Question Video: Calculating the Mass of a String given the Velocity of the Wave Traveling across It | Nagwa Question Video: Calculating the Mass of a String given the Velocity of the Wave Traveling across It | Nagwa

Question Video: Calculating the Mass of a String given the Velocity of the Wave Traveling across It

Transverse waves are sent along a 6.00-meter-long string with a speed of 25.00 m/s. The string is under a tension of 12.00 N. What is the mass of the string?

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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.

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