a 2m long string of mass 10g is clamped at boths ends.the tension in the string is 150N.the string is plucked so that it oscillate.what is the wavelength and frequency of the resulting wave it is produce a standing wave with two antinodes?
To find the wavelength and frequency of the resulting wave, we need to use the formula that relates them to the velocity and tension in the string.
The velocity of a wave in a stretched string can be calculated using the formula:
v = √(T/μ)
where:
- v is the velocity of the wave
- T is the tension in the string
- μ is the linear mass density of the string
The linear mass density (μ) is calculated by dividing the mass of the string (m) by its length (L):
μ = m/L
Given:
- The tension in the string, T = 150 N
- The length of the string, L = 2 m
- The mass of the string, m = 10 g = 0.01 kg
First, calculate the linear mass density:
μ = 0.01 kg / 2 m = 0.005 kg/m
Now, substitute the values into the formula to find the velocity of the wave:
v = √(150 N / 0.005 kg/m) = √(30000 m^2/s^2) ≈ 173.21 m/s
For a standing wave with two antinodes, there are three half-wavelengths present. Therefore, the wavelength (λ) can be calculated as:
λ = 2L / 3
λ = (2 * 2 m) / 3 = 4/3 m ≈ 1.33 m
Finally, we can calculate the frequency (f) of the wave using the formula:
f = v / λ
f = 173.21 m/s / 1.33 m ≈ 130.27 Hz
So, the wavelength of the resulting wave is approximately 1.33 m, and the frequency is approximately 130.27 Hz.