A string has a linear density of 8.5*10^-3 kg and is under the tension of 280 N. The string is 1.8 m long, is fixed at both ends, and vibrating in the standing wave pattern. What is the speed, length, and frequency?
A string has a linear density of 7.2 x 10-3 kg/m and is under a tension of 370 N
To find the speed, length, and frequency of the standing wave on the string, we can use the wave equation:
v = √(T/μ)
Where:
v = speed of the wave
T = tension in the string
μ = linear density of the string
We are given that:
T = 280 N
μ = 8.5*10^-3 kg/m
Let's start by calculating the speed (v):
v = √(280 N / 8.5*10^-3 kg/m)
v = √(32941.18 m^2/s^2)
v ≈ 181.29 m/s
So, the speed of the wave on the string is approximately 181.29 m/s.
Next, let's find the length (L) of the string. We are given that the string is 1.8 m long, so L = 1.8 m.
Finally, let's calculate the frequency (f) of the standing wave:
f = v / λ
Where:
f = frequency of the wave
v = speed of the wave
λ = wavelength of the standing wave
Since the string is fixed at both ends, the wavelength of the standing wave is twice the length of the string (2L):
λ = 2L = 2 * 1.8 m = 3.6 m
Now we can calculate the frequency:
f = 181.29 m/s / 3.6 m
f ≈ 50.36 Hz
So, the frequency of the standing wave on the string is approximately 50.36 Hz.
To summarize:
- The speed of the wave on the string is approximately 181.29 m/s.
- The length of the string is 1.8 m.
- The frequency of the standing wave is approximately 50.36 Hz.