CBSE Class 11 Physics Wave Motion Solved Examples

Ex.1 The vibration of a string of length 60 cm fixed at both ends are represented by the equation :
y = 4 (sinπx/15)cos (96 π t) where x and y are in cm and t is in seconds.
(a) What is the maximum displacement of a point at x = 5 cm ?
(b) Where are the nodes located along the string ?
(c) What is the velocity of a particle at x = 7.5 cm & at t = 0.25 sec.
(d) Write down the components waves which give the above wave on superposition.

Sol.: Comparing given equation with equation of standing wave,

Ex.2 A man standing in front of a mountain at a certain distance beats a drum at regular intervals. The drumming rate is gradually increased and he finds that the echo is not heard distinctly when the rate becomes 40 per minute. He then moves nearer to the mountain by 90 metres and finds that the echo is again not heard when the drumming rate becomes 60 per minute. Calculate :
(a) the distance between the mountain and the initial position of the man
(b) the velocity of sound.

Sol.: Let the distance between the man and mountain be x metres and the velocity of sounds be
v metres/sec.

Ex.3 A simple harmonic wave of amplitude 8 units traverses a line of particles in the direction of positive x-axis. At any given instant of time, the displacement of a particle at a distance of 10 cm from the origin is +6 units and the displacement of this particle at a distance of 25 cm from the origin is +4 units. Find the wavelength of wave (given sin 48.6º = 0.75)