the speed of a transverse wave on a string is 450m/s while the wavelength is 0.18m. The amplitude of the wave is 2.0mm. How much time is required for a particle of the string to move a total distance of 1.0km....
The thing that confuses me about this question is the amplitude of the wave as i do not know how to incorporate it into my calculations. Please help me.
Something has to be wrong. If the amplitude is 2mm, then the max the string particles move is 4mm (up and down). It cannot move 1km.
To solve this question, you'll need to use a formula that relates the speed of a wave, its frequency, and its wavelength:
speed = frequency × wavelength
First, calculate the frequency of the wave using the given speed and wavelength:
frequency = speed / wavelength
frequency = 450 m/s / 0.18 m
frequency ≈ 2500 Hz
Now, let's determine the period of the wave. The period (T) represents the time it takes for one complete cycle of the wave to pass a given point. The period is the reciprocal of the frequency:
T = 1 / frequency
T = 1 / 2500 Hz
T = 0.0004 s
Since the period represents the time for one complete cycle, we can find the time required for a particle of the string to move a total distance of 1.0 km by multiplying the period by the number of cycles:
Total time = T × Number of cycles
To find the number of cycles, we need to know the distance covered by one cycle. This distance is equal to the wavelength of the wave, which is 0.18 m.
Number of cycles = Total distance / Distance per cycle
Number of cycles = 1000 m / 0.18 m
Number of cycles ≈ 5555.56 cycles
Now, we can substitute the values into the formula to calculate the total time:
Total time = 0.0004 s × 5555.56 cycles
Total time ≈ 2.22 s
Therefore, it would take approximately 2.22 seconds for a particle of the string to move a total distance of 1.0 km.