Waves for IIT Mains Online Test

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 in water. The fundamental frequency of the air column in now

A wave represented by the equation y = a cos (kx — ?t) is superposed with another wave to form a stationary wave such that point x = 0 is a node. The equation for the other wave is

The extension in a string, obeying Hooke’s law, is x. The speed of sound in the stretched string is v. If the extensior in the string is increased to 1.5x, the speed of sound will be

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is found to be higher by 100Hz than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is

A whistle giving out 450 Hz approaches a stationary observer, at a speed of 33 m/s. The frequency heard by the

observer in Hz is

A travelling wave in a stretched string is described by the equation y = A sin (kx — ?t) The maximum particle velocity is

Two vibrating strings of the same material but lengths L and 2L have radii 2r and r respectively. They are stretched under the same tension. Both the strings vibrate in their fundamental nodes, the one of length L with frequency v1 and the other with frequency v2. The raio v1 / v2 is given by

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that train A is

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of 9 kg is suspended from the wire. When this mass is replaced by a mass M, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of M is

In the experiment for the determination of the speed of sound in air using the resonance column method, the length of the air column that resonates in the fundamental mode, with a tuning fork is 0.1 rn. When this length is changed to 0.35 m, the same tuning fork resonates with the first overtone. Calculate the end correction.


This test gives an idea about the type of questions you may expect in IIT Mains or other engineering entrance examinations. Prerequisite for taking this test is good understanding of concepts on waves. It is advisable to take this test in one sitting.

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