How to maintain the same stationary wave pattern?

[toforfiltum]

Homework Statement

Homework Equations

not sure

The Attempt at a Solution

The answer is C, though I answered B. I don't understand why C is the answer.I thought that to maintain the same stationary wave pattern, I must maintain the speed of the stationary wave, and one way to do this is by reducing the wavelength of the wave. Instead, the answer suggests that we increase the speed of wave instead. Is it done to match the increase in frequency? But even so, why is B wrong?

 

[Orodruin]

In order to have a standing wave, the string length needs to be a half-integer multiple of the wavelength. You therefore cannot change the wavelength. How would you achieve this when the frequency changes? (Hint: How does frequency relate to wave speed?)

 

[toforfiltum]

In order to have a standing wave, the string length needs to be a half-integer multiple of the wavelength. You therefore cannot change the wavelength. How would you achieve this when the frequency changes? (Hint: How does frequency relate to wave speed?)

Ah, I forgot the fact that the wavelength of a stationary wave cannot be simply changed. Anyway, how do you increase the speed of wave on the string?

 

[Orodruin]

Ah, I forgot the fact that the wavelength of a stationary wave cannot be simply changed. Anyway, how do you increase the speed of wave on the string?

Have you seen the derivation of the wave equation for a string? If not you should look it up, it will tell you the wave velocity in terms of the density and string tension. Changing either will change the wave velocity.

 

[toforfiltum]

Have you seen the derivation of the wave equation for a string? If not you should look it up, it will tell you the wave velocity in terms of the density and string tension. Changing either will change the wave velocity.

Ok, thanks.