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Asked by Vishal Last Modified
Answer Sure! Let's tackle this problem step by step.
(a) To find the speed of a transverse wave on the string, we can use the formula:
v=Tμv=μT
Where:
Given that the frequency of the fundamental mode is f=45f=45 Hz, we know that f=1Tf=T1, where TT is the period of the wave. Since the wire is vibrating in its fundamental mode, the frequency is the same as the frequency of the wave. So, T=1fT=f1.
Let's first find the period of the wave: T=145T=451 seconds.
Now, let's use the formula for wave speed:
v=Tμv=μT
v=1454.0×10−2v=4.0×10−2451
v=145×4.0×10−2v=45×4.0×10−21
v=11.8v=1.81
v=0.55556v=0.55556
v≈0.745 m/sv≈0.745m/s
So, the speed of the transverse wave on the string is approximately 0.745 m/s0.745m/s.
(b) Now, let's find the tension in the string. We'll use the formula:
T=μv2T=μv2
T=(4.0×10−2)×(0.745)2T=(4.0×10−2)×(0.745)2
T=4.0×10−2×0.55556T=4.0×10−2×0.55556
T≈0.0222 NT≈0.0222N
So, the tension in the string is approximately 0.0222 N0.0222N.
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