Respuesta :
Answer:
a) 218.8 Hz or 221.2 Hz
b) Increased by 1.087% or decreased by 0.11%
Explanation:
Number of beats = 3
Time = 2.5 s
Frequency of beat = [tex]F_1=\frac{3}{2.5}=1.2\ Hz[/tex]
a) If one string is vibrating at 220 Hz, then
[tex]F_1-F_2=220-1.2=218.8 Hz[/tex]
or
[tex]F_1+F_2=220+1.2=221.2 Hz[/tex]
So, the other string is vibrating at 218.8 Hz or221.2 Hz
b) If frequency is 218.8 Hz
[tex]\frac{F_2}{F_1}=\sqrt{\frac{T_1}{T_2}}\\\Rightarrow \frac{F_2^2}{F_1^2}=\frac{T_1}{T_2}\\\Rightarrow \frac{218.8^2}{220^2}=\frac{T_1}{T_2}\\\Rightarrow \frac{T_1}{T_2}=0.9891[/tex]
T, tension must be increased by = 1-0.9891 = 0.0108 = 1.087 %
T, tension must be increased by 1.087%
If frequency is 221.2 Hz
[tex]\frac{221.2^2}{220^2}=\frac{T_1}{T_2}\\\Rightarrow \frac{T_1}{T_2}=1.011[/tex]
T, tension must be increased by = 1-1.011 = -0.011 = -0.11 %
T, tension must be decreased by 0.11%
