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Wave Speed

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One among the important basic property of a wave is wave speed. It is nothing but the velocity through a medium. The requirement of medium depends on which type waves are propagating. This fundamental characteristic helps to find out the propagating wave speed which has lots of applications. The proper definition, formula and related problems are described in the following section.

Wave Speed Definition

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Wave speed is defined as the distance traveled by a crest or trough of a wave in a given interval of time. It is measured in the unit of m/s and denoted by v.

The formula to find out the wave speed is given below:
v = f$\lambda$
where,
f is the frequency,
$\lambda$ is the wavelength.

Speed of Radio Waves

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Radio waves are created by the oscillation of electrons in a conductor. They are used to transmit radio and TV signals between different points on the Earth's surface. Radio waves have a very wide range of wavelengths from a few kilometers to a few centimeters. Long wavelength can be used to transmit signals over very long distances.

The speed of radio waves is same as that of light velocity when it travel through vacuum.

Speed of Sound Waves

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The speed of sound depends on the medium. In general, the speed of sound is highest in solids and lowest in gases. The speed of sound in a solid is given by,
v = $\sqrt{\frac{Y}{\rho }}$
where,
Y is Young's modulus and
$\rho$ is the density.

Young's modulus is an elastic constant that measures the stiffness of a material.Hence the given equation can be written as,
v = $\sqrt{\frac{stiffness}{density }}$

This equation explains qualitatively how the speed of sound varies when we compare solids, liquids and gases.

Speed of Electromagnetic Waves

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Electromagnetic waves are the only waves that can travel through a vacuum. Like any other wave, electromagnetic waves can be reflected and refracted, but they are unique in the way they travel. Electromagnetic waves are nothing but the light waves. It travels with a velocity of 3x108 m/s in vacuum. When it is travel through a medium the velocity is less than that of vacuum.

What affects the Speed of a Wave?

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The important factors which affects the speed of waves are listed below.
  • Nature of the medium
  • Elasticity of a medium
  • Density of the medium

How to find the Speed of a Wave?

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Lets go through some solved problems which gives more idea about the topic.

Solved Examples

Question 1: Calculate the speed of the sound wave whose frequency is 450Hz and wavelength is 15m?

Solution:
 
Given that,
Frequency, f = 450Hz and
Wavelength, $\lambda$ = 15m

The equation for wave speed is,
v = f$\lambda$
v = 450×15 = 6750m/s
 

Question 2: Calculate the wavelength of a sound wave whose frequency is 800Hz and velocity is 25m/s?

Solution:
 
Given that,
Frequency, f = 800Hz and
Velocity, v = 25m/s

The equation for wave speed is,
v = f$\lambda$
$\lambda$ = $\frac{v}{f}$
$\lambda$ = $\frac{25}{800}$ = 0.03125m