A Piece of string 5.3-m long has a mass of 15.o g what must the tension in the string be to make the wavelength of a 125- Hz wave 120.0 cm
To calculate the tension in the string, we can use the formula for the speed of a wave:
Speed (v) = Frequency (f) × Wavelength (λ)
Since we are given the frequency (125 Hz) and the wavelength (120.0 cm), we can rearrange the formula to solve for the speed:
Speed (v) = Frequency (f) × Wavelength (λ)
v = 125 Hz × 120.0 cm
Next, we need to determine the speed of the wave. The speed of a wave can be calculated using the equation:
Speed (v) = √(Tension (T) / Linear Density (μ))
In this equation, the linear density (μ) is given by the mass (m) divided by the length (L):
Linear Density (μ) = mass (m) / length (L)
μ = 15.0 g / 5.3 m
Now, we can substitute the given values into the speed equation to solve for the tension (T):
v = √(T/μ)
125 Hz × 120.0 cm = √(T / (15.0 g / 5.3 m))
Now, let's convert the given length and mass into SI units. 1 cm = 0.01 m, and 1 g = 0.001 kg:
v = √(T / (15.0 × 0.001 kg / 5.3 m))
v = √(T / (0.015 kg / 5.3 m))
v = √(T / 0.002830 m)
(125 Hz × 120.0 × 0.01 m) = √(T / 0.002830 m)
Now, let's solve for Tension (T):
T / 0.002830 m = (125 Hz × 120.0 × 0.01 m)²
T / 0.002830 m = (150.0 m)²
T / 0.002830 m = 22500 m²
Finally, solve for T:
T = (22500 m²) × 0.002830 m
T ≈ 63.75 N
Therefore, the tension in the string must be approximately 63.75 Newtons to make the wavelength of a 125 Hz wave 120.0 cm.
To determine the tension in the string, we can use the equation that relates tension, mass, and wavelength for a wave traveling on a string. The equation is:
Tension (T) = (mass per unit length) × (wavelength) × (frequency)^2
First, we need to find the mass per unit length of the string. We divide the mass of the string by its length:
mass per unit length = (mass)/(length) = 15 g / 5.3 m = 2.83 g/m
Next, we convert the wavelength from centimeters to meters:
wavelength = 120.0 cm = 120.0 cm * (1 m/100 cm) = 1.20 m
Now, we can calculate the tension:
Tension = (2.83 g/m) × (1.20 m) × (125 Hz)^2 = 2.83 g × (1.20 × 10^(-2) m) × (125 × 125 Hz) = 4.20 N
Therefore, the tension in the string should be 4.20 N to produce a wavelength of 120.0 cm for a 125 Hz wave.
L =5.3 m, m = 0.015 kg, λ = 0.2 m,
f = 125 Hz, T = ?
Velocity in the stretched string is
v = sqrt(T/mₒ),
T =mₒ•v²,
mₒ = m/L,
λ = v/f, v = λ•f,
T =mₒ•v² = m • (λ•f)² /L =0.015•(1.2•125)²/5.3 = 63.7 N.