at mid point of the wire is (acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~ms}^{-2}\) )

In resonance tube, first and second resonance are obtained at depths \(22.7 \mathrm{~cm}\) and \(70.2 \mathrm{~cm}\) respectively. The third resonance will be obtained at a depth

A closed pipe and an open pipe have their first overtone equal in frequency. Then, the lengths of these pipe are in the ratio

A transverse wave strike against a wall,

The equation of a progressive wave is \(Y=a \sin 2 \pi\left(n t-\frac{x}{5}\right)\). The ratio of maximum particle velocity to wave velocity is

When two tuning forks are sounded together, 5 beats per second are heard. One of the forks is in unison with \(0.97 \mathrm{~m}\) length of sonometer wire and the other is in unison with \(0.96 \mathrm{~m}\) length of the same wire. The fre...

41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is

Two sounding sources send waves at certain temperature in air of wavelength \(50 \mathrm{~cm}\) and \(50.5 \mathrm{~cm}\) respectively. The frequency of sources differ by \(6 \mathrm{~Hz}\). The velocity of sound in air at same temperature ...

The displacement of two sinusoidal waves is given by the equation
$$\begin{aligned} & \mathrm{y}_1=8 \sin (20 \mathrm{x}-30 \mathrm{t}) \\ & \mathrm{y}_2=8 \sin (25 \mathrm{x}-40 \mathrm{t}) \end{aligned}$$
then the phase difference between...

A uniform string is vibrating with a fundamental frequency '\(n\)'. If radius and length of string both are doubled keeping tension constant then the new frequency of vibration is

A tuning fork of frequency \(220 \mathrm{~Hz}\) produces sound waves of wavelength \(1.5 \mathrm{~m}\) in air at N.T.P. The increase in wavelength when the temperature of air is \(27^{\circ} \mathrm{C}\) is nearly $$\left(\sqrt{\frac{300}{2...

A tuning fork gives 3 beats with \(50 \mathrm{~cm}\) length of sonometer wire. If the length of the wire is shortened by \(1 \mathrm{~cm}\), the number of beats is still the same. The frequency of the fork is

End correction at open end for air column in a pipe of length '\(l\)' is '\(e\)'. For its second overtone of an open pipe, the wavelength of the wave is

The equation of wave motion is \(Y=5 \sin (10 \pi t -0.02 \pi x+\pi / 3)\) where \(x\) is in metre and \(t\) in second. The velocity of the wave is

A transverse wave \(\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})\) moves on a stretched string from one end to another end in 0.5 second. If \(x\) and \(y\) are in \(\mathrm{cm}\) and \(t\) in second, then the length of the string is

A car sounding a horn of frequency \(1000 \mathrm{~Hz}\) passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is \(11: 9\). If the speed of sound is '\(v\)', the speed of ...

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '\(L\)'. The length of the open pipe will be

A string fixed at both the ends forms standing wave with node separation of \(5 \mathrm{~cm}\). If the velocity of the wave on the string is \(2 \mathrm{~m} / \mathrm{s}\), then the frequency of vibration of the string is

Two progressive waves are travelling towards each other with velocity \(50 \mathrm{~m} / \mathrm{s}\) and frequency \(200 \mathrm{~Hz}\). The distance between the two consecutive antinodes is

The path difference between two waves, represented by \(\mathrm{y}_1=\mathrm{a}_1 \sin \left(\omega \mathrm{t}-\frac{2 \pi \mathrm{x}}{\lambda}\right)\) and \(y_2=a_2 \cos \left(\omega t-\frac{2 \pi x}{\lambda}+\phi\right)\) is

A sonometer wire '\(A\)' of diameter '\(\mathrm{d}\)' under tension '\(T\)' having density '\(\rho_1\)' vibrates with fundamental frequency '\(n\)'. If we use another wire '\(B\)' which vibrates with same frequency under tension '$$2 \mathr...

