Sinusoidial waves: Frequency is not dependant on speed?

[Willjeezy]

Homework Statement

I am really confused.

v = λ f

doesn't that imply that speed is dependent on frequency?

There is a question in my book that says:

A sinusoidal wave of frequency f is traveling along a stretched string. The string is brought to rest, and a second traveling wave of frequency 2f is established on the string.
(i) what is the wave speed of the second wave?

Homework Equations

v = λ f

The Attempt at a Solution

so I figured the answer would be something like:

since v₁=λf
it follows that, if the second wave has frequency 2f
v₂ = λ(2f)
v₂ = 2 (λf)
v₂ = 2 (v₁)

but somehow the answer is: "the same as the first wave" Can someone explain this to me?

 

[Dick]

Homework Statement

I am really confused.

v = λ f

doesn't that imply that speed is dependent on frequency?

There is a question in my book that says:

A sinusoidal wave of frequency f is traveling along a stretched string. The string is brought to rest, and a second traveling wave of frequency 2f is established on the string.
(i) what is the wave speed of the second wave?

Homework Equations

v = λ f

The Attempt at a Solution

so I figured the answer would be something like:

since v₁=λf
it follows that, if the second wave has frequency 2f
v₂ = λ(2f)
v₂ = 2 (λf)
v₂ = 2 (v₁)

but somehow the answer is: "the same as the first wave" Can someone explain this to me?

You are assuming λ doesn't change. You have the wrong equation. What equation determines the speed of a wave on a stretched string? Might just involve tension and mass density, yes?

 

[Willjeezy]

Ohhhhh, right right. If frequency increases λ would get shorter.

i flipped two pages down and found:
v=√(T/μ)

problem solved. Thanks.