The speed of a wave depends upon

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In summary, the speed of a wave depends upon the properties of the medium through which it travels, the wavelength of the wave, and the frequency of the wave.
  • #1
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"The speed of a wave depends upon"

Homework Statement


The speed of a wave depends upon
a. the properties of the medium through which the wave travels

b. the wavelength of the wave.

c. the frequency of the wave.

d. both the wavelength and the frequency of the wave.


Homework Equations





The Attempt at a Solution


I thought the answer was d, as v = wavelength * frequency. Apparently the correct answer was A.

Could someone elaborate where i am wrong, or weather or not the textbook answer is wrong?
 
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  • #2
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.
 
  • #3
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.
 
  • #4
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 :)
 
  • #5
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.
 
  • #6
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.
 
Last edited:

1. What factors affect the speed of a wave?

The speed of a wave depends on three factors: the medium through which it travels, the frequency of the wave, and the wavelength of the wave.

2. How does the medium affect the speed of a wave?

The type of material that a wave travels through can greatly impact its speed. Generally, waves travel faster through denser materials, such as solids, compared to less dense materials like gases or liquids. This is because denser materials have more molecules that the wave can interact with, allowing it to travel faster.

3. Does the frequency of a wave affect its speed?

Yes, the frequency of a wave is directly proportional to its speed. This means that as the frequency increases, so does the speed of the wave. This is because a higher frequency wave has more energy, allowing it to travel faster.

4. How does wavelength impact the speed of a wave?

The wavelength of a wave is inversely proportional to its speed. This means that as the wavelength increases, the speed of the wave decreases. This is because longer wavelengths have less energy, causing them to travel slower.

5. What is the relationship between the speed of a wave and its amplitude?

The speed of a wave is not affected by its amplitude. The amplitude of a wave is the measure of its height or intensity, while the speed is determined by the medium, frequency, and wavelength. However, a wave with a higher amplitude may appear to travel faster because it carries more energy and can cover a greater distance in a shorter amount of time.

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