Question

A sine wave of peak amplitude 10 cm from the baseline (X-axis) has a time period of 5 sec. If a line parallel to X axis intersects this curve at a distance of 7 cm from the origin and clips the upper portion of the curve, the resultant curve will again be a sine curve but a flat upper portion, instead of a curved one. Will there be any change in time period of the curve. Find the new time period.

A. Time period will change and its equal to 8 secs.
B. Time period doesn’t change and is still 5 secs.
C. Time period will change and its equal to 2 secs.
D. Time period cannot be calculated, since the curve has a flat portion

Answer 1

The time taken by the wave to complete its one vibration i.e., one crest (wave above the x-axis) and one trough (wave below the x-axis) is known as time period. It does not depend on the height of the wave.

Complete step by step answer:
A sine wave whose peak i.e, highest amplitude is 10 cm from the X axis has a time period of 5 seconds. The time period is defined as the time taken by the particle of the wave to complete its one vibration. Now, a line parallel to X axis intersects this curve at a distance of 7 cm from the origin and clips the upper portion of the curve i.e., the portion above the line gets removed but the resultant curve is still a sine curve with it upper portion being flat due to this line drawn parallel to X-axis. The new time period in this case is also the same as the initial time period because the time period depends on the time that one vibration takes to complete it. The amplitude of the new sine wave decreases but its time period remains the same i.e., 5 secs.
Therefore, option B is correct.

Note: The time period of a wave only depends on the time taken to complete one vibration. The time period is not affected with the increase or decrease in the amplitude of the same wave.