Question

The am station kbor plays your favorite music from the 20's and 30's at 1290 khz. find the wavelength of these waves.

Answer 1

The useful information here is the frequency expressed in 1290 kHz or 1290 per 0.001 seconds. We use the formula relating the speed of light, frequency and wavelength written below:

c = λν
where c is the speed of light (3×10⁸ m/s)
λ is the wavelength
ν is the frequency

Solving for λ,
λ = c/v = (3×10⁸ m/s)/(1290/0.001 s) = 232.56 m

Answer 2

The required wavelength is $\boxed{232.56{\text{ m}}}$

Further Explanation:

Frequency is basically the rate at which an event occurs or gets repeated after a particular period. In other words, it is the number of times an event occurs in one unit time. It is denoted by ${{\nu }}$. Its SI unit is hertz (Hz). One hertz is defined as the occurrence of an event per second.

Wavelength is a characteristic property of wave and is defined as the distance between the identical points between two successive waves. These points can either be crests or troughs. So the distance between two consecutive crests or troughs is called wavelength. It is represented by $\lambda$. Its units are the same as those of lengths. The SI unit of wavelength is meter (m).

The relationship between frequency and wavelength of light is given by the following expression:

${\text{c}} = {{\nu \lambda }}$        …… (1)                                                                                  

Here,

c is the speed of light.

${\nu }}$ is the frequency.

$\lambda$ is the wavelength.

Rearrange equation (2) for the wavelength.

${\lambda }} = \dfrac{{\text{c}}}{{{\nu }}}$    …… (2)                                                                                           

The frequency is to be converted into Hz. The conversion factor for this is,

 ${\text{1 kHz}} = {\text{1}}{{\text{0}}^{\text{3}}}{\text{ Hz}}$

So the frequency can be calculated as follows:

$\begin{aligned}{{\nu }}&= \left( {1290{\text{ kHz}}} \right)\left( {\frac{{{\text{1}}{{\text{0}}^3}{\text{ Hz}}}}{{{\text{1 kHz}}}}} \right)\\&= 1290000{\text{ Hz}}\\\end{aligned}$  

But one Hz is defined as the occurrence of an event per second. So 1 Hz can also be written as $1{\text{ }}{{\text{s}}^{ - 1}}$ and therefore 1290000 Hz becomes $1290000{\text{ }}{{\text{s}}^{ - 1}}$.

The value of frequency is $1290000{\text{ }}{{\text{s}}^{ - 1}}$.

The speed of light is $3 \times {10^8}\;{\text{m/s}}$.

Substitute these values in equation (2).

$\begin{aligned}{{\lambda }} &= \dfrac{{3 \times {{10}^8}\;{\text{m/s}}}}{{{\text{1290000 }}{{\text{s}}^{ - 1}}}}\\&= 232.56{\text{ m}}\\\end{aligned}$  

Learn more:

1. Calculate the frequency of n = 6 in the Lyman series: brainly.com/question/5762197
2. The energy of a photon in light: brainly.com/question/7590814

Answer details:

Grade: Senior School

Chapter: Structure of the atom

Subject: Chemistry

Keywords: wavelength, frequency, speed of light, 1290 kHz, c, $3*10^8 m/s$, 232.56 m, 1290000 Hz, 1290000 $s^-1.$