Speed of a sound — lesson. Science State Board, Class 9.

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The distance travelled by a sound wave per unit time as it propagates through an elastic medium is known as the speed of sound.

Speed (v) = \frac{Distance}{Time}

If one wavelength (

λ

) represents the distance travelled by one wave, and one time period (\(T\)) represents the time taken for this propagation, then

Speed (v) = \frac{One wavelength (λ)}{One time period (T)}

And, we know

T = \frac{1}{v}

By applying this in speed formula, we get

v = n λ

Under the same physical conditions, the speed of sound in a given medium remains nearly constant for all frequencies.

Let us solve following example for better understanding.

Example:

A sound wave has a frequency of \(2\) \(kHz\) and a wavelength of \(15\) \(cm\). How much time will it take to travel \(1.5\) \(km\)?

Given data:

Frequency \(=\) \(2\) \(kHz\) \(=\) \(2000\) \(Hz\)

Wavelength \(=\) \(15\) \(cm\) \(=\) \(0.15\) \(m\)

Distance \(=\) \(1.5\) \(km\) \(=\) \(1500\) \(m\)

To find: Time period

Formula:

Time = \frac{Distance}{Speed}

We don't know the value of speed,

v = n λ

\begin{array}{l} v = 2000 \times 0.15 \\ = 300 m / s \end{array}

Now, apply in the value of speed in time formula

\begin{array}{l} Time = \frac{1500}{300} \\ = 5 s \end{array}

The sound will take \(5\) \(s\) to travel a distance of \(1.5\) \(km\).

Did you find an error?

6. Speed of a sound