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

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The discussion focuses on calculating the tension of a sinusoidal wave on a string, with the wave speed given as 110 cm/s and the linear density as 2.2 g/cm. The correct frequency is determined to be 1.15 Hz, and the wavelength is 95.7 cm. The tension was initially miscalculated due to incorrect unit conversions, leading to values that were too low. After correcting the units to standard measurements, the tension was found to be 0.266 Newtons. Proper unit conversion is crucial for accurate calculations in wave mechanics.
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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.
 
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Check your units. Convert everything into standard units--meters, kilograms--before plugging into the equation.
 
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
 
davegillmour said:
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.
 
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