In a sonometer, the wire vibrates and produces waves that propagate through the air. To calculate the wavelength and speed of the waves in the air, we can use the relationship between frequency, wavelength, and speed:
Speed = Frequency × Wavelength
Given that the frequency of the vibrating wire is 250 Hz, we need to find the wavelength.
In the case of a wire that is plucked at the center, the fundamental mode of vibration is produced, which corresponds to the lowest possible frequency and the longest possible wavelength. In this mode, the wire forms a half-wavelength.
Since the length of the wire is 1 m, the half-wavelength (λ/2) will also be 1 m. Therefore, the wavelength (λ) itself will be 2 m.
Now we can calculate the speed of the waves in the air using the formula:
Speed = Frequency × Wavelength
Substituting the values:
Speed = 250 Hz × 2 m Speed = 500 m/s
Therefore, the wavelength of the waves in the air is 2 meters, and the speed of the waves is 500 meters per second.