CBSE Class 11 Physics Mechanical Wave in Strings Solved Examples

Ex.1 A transverse harmonic wave on a string is described by y ( x,t) = 3.0 sin ( 36t + 0.018x + π / 4) Where x, y are in cm and t in sec. The positive direction of x is from left to right.
(i) Is this a travelling or stationary wave ? If is travelling, what are the speed and direction of propagation ?
(ii) What are its amplitude and frequency ?
(iii) What is the initial phase at the origin ?
(iv) What is the distance between two successive crests in the wave ?
Sol. The given equation of a transverse harmonic wave is ,y( x, t ) = 3.0 sin( 36t + 0.018 x+ π /4).....(1)
The standard equation for harmonic waves isy ( x, t ) = a sin 2π /Tt-2πx/λ+φ.....(2)

Ex.2 For the travelling harmonic wave y = 2.0 cos (10t - 0.0080 x + 0.35 ). Where x and y are in cm and t in sec. What is the phase difference between oscillatory motion at two points separated by a distance of
(i) 4 m, (ii) 0.5 m, (iii) A/2 , (iv) 3λ / 4
Sol. The given equation of harmonic waves is , y = 2.0 cos (10 t – 0.0080 x + 0.35).......(1)
The standard equation of harmonic wave is

Ex.3 A simple harmonic wave-train is travelling in a gas in the positive direction of the x-axis. Its amplitude is 2cm, velocity 45metre/sec and frequency 75per sec. Find out the displacement of the particle of the medium at a distance of 135 cm from the origin in the direction of the wave at the instant t = 3 second.
(A) 2cm (B) –2cm (C) –4cm (D) –1cm

Ex. 4 Two particles C and D are executing simple harmonic motion with same amplitude a and same frequency along same straight line. The maximum distance between two particles is

Ex.7 A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If a transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end.
Sol. Given that tension is the string, T = 200 N, length of the string, l = 20 m, mass of the
string = 2.50 kg
∴ (mass/length) of the string,
m = 250. kg/20m = 0.125 kg m^–1