A sound wave travelling at a speed of 330 m/s produces 20 crests and 20 troughs in 0.1 second. The wavelength of the sound wave is :

To find the wavelength, we first determine the frequency of the sound wave. One complete wave cycle consists of one crest and one trough. The problem states that 20 crests and 20 troughs are produced in 0.1 second, which corresponds to 20 complete wave cycles. Frequency is defined as the number of waves passing a point per second [1]. Thus, the frequency (f) is calculated as 20 waves divided by 0.1 second, resulting in 200 Hz. The relationship between wave speed (v), frequency (f), and wavelength (λ) is given by the formula v = fλ. Given the speed of sound is 330 m/s, the wavelength is calculated as λ = v / f = 330 / 200. This calculation yields a wavelength of 1.65 meters, matching option 3.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 15: Tsunami > Basics > p. 192