How Can I Calculate Tension and Amplitude in Standing Wave Problems?

[Superdreamer]

Hi I was wondering if someone could tell me if I am heading in the right direction with these Thanks in advance

Q1 In an experiment on standing waves, a string 90 cm long is
attached to the prong of an electrically driven tuning fork that oscillates
perpendicular to the length of the string at a frequency of 60 Hz. The
mass of the string is 0.044 kg. What tension must the string be under if it
is to vibrate in four loops?

I used the formula L=4(λ/2) giving 2λ=L L=1.8m
V=fλ v=108m/s then using the formula v=sq root(T/μ) giving me a tension of 279.936N Is this correct

Q2 Two sinusoidal waves with the same amplitude, frequency and
speed, travel in the same direction along a string and interfere with one
another to produce a resultant wave with a displacement
y = (3.0 x 10-3) sin(20x - 4.0t + 0.6) cos(0.6) m. What is (a) the amplitude
and (b) the wavelength of the waves and (c) the phase difference
between them?

Wave is in the form y'(x,t)=[2ym(cos(tetha/2)sin(Kx-wt+1/2(tetha)tetha/2

y'm=2ymcos1/2tetha
answer 1.13mm is this correct?

k=20 rad/m
w=4 rad/s

λ=2pi/k
=2pirad/20rad/m
=31.4cm

T=2pi/w
=1.57seconds
f=1/t
=0.6366hz
I know this is wrong please lead me in the right direction

 

[andrevdh]

Superdreamer,
for Q1: The standing wave has an antinode at the position of the tuning fork and a node at the fixed end. This means that the length of the string will be two and a quarter wavelengths long for four loops. The rest of the approach is correct.

 

[ramino]

Resistivity vs. Resistance

Hi,could you be so kind to explain me differences between resistance and resistivity?
I think the resistance is constant for each material.But we use resistivity to differentiate between various materials.

 

[ranger]

Hi,could you be so kind to explain me differences between resistance and resistivity?
I think the resistance is constant for each material.But we use resistivity to differentiate between various materials.

As far as I understand>>> Certain materials oppose current flow more than others. Even the same material allows current to flow at different rates depending upon shape. This property is called resistance. Resistivity is a physical property of a material to resist or oppose the movement of charge through the material.

So from that, resistance is not constant for each material.
$$R = p\frac{L}{A}$$

p = resistivity of conductor
L = length
A = area

 

[lightgrav]

Superdreamer, you were right about there being a node almost at the tuning fork. If the wave is actually in resonance, without great amounts of damping, the tuning fork oscillation will be less than about 1 mm, while the string wave will have amplitude of about 100mm . (Andrevdh is incorrect)

your wavelength and frequency look okay.
the decomposition into 2 waves with same amplitude but a phase shift
does NOT have a unique solution.