Video Transcript
Transverse waves are sent along a
6.00-meter-long string with a speed of 25.00 meters per second. The string is under a tension of
12.00 newtons. What is the mass of the string?
We can label the string mass
𝑚. And we’ll start on our solution by
recalling the relationship between wave speed, string tension, and string linear
mass density. The speed of a transverse wave
moving along a string can be determined by knowing the string’s tension and its
linear mass density, taking their ratio in the square root. The linear mass density 𝜇 of a
string is equal to its overall mass divided by its overall length.
If we combine these two equations,
we can say that the speed of the wave is equal to the square root of its tension
times its length all divided by its mass. Rearranging this equation to solve
for mass, we find it’s is equal to 𝑇 times 𝐿 over 𝑣 squared. In the problem statement, we’re
given 𝐿, 𝑣, and 𝑇, so we’re ready to plug in and solve for 𝑚. Entering this expression on our
calculator, to three significant figures, 𝑚 is 115 grams. That’s the mass of the string in
this example.
