Question

john attaches a large spring to a small spring for a job that he has to complete. he notices that as the wave travels from spring 1 to spring 2, its wavelength is decreased by 50%. which statement describes the change in the speed of the wave?
(1 point)

the speed increases by 50% because speed and wavelength are inversely proportional.

the speed decreases by 50% because speed and wavelength are inversely proportional.

the speed increases by 50% because speed and wavelength are directly proportional.

the speed decreases by 50% because speed and wavelength are directly proportional.

Explanation:

1. Recall the wave equation: \( v = f\lambda \), where \( v \) is speed, \( f \) is frequency, and \( \lambda \) is wavelength.
2. When a wave moves from one medium (spring 1) to another (spring 2) with the same source, the frequency \( f \) remains constant (frequency depends on the source, not the medium).
3. So, \( v \propto \lambda \) (direct proportionality, since \( f \) is constant).
4. If wavelength \( \lambda \) decreases by 50% (new \( \lambda = 0.5\lambda_{\text{original}} \)), and \( v = f\lambda \), then new speed \( v_{\text{new}} = f(0.5\lambda_{\text{original}})= 0.5(f\lambda_{\text{original}})= 0.5v_{\text{original}} \). Thus, speed decreases by 50% because speed and wavelength are directly proportional.

Answer:

The speed decreases by 50% because speed and wavelength are directly proportional. (The option corresponding to this statement, e.g., if it's the fourth option: "The speed decreases by 50% because speed and wavelength are directly proportional.")