Question

Write two differences between a light wave and sound wave. The separation between two consecutive crests of transverse waves is ${{150m}}$ .If the wave velocity is ${{15}}\dfrac{{{m}}}{{{s}}}$ . Find:
(A)The distance between crest and adjoining trough.
(B)Time period.

Answer 1

The separation between two consecutive crests in a transverse wave is called wavelength. So we have given $\left( {{{\lambda = 150m}}} \right)$ ;So by using a simple formula we can calculate the following things.

Formula Used::
${{Frequency = }}\dfrac{{{{Velocity}}}}{{{{Wavelength}}}}$
which can also be written as follows,
${{\nu = }}\dfrac{{{c}}}{{{\lambda }}}$

Complete step by step Answer:
$\to$ Light waves are electromagnetic waves while sound waves are mechanical waves.
$\to$ Light waves are transverse while sound waves are longitudinal waves.
$\to$ Light waves can travel in vacuum but sound waves require a material. But sound waves require a material medium to travel, hence they cannot travel in vacuum.

(A) In the Question, we are given that the separation between the $2$ consecutive crests in the transverse wave is ${{150m}}$ .
It means ${{\lambda = 150m}}$ and we are given the velocity of wave ${{15m}}{{{s}}^{{{ - 1}}}}$ .
So,
Separation between two consecutive crests is wavelength;
We get;
${{Wavelength = 150m}}{{{s}}^{{{ - 1}}}}$
${{Velocity = 15m}}{{{s}}^{{{ - 1}}}}$
Also, we know that;
${{Frequency = }}\dfrac{{{{Velocity}}}}{{{{Wavelength}}}}$
${{\nu = }}\dfrac{{{{15}}}}{{{{150}}}} = \dfrac{1}{{10}}$
So,
Time period= ${{T = }}\dfrac{{{1}}}{{{\nu }}}{{ = }}\dfrac{{{1}}}{{\dfrac{{{1}}}{{{{10}}}}}}$

Ans (B), ${{T = 10second}}$.

Now, in a wave the Distance between Crest and adjoining trough is equal to $\dfrac{{{\lambda }}}{{{2}}}$.
So, Distance between Crest adjoining trough = $\dfrac{{{\lambda }}}{{{2}}}{{ = }}\dfrac{{{{150}}}}{{{2}}}{{ = 75m}}$

Ans (A), ${{75m}}$.

Additional Information:
More Information about Sound and Light waves:
$\to$ Velocity of sound waves in air is approximately ${{330m}}{{{s}}^{{{ - 1}}}}$ & Velocity in air is ${{3 \times 1}}{{{0}}^{{8}}}{{m}}{{{s}}^{{{ - 1}}}}$
Sound requires a medium for propagation and hence cannot travel through vacuum & light can travel through vacuum. Sound waves are longitudinal and light waves are transverse waves. Sound waves are mechanical waves & light waves are a type of electromagnetic wave. Velocity of sound increases with the increase in density of the medium & Speed of light is lower in less dense medium. Exhibit reflection, refraction, diffraction and interference properties (sound waves) and Exhibit reflection, refraction, diffraction and interference properties (Light waves).

Note: The relation b/w the Wavelength, Velocity of wave and Frequency can be used to solve such a question. Remember the distance between the two successive crests is known as Wavelength $\left( {{\lambda }} \right){{.}}$