# 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 $0.85\ m$.

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Frequency: In a sound wave, the number of vibrations per second is called the frequency of the sound. it is denoted by $(f)$ Hz$Hz$.

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 13:28:57