Question

(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 $\frac{1}{256}\mathrm{s}$ produces a sound wave which travels in air with a velocity of 350 m/s. Calculate the wavelength.

Answer 1

(a) Frequency: The number of complete waves or cycles produced in one second.
Wavelength: The minimum distance in which a sound wave repeats itself.
Velocity of a wave: The distance travelled by a wave in one second.
We know the relation between velocity, frequency, and wavelength
ν = f × λ,
where ν is the velocity of sound, F the frequency, and λ the wavelength.

(b) We have to find the wavelength of the sound wave.
Given: Velocity of sound wave ν = 350 m/s
We have to first find the frequency of oscillation.
Time period $\left(T\right)=\frac{1}{256}\mathrm{s}$
We know the relation between frequency and time period $f=\frac{1}{T}$,
where f is the frequency and T the time period.
So,
$$\begin{gathered} f=\frac{256}{1}\mathrm{Hz} \\ =256\mathrm{Hz} \end{gathered}$$

Now we can calculate wavelength as $\lambda =\frac{v}{f}$,
where ν is the velocity, f the frequency, and λ the wavelength.
So,
$$\begin{gathered} \mathrm{\lambda }=\frac{350}{256}\mathrm{m} \\ =1.367\mathrm{m} \end{gathered}$$
Therefore, velocity of sound is 1.37 m.