A string is stretched between two points 50cm apart. It is then plucked at its center and the velocity of the wave produced is 300m/s. Calculate the number ...

A string is stretched between two points 50cm apart. It is then plucked at its center and the velocity of the wave produced is 300m/s. Calculate the number of vibrations made by the string in 1s.

Answer Details

The velocity of a wave, v is given by v = fλ, where f is the frequency of the wave and λ is the wavelength. For a standing wave in a string, the wavelength λ is equal to twice the length of the string, since it is fixed at both ends. Therefore, λ = 2 × 50 cm = 100 cm = 1 m The velocity of the wave is given as 300 m/s. So, 300 m/s = f × 1 m Hence, frequency f = 300 Hz The number of vibrations (cycles) per second is equal to the frequency of the wave, therefore the number of vibrations made by the string in 1s is 300. Therefore, the answer is 300 vibrations per second.