Wave Velocity and Frequency

[September24]

I was under the impression that factors that influence velocity (medium) don't influence wave frequency (wave source).

On Berkeley Review Sound Chapter, Passage one, it gives us the following formula.


Equation 1: V=sqrt(TL/M)

Equation 2: F=nv/2L


Question 3: The pitch of the standing wave on a violin string:

Answer: Increases as tension is increased.


I put "Is unaffected by tension in the string". At first, I look at the equation one and noticed an increase in Velocity due to an increase in tension. Since velocity increases, frequency increases by Equation 2:


BUT...I started to think that velocity and frequency are affected by different things. Tension is changing the frequency and since velocity is a function of medium only and not things that affect frequency, frequency should not change.


Basically, how is it that frequency and velocity are related here if the two are affected by different things.

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[dudewheresmymd]

I was under the impression that factors that influence velocity (medium) don't influence wave frequency (wave source).

On Berkeley Review Sound Chapter, Passage one, it gives us the following formula.
Equation 1: V=sqrt(TL/M)
Equation 2: F=nv/2L
Question 3: The pitch of the standing wave on a violin string:
Answer: Increases as tension is increased.
I put "Is unaffected by tension in the string". At first, I look at the equation one and noticed an increase in Velocity due to an increase in tension. Since velocity increases, frequency increases by Equation 2:
BUT...I started to think that velocity and frequency are affected by different things. Tension is changing the frequency and since velocity is a function of medium only and not things that affect frequency, frequency should not change.
Basically, how is it that frequency and velocity are related here if the two are affected by different things.

Velocity is a function of medium for the sound wave that your ear hears. The velocity of the actual string on the violin is given by sqrt (T/(mass/unit length of the string). These two waves have different velocities and wavelengths, but share the same frequency.

 

[September24]

I'm sorry im a bit confused still. What "two waves" share the same frequencies? The ones with the different tensions?

 

[dudewheresmymd]

I'm sorry im a bit confused still. What "two waves" share the same frequencies? The ones with the different tensions?

one is the wave actually propagating on the string that creates a longitudinal sound wave that propagates through the air. This longitudinal sound wave that reaches your air shares the same frequency as the transverse wave that travels along the violin string.

The velocity for both waves above are different and the wavelengths are different, but they share the same frequency (440Hz) for example.

To calculate the velocity of the transverse wave along the string you use the TBR formula V=sqrt (TL/M)

to calculate the velocity of the longitudinal sound wave in the air, you do not use the TBR formula, the velocity of the sound wave in the air = sqrt (bulk modulus of the medium/density of the medium)

 

[September24]

So I slept on this and still find myself unsure of the concept. If I were to be asked "what happens to sound velocity and frequency as the medium changes", I would know that velocity changes but frequency doesn't.

But if I were to be asked the same question regarding a transverse wave, I would hesitate since I know that f=nv/2L and that V=sqrt(T/u). It seems like both of them change at the same time, depending on the medium (if tension or u changes). Is it different for sound waves compared to transverse waves? I just cant connect intuitive knowledge and formulaic knowledge.

 

[NextStepTutor_1]

In this case, I think that you are making it more complicated that it needs to be, and the scope of the MCAT does not cover this type of distinction. The MCAT will expect you to know that the velocity of any wave changes based on the medium, but the frequency stays the same.