Wave Motion

Given below are some functions of x and t to represent the displacement of an elastic wave.

Q: Given below are some functions of x and t to represent the displacement of an elastic wave.

(i) y = 5 cos⁡(4x) sin⁡(20t)

(ii) y = 4 sin⁡(5x – t/2) + 3 cos⁡(5x – t/2)

(iii) y = 10 cos⁡[(252 – 250)πt]cos[(252+250)πt]

(iv) y = 100 cos⁡(100πt + 0.5x)

State which of these represent

(a) A travelling wave along – x-direction

(b) A stationary wave

(c) Beats

(d) A travelling wave along – x-direction

Ans: (a),(b),(c) & (d)

Which of the following statement are true for a stationary waves ?

Q: Which of the following statement are true for a stationary waves ?

(a) All the particles has a fixed amplitude which is different from the amplitude of its nearest particle

(b) All the particles cross their position at the same time

(c) There is no net transfer of energy across any plane

(d) There are some particle which are always at rest

Ans: (a) , (b) , (c) & (d)

The transverse displacement of a string (clamped at its both ends) is given by y(x,t) = 0.06 sin⁡(2πx/3) cos⁡(120πt). All the points on the string between two consecutive nodes vibrate with

Q: The transverse displacement of a string (clamped at its both ends) is given by y(x,t) = 0.06 sin⁡(2πx/3) cos⁡(120πt).
All the points on the string between two consecutive nodes vibrate with

(a) same frequency

(b) same phase

(c) same energy

(d)different amplitude

Ans: (a) , (b) & (d)

A train whistling at constant frequency is moving towards a station at a constant speed v. the train goes past a stationary observed on the station. The frequency n of the sound as hear by the observer is plotted as a function of time t (figure). Identify the expected curve.

Q: A train whistling at constant frequency is moving towards a station at a constant speed v. the train goes past a stationary observed on the station. The frequency n of the sound as hear by the observer is plotted as a function of time t (figure). Identify the expected curve.

(a) Numerical

(b) Numerical

(c) Numerical

(d) Numerical

Ans: (c)

With propagation of longitudinal waves through a medium, the quantity transmitted is

Q: With propagation of longitudinal waves through a medium, the quantity transmitted is

(a) matter

(b) Energy

(c) energy and matter

(d) energy, matter and momentum

Ans: (b)