Calculating Frequency, Wavelength, and Tension of a Sinusoidal Wave on a String

[davegillmour]

I've been working on this problem and I got every part right except part F which asks for tension.

A sinusoidal wave is traveling on a string with speed 110 cm/s. The displacement of the particles of the string at x = 23 cm is found to vary with time according to the equation
y = (4.9 cm) sin[1.5 - (7.2 s-1)t].
The linear density of the string is 2.2 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form
y(x,t) = ym sin(kx - (omega)t),
what are (c)ym, (d)k, and (e)Omega? (f) What is the tension in the string?

a)f=1.15 Hz
b)wavelength = 95.7cm
c)Ym=4.9cm
d)k=6.52 rad/m
e)omega=7.2 rad/s

f) my answers so far were 0.00266 N and 0.0000266 N and both were wrong (they seem too low). I tried the equation V = Sqrt(T/u) where T is tension, and u is linear density but I must be making a mistake somewhere.

 

[Doc Al]

Check your units. Convert everything into standard units--meters, kilograms--before plugging into the equation.

 

[davegillmour]

Yeah, after I triple checked my units, I realized they were wrong again. Got the correct answer of 0.266 Newtons. Thanks for the reply

 

[nrqed]

I've been working on this problem and I got every part right except part F which asks for tension.

A sinusoidal wave is traveling on a string with speed 110 cm/s. The displacement of the particles of the string at x = 23 cm is found to vary with time according to the equation
y = (4.9 cm) sin[1.5 - (7.2 s-1)t].
The linear density of the string is 2.2 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form
y(x,t) = ym sin(kx - (omega)t),
what are (c)ym, (d)k, and (e)Omega? (f) What is the tension in the string?

a)f=1.15 Hz
b)wavelength = 95.7cm
c)Ym=4.9cm
d)k=6.52 rad/m
e)omega=7.2 rad/s

f) my answers so far were 0.00266 N and 0.0000266 N and both were wrong (they seem too low). I tried the equation V = Sqrt(T/u) where T is tension, and u is linear density but I must be making a mistake somewhere.

Seems to be just a problem of units. To get the speed in m/s, you must put T in Newtons and u in kg/m. Notice that u = .22 kg/m (my guess is that you left u in g/m instead of kg/m)
Try this and you will get a much larger tension than what you wrote above.