Answer:
a. 17.145cm
b. 8.325cm
c. 0.846
d. 2.896
Step-by-step explanation:
It is known that frequency is inversely proportional to length.
Case 1: The player presses only the first valve.
f₁/fo = 2^{-2/12} = lo/l₁
given that lo= 140cm.
l₁ = 2^{2/12}lo = 157.145
change in length:
l₁ - lo = 157.145 - 140 = 17.145cm
Case 2: The player presses only the second valve.
f₂/fo = 2^{-1/12} = lo/l₂
l₂ = 2^{1/12}lo = 148.325cm
l₂ - lo= 148.325-140 = 8.325cm
Case 3: The player presses both the first and second valve.
Change in length is the sum of change in length when they are individually pressed.
l₃ - lo = 17.145+8.325 = 25.47cm
l₃ = 25.47cm+lo = 165.47cm
f₃/fo = 2^{-n/12} = lo/l₃
f₃/fo = 2^{-n/12} = 140/{165.47 = 0.846
2^{-n/12} = 0.846\Rightarrow n/12 = -log(0.846)/log(2) = 0.2413
n = 0.2413*12 = 2.896
