(a) Two microwave frequencies are authorized for use in microwave ovens: 900 and 2560 MHz. Calculate the wavelength of each.
1 cm (frequency = 900 MHz)
2 cm (frequency = 2560 MHz)
(b) Which frequency would produce smaller hot spots in foods due to interference effects?
3 MHz
(a)
λ1=c/f1 =3•10^8/900•10^6 =0.33 m =33 cm.
λ2=c/f2 = 3•10^8/2560•10^6 =0.12 m =12 cm
(b) 2560 MHz
oh its 11.7! got it
thank you!
λ = c/f.
f = 900*106/s, λ = (1/3) m
f = 2560*106/s, λ = 11.7 cm.
dfgs
To calculate the wavelength of each frequency, you can use the formula:
Wavelength (λ) = Speed of Light (c) / Frequency (f)
(a) For the first frequency of 900 MHz:
First, let's convert the frequency to Hz:
900 MHz = 900 × 10^6 Hz
The speed of light (c) is approximately 3 × 10^8 meters per second (m/s). Converting it to cm/s:
3 × 10^8 m/s = 3 × 10^10 cm/s
Plugging the values into the formula:
Wavelength (λ) = (3 × 10^10 cm/s) / (900 × 10^6 Hz)
Simplifying the equation:
Wavelength (λ) = 33.33 cm
Therefore, the wavelength at 900 MHz is approximately 33.33 cm.
For the second frequency of 2560 MHz:
Similarly, let's convert the frequency to Hz:
2560 MHz = 2560 × 10^6 Hz
Using the same speed of light value:
Wavelength (λ) = (3 × 10^10 cm/s) / (2560 × 10^6 Hz)
Simplifying the equation:
Wavelength (λ) = 11.72 cm
Therefore, the wavelength at 2560 MHz is approximately 11.72 cm.
(b) To determine which frequency would produce smaller hot spots in foods due to interference effects, we need to consider the concept of interference. When two waves with the same frequency interfere constructively, they reinforce each other, leading to larger amplitudes (intensities) and potentially creating hot spots. On the other hand, when the waves interfere destructively, they cancel each other out, resulting in smaller amplitudes (intensities) and minimizing hot spots.
Since the interference effects depend on wavelength and the wavelength of the 2560 MHz frequency is smaller (11.72 cm) compared to the wavelength of the 900 MHz frequency (33.33 cm), the 2560 MHz frequency would produce smaller hot spots in foods due to interference effects.