A sonometer wire having a length of 50 cm is vibrating in the fundamental mode with a frequency of 100 Hz. Which of the following is the type of propagating wave and its peed?

A sonometer wire is a classic example of a stretched string fixed at both ends. Waves propagating along such a string are transverse in nature, meaning the particles of the medium vibrate perpendicular to the direction of wave propagation [1][t1][t8]. For a string fixed at both ends, the fundamental mode of vibration occurs when the length of the string (L) is equal to half the wavelength (λ/2), thus λ = 2L. Given the length L = 50 cm (0.5 m), the wavelength λ is 1.0 m. The speed of the wave (v) is calculated using the formula v = fλ, where f is the frequency. With a fundamental frequency of 100 Hz and a wavelength of 1.0 m, the speed is v = 100 Hz × 1.0 m = 100 m/s [t6][t9]. Therefore, the wave is transverse with a speed of 100 m/s.

Sources

1. [1] Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.) > Chapter 4: Earths Interior > Secondary Waves (S-Waves) > p. 62