4. A light string is attatched to a heavy rope, and the whole thing is pulled tight. A wave is sent along the light string. When it hits the heavy rope, compared to the wave on the string, the wave that propagates along the rope has the same (A) frequency (B) wavelength (C) both frequency and wavelength (D) neither?

The correct answer to the question is (A)

When it hits the heavy rope, compared to the wave on the string, the wave that propagates along the rope has the same (A) frequency

Explanation:

The speed of a wave in a string is dependent on the square root of the tension ad inversely proportional  to the square root of the linear density of the string. Generally, the speed of a wave through a spring is dependent on the elastic and inertia properties of the string

Therefore if the linear density of the heavy rope is four times that of light rope the velocity is halved and since

v = f×λ therefore  v/2 = f×λ/2

Therefore the wavelength is halved, however the frequency remains the same as continuity requires the frequency of the incident pulse vibration to be transmitted to the denser medium for the wave to continue as the wave is due to vibrating particles from a source for example

when two balls of the different masses are dropped from equal height, they reach the ground at the same time .this is because they experience the same acceleration.

the acceleration is independent of mass.

thus when they are dropped they will always maintain the same velocity and travel the same distance (neglect air resistance of course) at the same time.