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    


Correct option is

3.0 m

Angular frequency ω = π or 2 π V = π or V = 0.5 Hz. Now v = 1.5 ms –1. Therefore λ = v/V = 1.5/0.5 = 3m.   



When a mass m is hung from the lower of a spring of negligible mass, an extension x is produced in the spring. The mass is set into vertical oscillations. The time period of oscillation is


A small spherical steel ball is placed a little away from the centre of a large concave mirror of radius of curvature R = 2.5 m. The ball is then released. What is the time period of the motion? Neglect friction and take 



Two masses m1 and m2 are suspended together by a massless spring of force constant k (see fig). When the masses are in equilibrium, mass m1 is removed without disturbing the system. The angular frequency of oscillation of mass m2 is   


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


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