What is the speed of a wave with a frequency of 100.0 Hz and a distance between adjacent nodes of 0.500 m?

To determine the speed of a wave, we can use the relationship between speed, frequency, and wavelength. The formula that relates these quantities is given by:

[ v = f \lambda ]

where ( v ) is the wave speed, ( f ) is the frequency, and ( \lambda ) is the wavelength.

In this case, the frequency of the wave is provided as 100.0 Hz. The distance between adjacent nodes in a wave is also critical; for standing waves, this distance is equal to half of the wavelength. Therefore, if the distance between adjacent nodes is 0.500 m, the wavelength can be calculated as:

[ \lambda = 2 \times \text{distance between adjacent nodes} = 2 \times 0.500 , m = 1.0 , m ]

Plugging in the frequency and the wavelength into the wave speed equation results in:

[ v = 100.0 , \text{Hz} \times 1.0 , \text{m} = 100.0 , \text{m/s} ]

This calculation shows that the speed of the wave is 100.0 m/s, which aligns with the