Particle displacements (in cm) in a standing wave are given by
The distance between a node and the next anti-node is
which gives . The distance between a node and the next antinode = λ/4 = 20/4 = 5 cm.
A mass m is suspended at the end of a massless wire of length L and cross-sectional area A. If Y is the Young’s modulus of the material of the wire, the frequency of oscillations along the vertical line is given by
A test tube of cross-sectional area a has some lead shots in it. The total mass is m. It floats upright in a liquid of density d. When pushed down a little and released, it oscillates up and down with a period T. Use dimensional considerations and choose the correct relationship from the following.
When a wave travels in a medium, the particle displacements are given by
Where y and x are in meters and t in seconds. The wavelength of the wave is
Transverse wave of amplitude 10 cm is generated at one end (x = 0) of a long string by a tuning fork of frequency 500 Hz. At a certain instant of time, the displacement of a particle A at x = 100 cm is – 5 cm and of particle B at x = 200 cm is +5 cm. What is the wavelength of the wave?
Transverse waves of the same frequency are generated in two steel wires A and B. The diameter of A is twice that of B and the tension in A is half that in B. The ratio of the velocities of waves in A and B is
A sonometer wire, with a suspended mass of M = 1 kg, is in resonance with a given tuning fork. The apparatus is taken to the moon where the acceleration due to gravity is 1/6 that on earth. To obtain resonance on the moon, the value of M should be
A source of sound vibrates according to the equation y = 0.05 cos π t. It sends waves of velocity 1.5 ms –1. The wavelength of the waves is
Two identical waves, each of frequency 10 Hz, are travelling in opposite directions in a medium with a speed of 20 cm s–1. The distance between adjacent nodes is
Figure shows the shape of part of a long string in which transverse waves are produced by attaching one end of the string to tuning fork of frequency 250 Hz. What is the velocity of the waves?
If Young’s modulus of the material of a rod is and its density is 8000 kg m–3, the time taken by a sound wave to traverse 1 m of the rod will be