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The speed of a sound wave is $330\text{m/s}$ and its frequency is $550 \mathrm{Hz}$. What is its wavelength?
(A) 0.4 m
(B) 4 m
(C) 0.6 m
(D) 6 m

Last updated date: 13th Jun 2024
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Hint We know that sound is a mechanical wave that results from the back and forth vibration of the particles of the medium through which the sound wave is moving. The motion of the particles is parallel (and anti-parallel) to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves. The speed varies depending on atmospheric conditions; the most important factor is the temperature. Humidity has little effect on the speed of sound, nor does air pressure by itself. Air molecules have more energy at higher temperatures, which means they vibrate faster. This allows the sound waves to also travel faster because they are propelled by collisions between the molecules.

Complete step by step answer:
We know that the relationship of the speed of sound $v_{\mathrm{w}}$, its frequency $f$, and its wavelength $\lambda$ is given by $v_{\mathrm{w}} f \lambda,$ which is the same relationship given for all waves. In air, the speed of sound is related to air temperature T by ${{v}_{\text{w}}}=(330\text{m}/\text{s})\sqrt{\dfrac{T}{273\text{K}}}$, $v_{\mathrm{w}}$ is the same for all frequencies and wavelengths.
Speed of the sound wave $=330\text{m}{{\text{s}}^{-1}}$
Frequency $=550\text{Hz}$
It is asked to find the wavelength of the sound wave
We have the equation,
Wavelength $=\dfrac{\text { Speed of the wave }}{\text { Frequency }}$
That is,
Wavelength $=\dfrac{330}{550}=0.6\text{m}$
Hence the wavelength of the sound wave is $0.6\text{m}$

Therefore, the correct answer is Option C.

Note: We know that sound waves enter the outer ear and travel through a narrow passageway called the ear canal, which leads to the eardrum. The eardrum vibrates from the incoming sound waves and sends these vibrations to three tiny bones in the middle ear. The stronger the particle interactions are, the more quickly the wave is transferred. So, in general, sound travels faster in solids than in liquids, and faster in liquids than in gas. Temperature actually increases the speed of sound, because warmer particles generally move at a faster rate. The speed of a sound wave depends on the properties of the medium through which it moves and the only way to change the speed is to change the properties of the medium.