Question

The speed of a wave is $340m{s}^{-1}$. What is the wavelength of the wave if its frequency is 500 Hz?

• A. 0.68 m
• B. 6.8 m
• C. 68 m
• D. 0.68 cm

Answer 1

The correct option is A

0.68 m

Step 1: Given data.

$$\begin{gathered} velocity=340m{s}^{-1} \\ frequency=500Hz \end{gathered}$$

Step 2: Finding the wavelength of a wave.

1. The wavelength and frequency of a sound wave are related mathematically as:
2. $$\begin{gathered} Thevelocityofsound=frequency\times wavelength \\ \Rightarrow V=\vartheta \times \lambda \\ \Rightarrow \lambda =\frac{V}{\vartheta } \\ \Rightarrow \lambda =\frac{340}{500}m \\ \Rightarrow \lambda =0.68m \end{gathered}$$
3. where $\lambda$ = wavelength, V = velocity, and $\vartheta$ = frequency.
4. Therefore, the wavelength of the wave is 0.68 m.

Hence, option (a) is correct.