What is the Wavelength of an FM Radio Wave at 107.5 MHz?

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In summary, the conversation discusses how to find the wavelength of a radio wave with only the frequency given. It is mentioned that the speed of light can be used as an approximation for the speed of the radio wave when traveling through space. The conversation also briefly touches on finding the time it takes for a message to reach astronauts on Mercury.
  • #1
shimizua
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Homework Statement


An FM station broadcasts at 107.5 MHz. What is the wavelength of this wave?


Homework Equations


well i know that speed = frequency X wavelenght but if i don't know the speed then how can i find the length


The Attempt at a Solution


so i found out that the average length of a radio wave is about 3 m and tried it but it was the wrong answer. i am just confused how to find the wavelength with only the frequency.
 
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  • #2
oh so i think this is a second part to the question also. How long will it take for a message from Earth to reach the first astronauts who arrive on Mercury; assume Mercury is at its closest approach to Earth (9.17×107km)?

well i just did that distance 9.17x10^7 km and got it to m and then divided is by 3x10^8 which is the speed of light so what did i do wrong for that part?
 
  • #3
shimizua said:
oh so i think this is a second part to the question also. How long will it take for a message from Earth to reach the first astronauts who arrive on Mercury; assume Mercury is at its closest approach to Earth (9.17×107km)?

well i just did that distance 9.17x10^7 km and got it to m and then divided is by 3x10^8 which is the speed of light so what did i do wrong for that part?
Nothing. You working is fine to either you have made a numerical error somewhere, or you have not entered the correct number of significant digits.
shimizua said:

Homework Statement


An FM station broadcasts at 107.5 MHz. What is the wavelength of this wave?

Homework Equations


well i know that speed = frequency X wavelenght but if i don't know the speed then how can i find the length

The Attempt at a Solution


so i found out that the average length of a radio wave is about 3 m and tried it but it was the wrong answer. i am just confused how to find the wavelength with only the frequency.
If you were to assume that the radio wave was traveling through space (which is a pretty good approximation for air), what would be its speed?
 
  • #4
would i just use 3x10^8 m/s?
 
  • #5
oh wait i think i did have my decimals mixed up for the problem about the time. haha thanks
 
  • #6
shimizua said:
would i just use 3x10^8 m/s?
Sounds good to me.
shimizua said:
oh wait i think i did have my decimals mixed up for the problem about the time. haha thanks
No problem.
 
  • #7
cool thanks it worked!
 

What is the wavelength?

The wavelength is the distance between two consecutive peaks or troughs in a wave. It is typically measured in meters or nanometers.

How is wavelength related to frequency?

Wavelength and frequency are inversely proportional. This means that as the wavelength increases, the frequency decreases, and vice versa. The relationship is described by the equation: wavelength = speed of light / frequency.

What is the unit of wavelength?

The unit of wavelength depends on the type of wave being measured. For electromagnetic waves, such as light, the unit is typically meters or nanometers. For sound waves, the unit is usually meters or centimeters.

How does wavelength affect the properties of waves?

Wavelength has a direct impact on the properties of waves. Waves with longer wavelengths have lower frequencies and lower energy, while waves with shorter wavelengths have higher frequencies and higher energy. Wavelength also determines the color of light and the pitch of sound.

What is the relationship between wavelength and energy?

Wavelength and energy are inversely proportional. This means that as the wavelength increases, the energy decreases, and vice versa. This relationship is described by the equation: energy = Planck's constant x speed of light / wavelength.

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