A string is under a tension of 700.0 N. A 1.5 m length of the string has a mass of 4.5 grams. What is the speed of a transverse wave of wavelength 0.50 m in this string? What is the frequency of the wave?
velocity= sqrt (tension/linearmassdensity)
One the last part, it am not certain that .50 equals one-half wavelength, it does not say that.
To find the speed of a transverse wave in the string, we can use the formula:
Speed = √(Tension / Mass per unit length)
Given:
Tension (T) = 700.0 N
Length (L) = 1.5 m
Mass (m) = 4.5 grams = 0.0045 kg
Wavelength (λ) = 0.50 m
First, we need to find the mass per unit length (μ) of the string:
Mass per unit length (μ) = Mass / Length
μ = 0.0045 kg / 1.5 m = 0.003 kg/m
Now we can substitute the values into the formula:
Speed = √(Tension / Mass per unit length)
Speed = √(700.0 N / 0.003 kg/m)
Calculating this value:
Speed = √(233333.33 m^2/s^2)
Speed = 482.39 m/s (rounded to 3 decimal places)
The speed of the transverse wave in the string is approximately 482.39 m/s.
To find the frequency (f) of the wave, we can use the formula:
Frequency = Speed / Wavelength
Substituting the values:
Frequency = 482.39 m/s / 0.50 m
Calculating this value:
Frequency = 964.78 Hz (rounded to 2 decimal places)
The frequency of the wave is approximately 964.78 Hz.
To find the speed of a transverse wave in a string, you can use the equation:
v = √(T/μ)
Where:
v = speed of the wave in meters per second (m/s)
T = tension in newtons (N)
μ = linear mass density of the string in kilograms per meter (kg/m)
First, let's find the linear mass density of the string. Linear mass density (μ) is the mass per unit length of the string, and it is given by the formula:
μ = m/L
Where:
m = mass of the string in kilograms (kg)
L = length of the string in meters (m)
Given that the mass of the 1.5 m length of the string is 4.5 grams (0.0045 kg), we can calculate the linear mass density:
μ = (0.0045 kg) / (1.5 m)
μ = 0.003 kg/m
Next, we can substitute the given values into the formula for the speed of the wave:
v = √(T/μ)
v = √(700.0 N / 0.003 kg/m)
v = √233,333.33 m²/s²
v ≈ 483 m/s
So, the speed of the transverse wave in the string is approximately 483 m/s.
To find the frequency (f) of the wave, we can use the equation:
v = λf
Where:
v = speed of the wave in meters per second (m/s)
λ = wavelength of the wave in meters (m)
f = frequency of the wave in hertz (Hz)
Given that the wavelength of the wave is 0.50 m, we can rearrange the equation to solve for the frequency:
f = v / λ
f = (483 m/s) / (0.50 m)
f = 966 Hz
So, the frequency of the wave is 966 Hz.