Calculate the speed of a wave in m/s along a taut string with tension 139 Newtons and a mass per unit length of 3.6 grams per metre.
The fundamental frequency of a wave along a taut string is
f=√(T/m)/(2L)
T=tension in N
m=mass of string in kg/m
Since the fundamental mode of vibration consists of only half a wave, the wave velocity is f*2L, or
λ=√(T/m).
Here N=139 N, m=0.0036 kg/m
v=√(139/0.0036)= 196.5 m/s
To calculate the speed of a wave on a taut string, you can use the formula:
v = sqrt(T/μ)
Where:
v is the speed of the wave,
T is the tension in the string, and
μ is the mass per unit length of the string.
In this case, we are given:
Tension (T) = 139 Newtons and
Mass per unit length (μ) = 3.6 grams per meter.
First, we need to convert the mass per unit length from grams per meter to kilograms per meter since the SI unit for mass is kilogram and not gram.
1 gram = 0.001 kilograms
So, 3.6 grams = 3.6 * 0.001 = 0.0036 kilograms.
Now, let's substitute the values into the formula:
v = sqrt(139 / 0.0036)
Next, divide the tension by the mass per unit length:
v = sqrt(38611.11)
Finally, take the square root:
v ≈ 196.48 m/s
Therefore, the speed of the wave along the taut string is approximately 196.48 m/s.