(1) If an electromagnetic wave has a period of 4.8 μs, what is the frequency and wavelength?
I know how to find the frequency but for the wavelength how can we find it without the velocity being given????
(2) The beam of a helium-neon laser (λ = 632.8 nm) is incident on a slit of width 0.085 mm. A screen is placed 95.0 cm away from the slit. How far from the central band is the first dark band? If the slit was two times wider, would the first dark band be closer or farther form the central band?
1. Since is is an electromagnetic wave, the velocity is c = 3.0*10^8 m/s
2. Use the single slit diffraction equation.
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslit.html
The first dark band is at an angular distance ë/d from the central bright band. Doubling the slit width decreases the band separation distance by half.
(1) To find the frequency of an electromagnetic wave, you can use the formula:
frequency (f) = 1 / period (T).
Given that the period of the wave is 4.8 μs (microseconds), we can convert it to seconds by dividing by 1,000,000:
T = 4.8 μs / 1,000,000 = 4.8 x 10^-6 seconds.
Now, plug this value into the formula to calculate the frequency:
f = 1 / (4.8 x 10^-6) = 208,333.33 Hz.
To find the wavelength, you normally need the velocity of the wave. However, in this case, we don't have the velocity given. Therefore, we cannot directly calculate the wavelength.
The wavelength of an electromagnetic wave can be determined using the formula:
wavelength (λ) = velocity (v) / frequency (f).
However, without knowing the velocity, we cannot calculate the wavelength accurately in this case. To find the wavelength, you would need additional information or measurements.
(2) To determine the distance from the central band to the first dark band in a diffraction pattern, you can use the formula for the position of the first dark band:
y = (λ * L) / d,
where y is the distance from the central band to the first dark band, λ is the wavelength, L is the distance from the slit to the screen, and d is the width of the slit.
Given that λ (wavelength) is 632.8 nm (nanometers) and d (slit width) is 0.085 mm (millimeters), we need to convert these values to the same unit before plugging them into the formula.
λ = 632.8 nm / 1,000,000 = 6.328 x 10^-4 mm,
d = 0.085 mm.
Now, we can calculate the position of the first dark band:
y = (6.328 x 10^-4 mm * 95.0 cm) / 0.085 mm = 7.07 cm.
Therefore, the first dark band is located 7.07 cm away from the central band.
If the slit is twice as wide (0.17 mm instead of 0.085 mm), we can again use the formula to calculate the position of the first dark band:
y' = (6.328 x 10^-4 mm * 95.0 cm) / 0.17 mm = 3.52 cm.
The first dark band would be closer to the central band, at a distance of 3.52 cm instead of 7.07 cm, if the slit width is doubled.