Question

Two waves have wavelengths $0.01{\text{ }}\mathop A\limits^ \circ$ and ${\text{9000 }}\mathop A\limits^ \circ$ respectively. Compare the speeds of these when they travel in vacuum.

Answer 1

Waves are defined as the dynamic disturbances which oscillate with some frequency. Here, two different waves are given with different wavelengths. We will use the property of speed of waves in this case to find out their respective speed in vacuum.

Complete step-by-step solution:
Waves of these wavelengths suggest electromagnetic waves. The electromagnetic spectrum consists of a wide range of electromagnetic waves including gamma rays, X-rays, ultraviolet light, visible light, infrared light, microwaves and radio waves. All of such waves produce oscillating charges or currents.
Electromagnetic waves are transverse in nature which travel with the speed of light associated with oscillating electric and magnetic fields at right angles to each other.
In the given question from the given wavelength is clear that the wave bearing $0.01{\text{ }}\mathop A\limits^ \circ$ is Gamma rays and the other with wavelength ${\text{9000 }}\mathop A\limits^ \circ$ is infrared rays.
Hence, both of them are electromagnetic waves. So, every electromagnetic wave in vacuum travels with the speed of light $3 \times {10^8}{\text{ }}\dfrac{m}{s}$.
Therefore, the two waves travel in vacuum with the same speed of $3 \times {10^8}{\text{ }}\dfrac{m}{s}$.

Additional information: The relation between wavelength $\lambda$, refractive index $\mu$ and speed of light $c$ is $\lambda = \dfrac{c}{\mu }$. Periodic waves are those waves which have the same frequency and travelling waves are defined as those which travel in one direction.

Note: It must be noted that every electromagnetic wave travels with the speed of light in vacuum. They do not get deflected either by electric field or magnetic field. They have the ability to show interference and diffraction.