Question

Establish the relationship between the speed of sound, wavelength, and frequency. If the velocity of sound in air is $340\mathrm{m}{\mathrm{s}}^{-1}$, calculate the wavelength when the frequency is $256\mathrm{Hz}$.

Answer 1

Relationship between the speed of sound, its wavelength, and frequency:

Speed of sound is written as $\mathrm{v}=\mathrm{f\lambda }$.

Here,

$\mathrm{f}$ is the frequency.

$\mathrm{\lambda }$ is wavelength.

Step 1: Given data

Velocity, $\mathrm{v}=340\frac{\text{m}}{\text{s}}$.

Frequency, $\mathrm{f}=256\mathrm{Hz}$.

Step 2: To find

The wavelength of sound.

Step 3: Calculate the wavelength of sound

$$\begin{gathered} \mathrm{v}=\mathrm{f\lambda } \\ 340=256\mathrm{\times }\mathrm{\lambda } \\ \mathrm{\lambda }=\frac{340}{256} \\ \mathrm{\lambda }=1.32\mathrm{m} \end{gathered}$$

Hence, Wavelength is $1.32\text{m}$.