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

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Homework Help Overview

The discussion revolves around calculating the wavelength of an FM radio wave broadcasting at 107.5 MHz, as well as determining the time it takes for a message to reach Mercury from Earth. The subject area includes wave properties and the speed of light.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between speed, frequency, and wavelength, questioning how to find wavelength without knowing the speed. There are attempts to apply known values for the speed of light and average radio wave lengths.

Discussion Status

Some participants have provided guidance on using the speed of light for calculations. There is acknowledgment of potential numerical errors in the time calculation for the message to Mercury, but no explicit consensus on the wavelength calculation has been reached.

Contextual Notes

Participants are working under the assumption that radio waves travel through space at the speed of light, and there are mentions of significant digits affecting calculations.

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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 wavelength 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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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?
 
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 wavelength 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?
 
would i just use 3x10^8 m/s?
 
oh wait i think i did have my decimals mixed up for the problem about the time. haha thanks
 
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.
 
cool thanks it worked!
 

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