Waves: Find mass of an object given L, Frequency & Density

[Efast]

Homework Statement

An oscillator is attached to one end of a horizontal string. The other end passes over a frictionless pulley and is held taught by a mass m. The distance between the oscillator and the pulley is 1.2m. The string has a linear mass density of 1.6g/m and the frequency of the oscillator is 120Hz. What must be m mass is the string is to oscillate in its fourth harmonic?
Be sure to draw a useful well labelled picture and sketch the standing wave pattern, and prove the units work.
Answer: 0.846kg

Homework Equations

V=λF

The Attempt at a Solution

Truly don't even know where to start on this question...
The density value has me stumped...
Where do I even start?

 

[gneill]

Hi Efast. Welcome to Physics Forums!

Start by investigating standing waves on a string. A web search will turn up plenty of references. For example, the Hyperphysics website entry is here.

The density is just the mass per unit length of the string. You'll see its relevance when you do your research.

 

[Efast]

Okay after doing some research I derived a formula;
F4 = V / (2/4)L , V = √(Ft/(m/L)).
Combine together to get; F4 = [√((Mg)/(m/l))] / (2/4)L
Solve for M = ([F4(2/4)L]^2(m/l))/g
But still not getting the correct answer...
What am I missing? Have you seen similar problems with an explanation around, I can't seem to find any similar examples around...

 

[gneill]

Presumably F4 is your 120 Hz. m/l is the string density 1.6 g/m. Note the units: grams per meter, not kg per meter. Do the conversion and call it ρ with units kg/m. Then your equation which you've written above looks like:

$F4 = \frac{ \sqrt{ \frac{M g}{ρ} } }{\frac{2}{4} L} = 4 \frac{ \sqrt{ \frac{M g}{ρ} } }{2 L}$

Can you show the details of your work from there?

 

[Efast]

How did you make those equations look so beautiful haha
Anyways,
I used my formula to solve for M (mass of the object);
F4=4[(√Mg/ρ)]/2L
Which gave me,
M = ρ[(2L*F4)/4]/g
Which gave me; 0.846kg (CORRECT!)

Just to further my understanding; how would I prove that the units work from this equation?

 

[gneill]

How did you make those equations look so beautiful haha

LaTeX syntax, which is interpreted automatically for display. You can type in equations using LaTeX formatting and it will be rendered as you see it. To see what LaTeX syntax looks like, mouse over one of the equations and right-click. Select: Show Math As ---> TeX Commands.

Anyways,
I used my formula to solve for M (mass of the object);
F4=4[(√Mg/ρ)]/2L
Which gave me,
M = ρ[(2L*F4)/4]/g
Which gave me; 0.846kg (CORRECT!)

Well done!

Just to further my understanding; how would I prove that the units work from this equation?

Replace each variable with its units and reduce them as you would an algebraic expression. If your equation contains compound units such as Joules, you should know how to break them down in terms of more fundamental units or even dimensions (length, mass, time, charge,...).