Question

A certain sound has a frequency of $256hertz$ and a wave length of $1.3m.$
(a) Calculate the speed with which this sound travels.
(b) What difference would be felt by a listener between the above sound and another sound travelling at the same speed, but of wavelength $2.6\mathrm{m}$?

Answer 1

Step 1: Given data:

Frequency of sound wave $=256hertz$

The wavelength of sound wave $=1.3m$

Step 2: (a) Calculation of the speed with which this sound travels.

We know that the speed with which the sound waves travel $\mathrm{v}=f\lambda$

Where, $f$ frequency of the sound wave and $\lambda$ is the wavelength of the sound wave.

So, the value of the speed will be:

$$\begin{gathered} \therefore \mathrm{v}=256\times 1.3 \\ \Rightarrow \mathrm{v}=332.8\mathrm{m}/\mathrm{s} \end{gathered}$$

Hence, the value of the speed with which the sound wave travels will be $=332.8m/s$

Step 3: (b) Calculation of the difference which would be felt by a listener between the above sound and another sound traveling at the same speed, but of wavelength $2.6\mathrm{m}$.

Since, the speed with which the sound waves travel $\mathrm{v}=f\lambda$

As it is given that the speed of both the sound waves is the same.

So, $f_1\times {\lambda }_1={\lambda }_2\times f_2$

$$\begin{gathered} \Rightarrow 256\times 1.3=f_2\times 2.6 \\ \Rightarrow f_2=\frac{256\times 1.3}{2.6} \\ \Rightarrow f_2=128Hz \end{gathered}$$

Since the frequency of the second sound is less compared to the first sound, so the listener would find the second has less pitch.