The speed of a transverse wave on a string is 450 m/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 through a total distance of 1.0km?
To find the time required for a particle of the string to move through a total distance of 1.0 km, we need to use the formula:
Time = Distance / Speed
First, we need to find the total distance covered by a particle in one full wavelength. The total distance covered by a particle is twice the amplitude.
Total Distance = 2 * Amplitude
Given that the amplitude of the wave is 2.0 mm, we convert it to meters:
Amplitude = 2.0 mm = 2.0 × 10^(-3) m
Therefore, the total distance covered by a particle in one full wavelength is:
Total Distance = 2 * 2.0 × 10^(-3) m = 4.0 × 10^(-3) m
Next, we need to find the number of wavelengths in a distance of 1.0 km. To do that, we divide the distance by the wavelength:
Number of Wavelengths = Total Distance / Wavelength
Given that the wavelength is 0.18 m:
Number of Wavelengths = 4.0 × 10^(-3) m / 0.18 m
Now we can calculate the total number of wavelengths in a distance of 1.0 km:
Total Number of Wavelengths = (1.0 × 10^(3) m) / (4.0 × 10^(-3) m / 0.18 m)
Once we have the total number of wavelengths, we can calculate the time required for a particle to move through a total distance of 1.0 km. Since the wave speed is given, we can use the formula:
Time = Total Number of Wavelengths / Speed
Finally, we substitute the given values into the equation:
Time = (1.0 × 10^(3) m) / (Total Number of Wavelengths / 450 m/s)
Calculating the final result will give us the time required for a particle of the string to move through a total distance of 1.0 km.