# Did my tutor give an incorect equation?

1. Homework Statement

An FM radio station generates radio waves that have a frequency of 95.5 MHz. The frequency of the waves from a competing station have a frequency of 102.7 MHz. What is the difference in wavelength between the waves emitted from the two stations?

f1= 95.5
f2=102.7

2. Homework Equations

From what I know

Speed = Frequency x wavelength (v=fλ)

I need to find out wavelength 2 - wavelength 1. This i understand no problem thing thats got me is the equation the tutor gave to work out the equation is...

λ2-λ1=v/f2 - v/f2 <-- Why would I be subtracting the same from the same the answer would be = to zero, would the equation not be...

λ2-λ1=v/f2 - v/f1

I love my physics classes but sadly our tutor 80% of the time runs out of time before he finishes the class but still tests us on the things he missed out (this being one of them) So, im a little stuck from this point on since im not sure what the speed would be, since we have not been told what it is nor how to find it out.

I tryed to look up the speed online and what I found (hopfully corect) is 343 m/s,

3. The Attempt at a Solution

My attempt.

λ1-λ2=v/f1 - v/f2

343/95.5 = 3.59(2dp) - 343/102.7 = 3.34 (2dp)

= 3.59-3.34

=0.25m

Now, im not sure if this is corect, since its actually a multi choice on the answer and the nearest answer is actually 0.22m (interactive test so told me that the right answer when expermented)

my main problem is where did I go wrong to get 0.25 where he got 0.22.

Anyone able to give me some help/advice on this?

thanks

Ritchie.

p.s. really sorry on spelling, cant attach my disleaxer form on here (smiles)

## Answers and Replies

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Dick
Homework Helper
You put in the speed of sound for the waves and dropped the M in MHz. Radio waves travel at the speed of light. Your tutors equation certainly does have a typo. Guess he has disleaxer...

1. Your take on the equation is correct.

2. Your Velocity is wrong. 343m/s looks like the spped of sound but radio waves travel at the speed of light 'C', find a value for 'C'.

3. Looking at your calculations you have applied the frequency incorrectly, this may have been because you were struggling with the wrong velocity and trying to get it to fit. What does the M represent in MHz?

p.s. Dyslexia didn't stop me once I left school, modern "speil chockers" are a god send.

f2 in both terms must've been a typo. It is v/f1 - v/f2, if you want the difference to be positive. Also, you're dealing with electromagnetic waves here, not sound. These are radio waves, which have the same speed as light.

λ2-λ1=v/f2 - v/f2 <-- Why would I be subtracting the same from the same the answer would be = to zero, would the equation not be...

λ2-λ1=v/f2 - v/f1
You're right.

I tryed to look up the speed online and what I found (hopfully corect) is 343 m/s
The radio waves, like any other electromagnetic waves travel at the speed of light.
The speed of light in the air is approximately the speed of light in the vacuum, which is 299,792,458 m/s

EDIT: crossposted with neutrino, Panda and Dick

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My brain must be taking a small vacation on this one.

ok, the speed of light I knew, just did not relise they used same speed, should have most dence of me lol.

Anyways Ive tryed to put the numbers in and its spiting out the wrong answer to what Im looking for, i account this to the M i droped as was mentioned, M = mega MHz megahertz (right?)

and thats em ???x10^6 I beleave. but im not sure how to take this and add it into the equation to help if im even right on this.

as for spell check, love it also, just the old computer im useing at the moment does not have one working at the moment.

EDIT:

ok think i got it figured.

I see now where i was forgeting the M and have that figured and if im right, and according to my calc im only off by 0.01 and that I put down to useing 2.9x10^8 not 3.0x10^8.

Calculation:

2.9x10^8 / 95.5x10^6(to turn into that wonderfull M)
=3.0366

2.9x10^8 / 102.7x10^6
=2.8238

3.0366-2.8238

= 0.21m

Thanks for all the help!

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Speed of light 299,792,458 approximates closer to 3.0x10^8 than 2.9x10^8. If you take out the rounding error you should get 0.22m