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(a) Define the terms ‘frequency’, ‘wavelength’ and ‘velocity’ of a sound wave. What is the relation between them?
(b) A body vibrating with a time-period of $\frac{1}{ 256}\ s$ produces a sound wave which travels in air with a velocity of $350\ m/s$. Calculate the wavelength.
(a). Frequency: In a sound wave, the number of vibrations per second is called the frequency of the sound. it is denoted by $f$ and its SI unit is $per\ second$ or $Hz$.
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:
Velocity of the sound$=$wavelength$(\lambda)\times$frequency$(f)$
(b). Here given time period $T=\frac{1}{256}\ s$
Velocity of the sound wave $v=350\ m/s$
Therefore, wavelength of the sound wave $\lambda=\frac{velocity(v)}{frequency(f)}$
$=velocity(v)\times time-period(T)$
$=350\ m/s\times \frac{1}{256}\ s$
$=1.36\ m$
Thus, the wavelength of the sound is $1.3\ m$