A wire of mass kg per metre passes over a frictionless pulley fixed on the top of an inclined frictionless plane which makes an angle of 30o with the horizontal. Masses M1 and M2 are tied at the two ends of the wire. The mass M1 rests on the plane and the mass M2 hangs vertically downwards. The whole system is in equilibrium. Now a transverse wave propagates along the wire with a velocity of 100 m/s. Find the value of masses M1 and M2. (g = 9.8 m/s2)
For equilibrium of M1 along and perpendicular to the plane we have respectively:
And for equilibrium of M2,
Now as the velocity of a wave on a string is given by
and as here v = 100 m/s and m = 9.8 × 10–3 kg/m
Substituting the value of T from Eqn. (3) in Eqns. (2) and (1),
If the amplitude of velocity of a particle acted on by a force F = F0 cos ωtalong x-axis is given by:
Find the condition of resonance and resonant frequency.
An observer standing at sea coast observers 54 waves reaching the coast per minute. If the wavelength of the waves is 10 m, find the velocity. What type of waves did he observe?
A light pointer fixed to one prong of a tuning fork touches a vertical plane. The fork is set vibrating and the plate is allowed to fall freely. 8 complete oscillations are counted when the plate falls through 10 cm. What is the frequency of the tuning fork?
A progressive wave of frequency 500 Hz is travelling with a velocity of 360 m/s. How far apart are two points 60o out of phase?
A travelling wave pulse is given by
In which direction and with what velocity is the pulse propagating? What is the amplitude of pulse?
The amplitude of a wave disturbance propagating in the positive xdirection is given by
Where x and y are in m. The shape of the wave disturbance does not change during the propagation. What is the velocity of the wave?
A wire of uniform cross-section is stretched between two points 1 mapart. The wire is fixed at one end and a weight of 9 kg is hung over a pulley at the other end produces fundamental frequency of 750 Hz. (a) What is the velocity of transverse waves propagating in the wire? (b) If now the suspended weight is submerged in a liquid of density (5/9) that of the weight, what will be the velocity and frequency of the waves propagating along the wire?
A copper wire is held at the two ends by rigid supports. At 30oC, the wire is just taut, with negligible tension. Find the speed of transverse waves in this wire at 10oC if ,
A uniform rope of length 12 m and mass 6 kg hangs vertically from a rigid support. A block of mass 2 kg is attached to the free end of the rope. A transverse pulse of wavelength 0.06 m is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope?
A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. (a) Find the speed of transverse wave in the rope at a point 0.5 m distant from the lower end, (b) Calculate the time taken by a transverse wave to travel the full length of the rope (g = 9.8 m/s2)