# Electromagnetic waves and sound waves can have the same frequency. (a) What is the wavelength of...

## Question:

Electromagnetic waves and sound waves can have the same frequency.

(a) What is the wavelength of a 1.00-kHz electromagnetic wave?

(b) What is the wavelength of a 1.00-kHz sound wave? (The speed of sound in air is 341 m/s.)

(c) Can you hear a 1.00-kHz electromagnetic wave?

## Waves

A wave is an organized propagation of a disturbance. It is organized in the sense that it has to propagate in conformity with the classical ave equation. This is a linear second-order partial differential equation. In one dimension the equation has the form,

{eq}\displaystyle {\frac{\partial^2 \psi }{\partial x^2}=\frac{1}{v^2}\frac{\partial^2 \psi }{\partial t^2}} {/eq}

The solutions of this equation have the mathematical form {eq}\displaystyle { \psi (kx-\omega t)} {/eq}.

Here {eq}\displaystyle {\psi} {/eq} is the wavefunction that gives the displacement at any {eq}\displaystyle {x} {/eq} at any instant of time {eq}\displaystyle {t} {/eq}. Here {eq}\displaystyle { k=\frac{2 \pi}{\lambda}} {/eq} is the propagation constant and {eq}\displaystyle { \omega}=2 \pi \nu {/eq} is the angular frequency.

The speed {eq}\displaystyle {v} {/eq} of any wave is related to the frequency {eq}\displaystyle {\nu} {/eq} and the wavelength {eq}\displaystyle {\lambda} {/eq} according to

{eq}\displaystyle {v=\nu \lambda} {/eq}.