The speed of a wave depends upon

The frequency of a wave doesn't change from one medium to another, but the wavelength does. The medium that a wave travels in affects the wavelength, which affects the wave speed.

 

This is one of those cases where multiple choice requires selecting the "best" answer. The speed of a wave often depends, but only very slightly, on the frequency and wavelength, and it may be such a slight dependence that you may have to go out some digits of precision to notice it. But the speed of a wave depends very, very strongly on the properties of the medium. So the best answer is A.

There are two main properties of a medium that determine the speed of a wave. One is called the elastic property, the tendency of something that is displaced from its center position to bounce back to the center position. The other is called the inertial property, which makes the medium, while bouncing back to the center position, overshoot the center position, and then go to the opposite extreme, and then it will have to bounce back toward the center from the opposite side.

 

speed ONLY depends on medium. its just one of those things you have to memorize. maybe someone else can explain it better, but i just know the fact. good luck :)

 

speed_of_wave (in strings) = sqrt (tension in string/ mass density)
speed_of_wave (in mediums - water) = sqrt (bulk modulus/density)

There are derivations (for string is easy - Halliday has it).

mikelepore explained this in words.

 

If it were *exactly* true that the speed of a wave depends only on the medium, then a spectrum wouldn't come out of a prism, or a rainbow from a water droplet.

http://en.wikipedia.org/wiki/Dispersion_(optics)

But that effect can be neglected for the present discussion. The medium is the main thing.

Suppose light crossed the boundary from one medium to another and it slowed down by 30 percent. Suppose I got more precise, and said: make that 29.99 percent for red, and 30.01 percent for blue. You would see that the medium is the main thing. The dependence on the color is a minor issue.