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Establish the relationship between speed of sound, its wavelength and frequency. If velocity of sound in air is $340\ ms^{-1}$, calculate
$(i)$. wavelength when frequency is $256\ Hz$.
$(ii)$. frequency when wavelength is $0.85\ m$.
Frequency: In a sound wave, the number of vibrations per second is called the frequency of the sound. it is denoted by $(f)$ Hz.
Wavelength: Distance between two consecutive crests or troughs is called the wavelength of the wave. Its denoted by $\lambda$ and its SI unit is meter.
Velocity: Distance traveled in a second by a wave is known as the velocity of the sound wave.
Relation between frequency, wavelength, and velocity of a sound wave:
$\boxed{velocity\ of\ sound(v)=wavelength(\lambda)\times frequency(f)}$
$(i)$. As given, speed of sound, $v=340\ ms^{-1}$
Frequency $(f)=256\ Hz$
Therefore, wavelength of sound $=\frac{v}{f}$
$=\frac{340\ ms^{-1}}{256\ Hz}$
$=1.33\ m$
$(ii)$. If wavelength $(\lambda)=0.85\ m$
Then, frequency$(f)=\frac{v}{\lambda}$
$=\frac{340\ ms^{-1}}{0.85\ m}$
$=400\ Hz$
Updated on: 10-Oct-2022
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