A sound of frequency \(480 \mathrm{~Hz}\) is emitted from the stringed instrument. The velocity of sound in air is \(320 \mathrm{~m} / \mathrm{s}\). After completing 180 vibrations, the distance covered by a wave is

A rectangular block of mass '\(\mathrm{m}\)' and crosssectional area A, floats on a liquid of density '\(\rho\)'. It is given a small vertical displacement from equilibrium, it starts oscillating with frequency '\(n\)' equal to ( \(g=\) acc...

A transverse wave in a medium is given by \(y=A \sin 2(\omega t-k x)\). It is found that the magnitude of the maximum velocity of particles in the medium is equal to that of the wave velocity. What is the value of \(A\) ?

Consider the Doppler effect in two cases. In the first case, an observer moves towards a stationary source of sound with a speed of \(50 \mathrm{~m} / \mathrm{s}\). In the second case, the observer is at rest and the source moves towards th...

If the length of stretched string is reduced by \(40 \%\) and tension is increased by \(44 \%\) then the ratio of final to initial frequencies of stretched string is

In case of a stationary wave pattern which of the following statement is CORRECT?

An open organ pipe having fundamental frequency (n) is in unison with a vibrating string. If the tube is dipped in water so that \(75 \%\) of the length of the tube is inside the water then the ratio of fundamental frequency of the air colu...

A uniform rope of length '\(L\)' and mass '\(m_1\)' hangs vertically from a rigid support. A block of mass '\(m_2\)' is attached to the free end of the rope. A transverse wave of wavelength '\(\lambda_1\)' is produced at the lower end of th...

Two uniform wires of same material are vibrating under the same tension. If the first overtone of first wire is equal to the \(2^{\text {nd }}\) overtone of \(2^{\text {nd }}\) wire and radius of the first wire is twice the radius of the $$...

The equation of wave is \(Y=6 \sin\) \(\left(12 \pi t-0.02 \pi x+\frac{\pi}{3}\right)\) where '\(x\)' is in \(m\) and '\(t\)' in \(\mathrm{s}\). The velocity of the wave is

The fundamental frequency of air column in pipe 'A' closed at one end is in unison with second overtone of an air column in pipe 'B' open at both ends. The ratio of length of air column in pipe '\(\mathrm{A}\)' to that of air column in pipe...

A hollow pipe of length \(0.8 \mathrm{~m}\) is closed at one end. At its open end, a \(0.5 \mathrm{~m}\) long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of pipe. If the tension in the ...

Two waves are superimposed whose ratio of intensities is \(9: 1\). The ratio of maximum and minimum intensity is

Consider the following statements about stationary waves.
A. The distance between two adjacent nodes or antinodes is equal to \(\frac{\lambda}{2}(\lambda=\) wavelength of the wave)
B. A node is always formed at the open end of the open orga...

A stationary wave is represented by
\(\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t})\)
where \(\mathrm{x}\) and \(\mathrm{y}\) are in \(\mathrm{cm}\) and \(\mathrm{t}\) in second. The distance between two ...

When an air column in a pipe open at both ends vibrates such that four antinodes and three nodes are formed, then the corresponding mode of vibration is

Two tuning forks of frequencies \(320 \mathrm{~Hz}\) and \(480 \mathrm{~Hz}\) are sounded together to produce sound waves. The velocity of sound in air is \(320 \mathrm{~ms}^{-1}\). The difference between wavelengths of these waves is nearl...

The wavelength of sound in any gas depends upon

A sonometer wire of length 25 cm vibrates in unison with a tuning fork. When its length is decreased by 1 cm, 6 beats are heard per second. What is the frequency of the tuning fork?

Velocity of sound waves in air is '\(\mathrm{V}\)' \(\mathrm{m} / \mathrm{s}\). For a particular sound wave in air, path difference of 'x' \(\mathrm{cm}\) is equivalent to phase difference \(n \pi\). The frequency of this wave is