The frequency of a radio wave is inversely proportional to the wavelength. If a wave 250 m long has a frequency of about 1200 kHz, what is the approximate length of a wave with a frequency of 800 kHz?
A. 167 m
B. 258 m
C. 325 m
D. 375 m
L = 1200/800 * 250 = 375 m.
To solve this problem, we can use the formula for the inverse proportionality between frequency (f) and wavelength (λ):
f ∝ 1/λ
Given that a wave with a wavelength of 250 m has a frequency of 1200 kHz, we can set up the following proportion:
f₁/λ₁ = f₂/λ₂
Substituting the given values:
1200 kHz / 250 m = 800 kHz / λ₂
Now, we can solve for λ₂:
λ₂ = (800 kHz * 250 m) / 1200 kHz
= (200000 / 1200) m
= 166.67 m
Rounded to the nearest whole number, the approximate length of a wave with a frequency of 800 kHz is 167 m. Therefore, the correct answer is A. 167 m.
To solve this problem, we can use the mathematical relationship between frequency and wavelength for radio waves:
Frequency = Speed of Light / Wavelength
This relationship tells us that frequency and wavelength are inversely proportional. In other words, as the frequency increases, the wavelength decreases and vice versa.
Given that a wave with a wavelength of 250 meters has a frequency of about 1200 kHz, we can set up the following equation:
1200 kHz = Speed of Light / 250 meters
To find the approximate length of a wave with a frequency of 800 kHz, we can rearrange the equation as follows:
800 kHz = Speed of Light / Wavelength
Now, we can solve for the wavelength:
Wavelength = Speed of Light / 800 kHz
To find the approximate length, we need to know the speed of light, which is approximately 299,792,458 meters per second. Substituting this value into the equation, we get:
Wavelength = 299,792,458 meters/second / 800 kHz
Now, we need to convert kHz to Hz by multiplying by 1000:
Wavelength = 299,792,458 meters/second / 800,000 Hz
Simplifying the equation, we have:
Wavelength = 374.743 meters
Therefore, the approximate length of a wave with a frequency of 800 kHz is 375 meters.
So, the answer is option D.