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This generally happens when a wave moves from one medium into another.

Now, the velocity (v) of a wave (mechanical and electromagnetic) is equal to the product of its frequency (f) and wavelength (Î»).

So, v = f x Î»

That means if frequency is constant, the wavelength is directly proportional to the velocity.

So, if the speed of the wave increases (while frequency remains the same), the wavelength will also increase.

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Q: If the speed of a wave increases and its frequency does not change then what will happen to its wavelength?

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Then the wavelength decreases.

wavelength decreases

It would change, depending on how much the frequency and the wavelength changes. It varies based on v = fλ.

That means that the frequency increases. In that case, and assuming the speed of the wave doesn't change, the wavelength gets shorter. The general rule is: frequency x wavelength = speed (of the wave)

That doesn't happen. You're fishing for "frequency increases", because you're unclear on the independent and dependent quantities. Once the wave leaves the source, the frequency doesn't change.

The frequency of a wave is inversly proportional to the wavelength of a wave. Therefore if the wavelength were to increase, the frequency of will decrease.

If the frequency stays the same, then the wavelength stays the same.

The wavelength would double.

Whatever the wavelength and frequency happen to be, their product is always equal to the speed.

the wave length will increase

Pitch is a characteristic decided by the frequency. So high pitch high frequency. Low frequency is the cause of low Pitch. Frequency and wavelength are always inversely related. So wavelength increases. But amplitude in no way is related to the pitch. Hence amplitude could remain the same.

That can't happen. The product of (frequency) times (wavelength) is always the wave's speed. There's no way to increase frequency without also decreasing the wavelength. If the wave happens to encounter a different medium ... like a sound hitting jello or a beam of light hitting air ... then its speed changes while the frequency remains constant, which means that the wavelength changes in the new medium.

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