First, we need to calculate the mass per unit length of the string:
Mass per unit length (µ) = (mass of string) / (length of string)
= 13.5 g / 5.30 m
= 2.55 g/m
Next, we need to convert the mass per unit length to kg/m:
µ = 2.55 g/m * (1 kg / 1000 g)
= 0.00255 kg/m
Now, we can calculate the velocity of the wave using the formula:
v = √(FT / µ)
Rearranging the formula, we get:
FT = v^2 * µ
Given that the frequency of the wave is 129 Hz and the wavelength is 120.0 cm = 1.20 m, we can use the formula:
v = f * λ
v = 129 Hz * 1.20 m
v = 154.8 m/s
Now, plug in the values for v and µ to find the tension in the string:
FT = (154.8 m/s)^2 * 0.00255 kg/m
FT = 38100.6 N
Therefore, the tension in the string must be approximately 38100.6 N to make the wavelength of a 129 Hz wave 120.0 cm on a 5.30 m long string.
The velocity of a wave on a string depends on how hard the string is stretched, and on the mass per unit length of the string. If FT is the tension in the string, and µ is the mass/unit length, then the velocity, v, can be determined.
A piece of string 5.30 m long has a mass of 13.5 g. What must the tension in the string be to make the wavelength of a 129 Hz wave 120.0 cm?
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