Answer:
3.68×10¯⁶ m
Explanation:
The following data were obtained from the question:
Mass (m) = 5 g
Tension (T) = 180 N
Frequency (f) = 260 Hz
Wavelength (λ) = 0.60 m.
Length (L) =?
Next, we shall determine the period of the wave. This can be obtained as follow:
Period is simply defined as the time taken to complete 1 oscillation. Mathematically, it is represented as:
Period (T) = 1/frequency (f)
T = 1/f
Thus, with the above formula, the period of the wave can be obtained as shown below:
Frequency (f) = 260 Hz
Period (T) =?
T = 1/f
T = 1/260
T = 3.85×10¯³ s
Finally, we shall determine the length of the string as follow:
Period (T) = 3.85×10¯³ s
Acceleration due to gravity (g) = 9.8 m/s²
Pi (π) = 3.14
Length (L) =?
T = 2π√(L/g)
3.85×10¯³ = 2 × 3.14 × √(L/9.8)
3.85×10¯³ = 6.28 × √(L/9.8)
Divide both side by 6.28
3.85×10¯³ / 6.28 = √(L/9.8)
Take the square of both side
(3.85×10¯³ / 6.28)² = L/9.8
Cross multiply
L = (3.85×10¯³ / 6.28)² × 9.8
L = 3.68×10¯⁶ m
Therefore, the length of the string is 3.68×10¯⁶ m
