Final answer:
To calculate the time for 55.9 cycles of the wave to pass a stationary observer, you multiply the number of cycles by the period of the wave. With a frequency of 3.13 Hz, the period is 0.32 seconds. Thus, it takes approximately 17.888 seconds for 55.9 cycles to pass.
Step-by-step explanation:
To find the time required for 55.9 cycles of a sinusoidal transverse wave to pass a stationary observer, we first need to understand the relationship between frequency and period (which is the inverse of frequency). The frequency of this wave is given as 3.13 Hz, which means that 3.13 cycles occur every second. To calculate the period (T), which is the time for one cycle to occur, we use the formula T = 1/f, where f is the frequency.
Now, we can calculate the period:
T = 1/3.13 Hz = 0.32 seconds
To find out how long it takes for 55.9 cycles to occur, we simply multiply the period by the number of cycles:
Time required = 55.9 cycles × 0.32 seconds/cycle = 17.888 seconds
Therefore, it will take approximately 17.888 seconds for 55.9 cycles of the wave to pass a stationary observer.