- #1

FaraDazed

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This is not coursework; I am preparing for an exam and this question is from a past paper. We have access to past papers but we are not given the answers to them.

Two waves are generated on a string of length 2m, to produce a three-loop standing wave with an amplitude of 2cm. The wave speed is 50m/s.

A: What is the resonant frequency of the wave in Hz.

B: If the equation for one of the waves is of the form [itex]y(x,t)=y_m \sin(kx+ \omega t) [/itex] , what are the values of [itex]y_m[/itex] , [itex]k[/itex] and [itex]\omega[/itex] for the second wave?

C: What is the sign in front of [itex]\omega[/itex] for the second wave.

[itex]

L=\frac{n \lambda}{2} \\

k=\frac{2 \pi}{\lambda} \\

v= \lambda f = \frac{\omega}{k} \\

[/itex]

Other related equations

The question does not specify whether the ends are open or closed (fixed) so I am assuming they are both open ends.

A:

I have no come across the terminology "Three-loop" before but after searching the web I think it means the same thing as being in the third harmonic, if so then this is what I have done.

[itex]

L=\frac{n \lambda}{2} \\

2=\frac{3 \lambda}{2} \\

\lambda = (\frac{2}{3})(2) = \frac{4}{3}m \\

f = \frac{v}{\lambda} = \frac{50}{4/3}=37.5Hz

[/itex]

And that is the frequency of the third harmonic so the first harmonic would be 37.5/3=12.5 Hz

EDIT: I just noticed I didn't need to use n=3 and could have just done it with n=1 from the beginning. Why is there any need to tell me its in the third-harmonic?

B:

Bit unsure of part B, I think it may be a bit of a trick question as throughout the course we have only dealt with standing waves where the two constituent waves have the same magnitude of amplitude wave-number and angular frequency, only have the phases differed.

So if its a trick question and they're both the same then I think this part is no problem. Oh and for part C, wouldn't it be the opposite, i.e. it would be negative.

1. Homework Statement1. Homework Statement

Two waves are generated on a string of length 2m, to produce a three-loop standing wave with an amplitude of 2cm. The wave speed is 50m/s.

A: What is the resonant frequency of the wave in Hz.

B: If the equation for one of the waves is of the form [itex]y(x,t)=y_m \sin(kx+ \omega t) [/itex] , what are the values of [itex]y_m[/itex] , [itex]k[/itex] and [itex]\omega[/itex] for the second wave?

C: What is the sign in front of [itex]\omega[/itex] for the second wave.

## Homework Equations

[itex]

L=\frac{n \lambda}{2} \\

k=\frac{2 \pi}{\lambda} \\

v= \lambda f = \frac{\omega}{k} \\

[/itex]

Other related equations

## The Attempt at a Solution

The question does not specify whether the ends are open or closed (fixed) so I am assuming they are both open ends.

A:

I have no come across the terminology "Three-loop" before but after searching the web I think it means the same thing as being in the third harmonic, if so then this is what I have done.

[itex]

L=\frac{n \lambda}{2} \\

2=\frac{3 \lambda}{2} \\

\lambda = (\frac{2}{3})(2) = \frac{4}{3}m \\

f = \frac{v}{\lambda} = \frac{50}{4/3}=37.5Hz

[/itex]

And that is the frequency of the third harmonic so the first harmonic would be 37.5/3=12.5 Hz

EDIT: I just noticed I didn't need to use n=3 and could have just done it with n=1 from the beginning. Why is there any need to tell me its in the third-harmonic?

B:

Bit unsure of part B, I think it may be a bit of a trick question as throughout the course we have only dealt with standing waves where the two constituent waves have the same magnitude of amplitude wave-number and angular frequency, only have the phases differed.

So if its a trick question and they're both the same then I think this part is no problem. Oh and for part C, wouldn't it be the opposite, i.e. it would be negative.

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