Question

The graphical representation of two sound waves A and B propagating at the same speed of 345 m s^-1 is shown in Fig. What is the wavelength of each of them? Also, calculate their frequencies.

Answer 1

Given:

Speed of propagating sound waves ($v$) = 345 m s^-1

For Wave A: Observing the graph, Wave A (the pink curve) completes one full cycle at a distance of 2.5 cm.

Wavelength ($\lambda_A$) = 2.5 cm = 0.025 m

Calculation for Frequency ($f_A$):

$$f_A = \frac{v}{\lambda_A}$$

$$f_A = \frac{345}{0.025}$$

$$f_A = 13800 \text{ Hz}$$

For Wave B: Observing the graph, Wave B (the blue curve) completes one full cycle at a distance of 5.0 cm.

Wavelength ($\lambda_B$) = 5.0 cm = 0.05 m

Calculation for Frequency ($f_B$):

$$f_B = \frac{v}{\lambda_B}$$

$$f_B = \frac{345}{0.05}$$

$$f_B = 6900 \text{ Hz}$$