Question

A sound wave whose frequency is $220Hz$ has a speed of $440m{{s}^{-1}}$ in a given medium. Find the wavelength of the sound.

Answer 1

Hint : Sound waves are long-distance waves that travel through a medium such as air or water. When we think of sound, we frequently consider its amplitude (or intensity) and pitch (frequency).

Complete step-by-step solution:
The speed of sound is the distance traveled by a sound wave per unit of time as it propagates through an elastic medium. At ${{20}^{o}}C$($68{}^{o}F$), the speed of sound in air is approximately $343$ meters per second ($1,235\text{ }km/h$;$1,125\text{ }ft/s$;$767\text{ }mph$;$667\text{ }kn$), or $2.9$seconds for a kilometer and $4.7$seconds for a mile. It is strongly influenced by temperature as well as the medium through which a sound wave travels.
The speed of sound in an ideal gas is solely determined by its temperature and composition. In ordinary air, the speed has a weak dependence on frequency and pressure, deviating slightly from ideal behavior.
The speed of sound in colloquial speech refers to the speed of sound waves in the air. However, the speed of sound varies depending on the substance: sound travels most slowly in gases and fastest in liquids, and fastest in solids.
In the above given example,
$Velocity(V)=440m/s$
$Frequency(~n)=220Hz$
$Wavelength~(\lambda )=?$
We have two equations,
$V=\lambda \times n$
$440=\lambda \times 220$
\lambda $$$$=$$$$\dfrac{440}{220}$$$$=$$$$2m
Thus, the wavelength of the sound is$2m$.

Note: The speed of sound in a fluid medium (gas or liquid) is used as a relative measure for the speed of an object moving through the medium in fluid dynamics. The ratio of an object's speed to the speed of sound in a fluid is known as the object's Mach number. Objects moving faster than Mach 1 are said to be traveling at supersonic speeds.