Question

Prove that 𝒗 = v𝝀, where the symbols have their usual meanings.

August 7, 2024

Answer

Let the time period of a wave be T seconds.

In T seconds, number of waves generated = 1.

So, in I second number of waves generated = ${1\over 𝑇}$

But number of waves generated in 1 second is frequency.

∴ v = ${1\over 𝑇}$

Now, Velocity = ${Distance\ travelled \over Time\ taken}$

⇒ 𝑣 = ${ \lambda \over 𝑇}$

⇒ 𝑣 = ${1\over 𝑇}$ .𝜆

⇒ 𝑣 = v𝜆

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