Question

A. An FM radio station broadcasts at a frequency of 101.3 MHz. What is the wavelength?

Answer 1

Answer:

a) $\lambda = \frac{3x10^8 m/s}{101300000 Hz}= 2.962 m$

b)  $f= \frac{343 m/s}{2.962 m}= 115.8 Hz$

Explanation:

For this case we have the following frequency given:

$f= 101.3 MHz$

We can convert this into Hz like this:

$f= 101.3 MHz * \frac{10^6 Hz}{1 MHz}= 101300000 Hz$

If we have a fundamental wave we need to satisfy the following condition:

$v = \lambda f$

If we solve for the wavelength we got:

$\lambda = \frac{v}{f}$

We know that the velocity of the light is $v= 3x10^8 m/s$

And if we replace into the last formula we got:

$\lambda = \frac{3x10^8 m/s}{101300000 Hz}= 2.962 m$

Part b

For this case we can use the same formula but on this case the velocity of the sound at 20C is approximately 343 m/s, the frequency is given by:

$f = \frac{v}{\lambda}$

We use the same wavelenght from the previous part $\lamba = 2.962 m$

And if we replace the new values we got:

$f= \frac{343 m/s}{2.962 m}= 115.8 Hz$